{"question": "Find the indefinite integral: ∫ (16*x + 4)*exp(4*x**2 + 2*x + 10) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*exp(4*x**2 + 2*x + 10) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 0, "integrand": "(16*x + 4)*exp(4*x**2 + 2*x + 10)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -3*(8*x + 6)**3 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-384*x**4 - 1152*x**3 - 1296*x**2 - 648*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 1, "integrand": "-3*(8*x + 6)**3", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -4*sin(4*x + 1)**2*cos(4*x + 1) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-sin(4*x + 1)**3/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 2, "integrand": "-4*sin(4*x + 1)**2*cos(4*x + 1)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -2*asin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*x*asin(x) - 2*sqrt(1 - x**2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 3, "integrand": "-2*asin(x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 3*x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(3*x**3 - 9*x**2 + 18*x - 18)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 4, "integrand": "3*x**3*exp(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -3*atan(2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*x*atan(2*x) + 3*log(4*x**2 + 1)/4 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 5, "integrand": "-3*atan(2*x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 2*x**3*cos(3*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*Integral(x**3*cos(3*x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 6, "integrand": "2*x**3*cos(3*x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -(2*x + 6)**4 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-16*x**5/5 - 48*x**4 - 288*x**3 - 864*x**2 - 1296*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 7, "integrand": "-(2*x + 6)**4", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -8*sin(8*x - 2)*cos(8*x - 2)**3 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "cos(8*x - 2)**4/4 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 8, "integrand": "-8*sin(8*x - 2)*cos(8*x - 2)**3", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -12*sqrt(4*x - 7) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*(4*x - 7)**(3/2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 9, "integrand": "-12*sqrt(4*x - 7)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 2*x**3*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*x**3*sin(x) + 6*x**2*cos(x) - 12*x*sin(x) - 12*cos(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 10, "integrand": "2*x**3*cos(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -2*x**2*cos(3*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*Integral(x**2*cos(3*x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 11, "integrand": "-2*x**2*cos(3*x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -2*x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(-2*x**3 + 6*x**2 - 12*x + 12)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 12, "integrand": "-2*x**3*exp(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -(3*x + 5)**4 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-81*x**5/5 - 135*x**4 - 450*x**3 - 750*x**2 - 625*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 13, "integrand": "-(3*x + 5)**4", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -3*x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(-3*x**3 + 9*x**2 - 18*x + 18)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 14, "integrand": "-3*x**3*exp(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -2*(4*x - 9)**3 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-32*x**4 + 288*x**3 - 972*x**2 + 1458*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 15, "integrand": "-2*(4*x - 9)**3", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ x**3*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "Integral(x**3*cos(x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 16, "integrand": "x**3*cos(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 9*sqrt(3*x - 1) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*(3*x - 1)**(3/2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 17, "integrand": "9*sqrt(3*x - 1)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -2*asin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*x*asin(x) - 2*sqrt(1 - x**2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 18, "integrand": "-2*asin(x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -12*sin(6*x - 8)*cos(6*x - 8)**3 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "cos(6*x - 8)**4/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 19, "integrand": "-12*sin(6*x - 8)*cos(6*x - 8)**3", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -2*x**3*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*x**3*cos(x) - 6*x**2*sin(x) - 12*x*cos(x) + 12*sin(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 20, "integrand": "-2*x**3*sin(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -6*sin(2*x + 2)*cos(2*x + 2) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*sin(2*x + 2)**2/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 21, "integrand": "-6*sin(2*x + 2)*cos(2*x + 2)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -10*sin(5*x + 3)*cos(5*x + 3) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-sin(5*x + 3)**2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 22, "integrand": "-10*sin(5*x + 3)*cos(5*x + 3)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -24*sin(8*x + 9)**3*cos(8*x + 9) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*sin(8*x + 9)**4/4 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 23, "integrand": "-24*sin(8*x + 9)**3*cos(8*x + 9)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 3*(4*x - 8)**3 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "48*x**4 - 384*x**3 + 1152*x**2 - 1536*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 24, "integrand": "3*(4*x - 8)**3", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -2*(8*x - 7)**4 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-8192*x**5/5 + 7168*x**4 - 12544*x**3 + 10976*x**2 - 4802*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 25, "integrand": "-2*(8*x - 7)**4", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 16*exp(-8*x - 6) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*exp(-8*x - 6) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 26, "integrand": "16*exp(-8*x - 6)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -30*exp(10*x - 6) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*exp(10*x - 6) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 27, "integrand": "-30*exp(10*x - 6)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -x**3*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-x**3*sin(x) - 3*x**2*cos(x) + 6*x*sin(x) + 6*cos(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 28, "integrand": "-x**3*cos(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -asin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-x*asin(x) - sqrt(1 - x**2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 29, "integrand": "-asin(x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 3*(6*x - 9)**3 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "162*x**4 - 972*x**3 + 2187*x**2 - 2187*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 30, "integrand": "3*(6*x - 9)**3", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -2*atan(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*x*atan(x) + log(x**2 + 1) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 31, "integrand": "-2*atan(x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -exp(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-exp(x)*sin(x)/2 - exp(x)*cos(x)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 32, "integrand": "-exp(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 27*sin(9*x - 6)*cos(9*x - 6) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*sin(9*x - 6)**2/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 33, "integrand": "27*sin(9*x - 6)*cos(9*x - 6)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -log(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-x*log(x) + x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 34, "integrand": "-log(x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ exp(x)*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "exp(x)*sin(x)/2 - exp(x)*cos(x)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 35, "integrand": "exp(x)*sin(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -3*exp(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*exp(x)*sin(x)/2 - 3*exp(x)*cos(x)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 36, "integrand": "-3*exp(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 4*sqrt(4*x + 8) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*(4*x + 8)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 37, "integrand": "4*sqrt(4*x + 8)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -3*asin(2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*x*asin(2*x) - 3*sqrt(1 - 4*x**2)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 38, "integrand": "-3*asin(2*x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -2*x**2*cos(3*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*Integral(x**2*cos(3*x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 39, "integrand": "-2*x**2*cos(3*x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -3*sqrt(5 - 3*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*(5 - 3*x)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 40, "integrand": "-3*sqrt(5 - 3*x)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 7*sin(7*x + 1)**2*cos(7*x + 1) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "sin(7*x + 1)**3/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 41, "integrand": "7*sin(7*x + 1)**2*cos(7*x + 1)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ (12 - 54*x)*exp(9*x**2 - 4*x - 8) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*exp(9*x**2 - 4*x - 8) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 42, "integrand": "(12 - 54*x)*exp(9*x**2 - 4*x - 8)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -8*sqrt(8 - 4*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "4*(8 - 4*x)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 43, "integrand": "-8*sqrt(8 - 4*x)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 2*sin(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "sin(x)**2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 44, "integrand": "2*sin(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -15*sqrt(5*x - 9) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*(5*x - 9)**(3/2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 45, "integrand": "-15*sqrt(5*x - 9)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -sin(x + 6)*cos(x + 6)**4 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "cos(x + 6)**5/5 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 46, "integrand": "-sin(x + 6)*cos(x + 6)**4", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -2*(3*x + 6)**2 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-6*x**3 - 36*x**2 - 72*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 47, "integrand": "-2*(3*x + 6)**2", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 20*sqrt(-10*x - 6) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-4*(-10*x - 6)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 48, "integrand": "20*sqrt(-10*x - 6)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -2*(3*x - 7)**4 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-162*x**5/5 + 378*x**4 - 1764*x**3 + 4116*x**2 - 4802*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 49, "integrand": "-2*(3*x - 7)**4", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 3*sin(3*x - 10)**3*cos(3*x - 10) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "sin(3*x - 10)**4/4 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 50, "integrand": "3*sin(3*x - 10)**3*cos(3*x - 10)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -x**3*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "x**3*cos(x) - 3*x**2*sin(x) - 6*x*cos(x) + 6*sin(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 51, "integrand": "-x**3*sin(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -x**2*sin(2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-Integral(x**2*sin(2*x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 52, "integrand": "-x**2*sin(2*x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ exp(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "exp(x)*sin(x)/2 + exp(x)*cos(x)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 53, "integrand": "exp(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 3*log(x**2) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*x*log(x**2) - 6*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 54, "integrand": "3*log(x**2)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 10*sqrt(10*x + 9) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*(10*x + 9)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 55, "integrand": "10*sqrt(10*x + 9)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -asin(2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-x*asin(2*x) - sqrt(1 - 4*x**2)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 56, "integrand": "-asin(2*x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -12*sin(4*x + 2)**3*cos(4*x + 2) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*sin(4*x + 2)**4/4 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 57, "integrand": "-12*sin(4*x + 2)**3*cos(4*x + 2)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 21*sqrt(7*x - 7) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*(7*x - 7)**(3/2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 58, "integrand": "21*sqrt(7*x - 7)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ x**3*sin(2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "Integral(x**3*sin(2*x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 59, "integrand": "x**3*sin(2*x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -18*sqrt(9*x + 7) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-4*(9*x + 7)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 60, "integrand": "-18*sqrt(9*x + 7)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(x**3 - 3*x**2 + 6*x - 6)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 61, "integrand": "x**3*exp(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 2*x**3*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*x**3*sin(x) + 6*x**2*cos(x) - 12*x*sin(x) - 12*cos(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 62, "integrand": "2*x**3*cos(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -2*x**3*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*x**3*cos(x) - 6*x**2*sin(x) - 12*x*cos(x) + 12*sin(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 63, "integrand": "-2*x**3*sin(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ exp(-x - 2) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-exp(-x - 2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 64, "integrand": "exp(-x - 2)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -15*sqrt(7 - 5*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*(7 - 5*x)**(3/2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 65, "integrand": "-15*sqrt(7 - 5*x)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 5*sqrt(-5*x - 4) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*(-5*x - 4)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 66, "integrand": "5*sqrt(-5*x - 4)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ asin(3*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "x*asin(3*x) + sqrt(1 - 9*x**2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 67, "integrand": "asin(3*x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -2*x**3*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*x**3*sin(x) - 6*x**2*cos(x) + 12*x*sin(x) + 12*cos(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 68, "integrand": "-2*x**3*cos(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 2*exp(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "exp(x)*sin(x) + exp(x)*cos(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 69, "integrand": "2*exp(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 3*sin(3*x + 4)*cos(3*x + 4)**4 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-cos(3*x + 4)**5/5 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 70, "integrand": "3*sin(3*x + 4)*cos(3*x + 4)**4", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 2*(x - 8)**2 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*x**3/3 - 16*x**2 + 128*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 71, "integrand": "2*(x - 8)**2", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 12*sqrt(3 - 4*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*(3 - 4*x)**(3/2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 72, "integrand": "12*sqrt(3 - 4*x)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(-x**3 + 3*x**2 - 6*x + 6)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 73, "integrand": "-x**3*exp(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 3*exp(x)*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*exp(x)*sin(x)/2 - 3*exp(x)*cos(x)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 74, "integrand": "3*exp(x)*sin(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 14*sqrt(7*x + 9) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "4*(7*x + 9)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 75, "integrand": "14*sqrt(7*x + 9)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ (1 - 12*x)*exp(6*x**2 - x - 6) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-exp(6*x**2 - x - 6) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 76, "integrand": "(1 - 12*x)*exp(6*x**2 - x - 6)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -x**3*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "x**3*cos(x) - 3*x**2*sin(x) - 6*x*cos(x) + 6*sin(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 77, "integrand": "-x**3*sin(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -3*x**3*cos(3*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*Integral(x**3*cos(3*x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 78, "integrand": "-3*x**3*cos(3*x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 2*(3*x + 10)**3 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "27*x**4/2 + 180*x**3 + 900*x**2 + 2000*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 79, "integrand": "2*(3*x + 10)**3", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -x*cos(2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-Integral(x*cos(2*x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 80, "integrand": "-x*cos(2*x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -2*(7*x + 5)**2 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-98*x**3/3 - 70*x**2 - 50*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 81, "integrand": "-2*(7*x + 5)**2", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -2*x**3*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*x**3*cos(x) - 6*x**2*sin(x) - 12*x*cos(x) + 12*sin(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 82, "integrand": "-2*x**3*sin(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 3*x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(3*x**3 - 9*x**2 + 18*x - 18)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 83, "integrand": "3*x**3*exp(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -2*x*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*Integral(x*cos(x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 84, "integrand": "-2*x*cos(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 2*(x - 1)**2 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*x**3/3 - 2*x**2 + 2*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 85, "integrand": "2*(x - 1)**2", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 2*x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(2*x**3 - 6*x**2 + 12*x - 12)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 86, "integrand": "2*x**3*exp(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 3*x*cos(2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*Integral(x*cos(2*x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 87, "integrand": "3*x*cos(2*x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -3*x**3*cos(2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*Integral(x**3*cos(2*x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 88, "integrand": "-3*x**3*cos(2*x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -asin(2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-x*asin(2*x) - sqrt(1 - 4*x**2)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 89, "integrand": "-asin(2*x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -sin(x - 2)*cos(x - 2) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-sin(x - 2)**2/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 90, "integrand": "-sin(x - 2)*cos(x - 2)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 27*sin(9*x - 2)*cos(9*x - 2)**3 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*cos(9*x - 2)**4/4 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 91, "integrand": "27*sin(9*x - 2)*cos(9*x - 2)**3", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 16*sin(8*x + 7)**2*cos(8*x + 7) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*sin(8*x + 7)**3/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 92, "integrand": "16*sin(8*x + 7)**2*cos(8*x + 7)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ (4*x + 5)*exp(-2*x**2 - 5*x + 10) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-exp(-2*x**2 - 5*x + 10) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 93, "integrand": "(4*x + 5)*exp(-2*x**2 - 5*x + 10)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 2*x**2*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*Integral(x**2*sin(x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 94, "integrand": "2*x**2*sin(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 2*(6*x + 4)**3 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "108*x**4 + 288*x**3 + 288*x**2 + 128*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 95, "integrand": "2*(6*x + 4)**3", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -4*sqrt(-4*x - 4) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*(-4*x - 4)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 96, "integrand": "-4*sqrt(-4*x - 4)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 2*(9*x - 1)**3 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "729*x**4/2 - 162*x**3 + 27*x**2 - 2*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 97, "integrand": "2*(9*x - 1)**3", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 2*exp(x)*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "exp(x)*sin(x) - exp(x)*cos(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 98, "integrand": "2*exp(x)*sin(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -3*x**3*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*Integral(x**3*sin(x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 99, "integrand": "-3*x**3*sin(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -2*x*sin(2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*Integral(x*sin(2*x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 100, "integrand": "-2*x*sin(2*x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ x**3*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-x**3*cos(x) + 3*x**2*sin(x) + 6*x*cos(x) - 6*sin(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 101, "integrand": "x**3*sin(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 21*sin(7*x + 7)**4*cos(7*x + 7) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*sin(7*x + 7)**5/5 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 102, "integrand": "21*sin(7*x + 7)**4*cos(7*x + 7)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -sin(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-sin(x)**2/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 103, "integrand": "-sin(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 6*sqrt(3*x - 2) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "4*(3*x - 2)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 104, "integrand": "6*sqrt(3*x - 2)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 2*x**2*sin(3*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*Integral(x**2*sin(3*x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 105, "integrand": "2*x**2*sin(3*x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -10*sin(5*x + 2)*cos(5*x + 2)**2 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*cos(5*x + 2)**3/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 106, "integrand": "-10*sin(5*x + 2)*cos(5*x + 2)**2", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ (7*x + 3)**2 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "49*x**3/3 + 21*x**2 + 9*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 107, "integrand": "(7*x + 3)**2", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -exp(x)*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-exp(x)*sin(x)/2 + exp(x)*cos(x)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 108, "integrand": "-exp(x)*sin(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ (12*x - 8)*exp(-6*x**2 + 8*x - 10) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-exp(-6*x**2 + 8*x - 10) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 109, "integrand": "(12*x - 8)*exp(-6*x**2 + 8*x - 10)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ x**3*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "x**3*sin(x) + 3*x**2*cos(x) - 6*x*sin(x) - 6*cos(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 110, "integrand": "x**3*cos(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -3*x**3*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*x**3*sin(x) - 9*x**2*cos(x) + 18*x*sin(x) + 18*cos(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 111, "integrand": "-3*x**3*cos(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 4*sqrt(-4*x - 9) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*(-4*x - 9)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 112, "integrand": "4*sqrt(-4*x - 9)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -3*x**3*sin(3*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*Integral(x**3*sin(3*x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 113, "integrand": "-3*x**3*sin(3*x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 8*sin(4*x + 3)*cos(4*x + 3)**4 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*cos(4*x + 3)**5/5 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 114, "integrand": "8*sin(4*x + 3)*cos(4*x + 3)**4", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -x*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(1 - x)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 115, "integrand": "-x*exp(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 21*exp(7*x - 8) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*exp(7*x - 8) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 116, "integrand": "21*exp(7*x - 8)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 20*sin(10*x + 1)**4*cos(10*x + 1) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*sin(10*x + 1)**5/5 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 117, "integrand": "20*sin(10*x + 1)**4*cos(10*x + 1)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -3*(7*x - 3)**4 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-7203*x**5/5 + 3087*x**4 - 2646*x**3 + 1134*x**2 - 243*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 118, "integrand": "-3*(7*x - 3)**4", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 2*x*cos(3*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*Integral(x*cos(3*x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 119, "integrand": "2*x*cos(3*x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -3*(9*x - 4)**3 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2187*x**4/4 + 972*x**3 - 648*x**2 + 192*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 120, "integrand": "-3*(9*x - 4)**3", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -2*x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(-2*x**3 + 6*x**2 - 12*x + 12)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 121, "integrand": "-2*x**3*exp(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 2*(5*x - 8)**4 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "250*x**5 - 2000*x**4 + 6400*x**3 - 10240*x**2 + 8192*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 122, "integrand": "2*(5*x - 8)**4", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -2*(2*x + 8)**2 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-8*x**3/3 - 32*x**2 - 128*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 123, "integrand": "-2*(2*x + 8)**2", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 2*sqrt(-x - 1) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-4*(-x - 1)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 124, "integrand": "2*sqrt(-x - 1)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -21*sqrt(-7*x - 2) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*(-7*x - 2)**(3/2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 125, "integrand": "-21*sqrt(-7*x - 2)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ (-8*x - 4)*exp(4*x**2 + 4*x - 10) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-exp(4*x**2 + 4*x - 10) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 126, "integrand": "(-8*x - 4)*exp(4*x**2 + 4*x - 10)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -atan(3*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-x*atan(3*x) + log(9*x**2 + 1)/6 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 127, "integrand": "-atan(3*x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ exp(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "exp(x)*sin(x)/2 + exp(x)*cos(x)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 128, "integrand": "exp(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -exp(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-exp(x)*sin(x)/2 - exp(x)*cos(x)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 129, "integrand": "-exp(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 3*asin(2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*x*asin(2*x) + 3*sqrt(1 - 4*x**2)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 130, "integrand": "3*asin(2*x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -log(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-x*log(x) + x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 131, "integrand": "-log(x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -2*exp(x)*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-exp(x)*sin(x) + exp(x)*cos(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 132, "integrand": "-2*exp(x)*sin(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -20*sin(10*x - 8)**4*cos(10*x - 8) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*sin(10*x - 8)**5/5 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 133, "integrand": "-20*sin(10*x - 8)**4*cos(10*x - 8)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -3*(2*x - 7)**4 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-48*x**5/5 + 168*x**4 - 1176*x**3 + 4116*x**2 - 7203*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 134, "integrand": "-3*(2*x - 7)**4", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(-x**3 + 3*x**2 - 6*x + 6)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 135, "integrand": "-x**3*exp(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -3*x**3*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*x**3*sin(x) - 9*x**2*cos(x) + 18*x*sin(x) + 18*cos(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 136, "integrand": "-3*x**3*cos(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -x**3*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "x**3*cos(x) - 3*x**2*sin(x) - 6*x*cos(x) + 6*sin(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 137, "integrand": "-x**3*sin(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -6*sqrt(-2*x - 4) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*(-2*x - 4)**(3/2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 138, "integrand": "-6*sqrt(-2*x - 4)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -x*sin(2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-Integral(x*sin(2*x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 139, "integrand": "-x*sin(2*x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -6*sin(6*x + 2)**3*cos(6*x + 2) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-sin(6*x + 2)**4/4 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 140, "integrand": "-6*sin(6*x + 2)**3*cos(6*x + 2)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 3*(6*x + 5)**2 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "36*x**3 + 90*x**2 + 75*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 141, "integrand": "3*(6*x + 5)**2", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -2*atan(3*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*x*atan(3*x) + log(9*x**2 + 1)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 142, "integrand": "-2*atan(3*x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -2*x**3*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*x**3*cos(x) - 6*x**2*sin(x) - 12*x*cos(x) + 12*sin(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 143, "integrand": "-2*x**3*sin(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -atan(2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-x*atan(2*x) + log(4*x**2 + 1)/4 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 144, "integrand": "-atan(2*x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 3*atan(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*x*atan(x) - 3*log(x**2 + 1)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 145, "integrand": "3*atan(x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ exp(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "exp(x)*sin(x)/2 + exp(x)*cos(x)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 146, "integrand": "exp(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 21*sin(7*x + 9)*cos(7*x + 9) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*sin(7*x + 9)**2/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 147, "integrand": "21*sin(7*x + 9)*cos(7*x + 9)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 2*(6*x + 4)**3 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "108*x**4 + 288*x**3 + 288*x**2 + 128*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 148, "integrand": "2*(6*x + 4)**3", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -3*exp(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*exp(x)*sin(x)/2 - 3*exp(x)*cos(x)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 149, "integrand": "-3*exp(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -2*log(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*x*log(x) + 2*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 150, "integrand": "-2*log(x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 3*x**2*cos(2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*Integral(x**2*cos(2*x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 151, "integrand": "3*x**2*cos(2*x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -sin(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-sin(x)**2/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 152, "integrand": "-sin(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 3*x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(3*x**3 - 9*x**2 + 18*x - 18)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 153, "integrand": "3*x**3*exp(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -18*exp(5 - 6*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*exp(5 - 6*x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 154, "integrand": "-18*exp(5 - 6*x)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 3*x*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(3*x - 3)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 155, "integrand": "3*x*exp(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -3*(2*x - 8)**2 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-4*x**3 + 48*x**2 - 192*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 156, "integrand": "-3*(2*x - 8)**2", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -3*asin(3*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*x*asin(3*x) - sqrt(1 - 9*x**2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 157, "integrand": "-3*asin(3*x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -3*(x - 3)**2 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-x**3 + 9*x**2 - 27*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 158, "integrand": "-3*(x - 3)**2", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -3*(7*x - 1)**3 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-1029*x**4/4 + 147*x**3 - 63*x**2/2 + 3*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 159, "integrand": "-3*(7*x - 1)**3", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ exp(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "exp(x)*sin(x)/2 + exp(x)*cos(x)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 160, "integrand": "exp(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 2*(10*x + 4)**4 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "4000*x**5 + 8000*x**4 + 6400*x**3 + 2560*x**2 + 512*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 161, "integrand": "2*(10*x + 4)**4", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 21*sin(7*x - 6)*cos(7*x - 6) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*cos(7*x - 6)**2/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 162, "integrand": "21*sin(7*x - 6)*cos(7*x - 6)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -12*sin(4*x - 2)*cos(4*x - 2)**2 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "cos(4*x - 2)**3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 163, "integrand": "-12*sin(4*x - 2)*cos(4*x - 2)**2", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -(4*x + 3)**2 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-16*x**3/3 - 12*x**2 - 9*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 164, "integrand": "-(4*x + 3)**2", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(-x**3 + 3*x**2 - 6*x + 6)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 165, "integrand": "-x**3*exp(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -2*log(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*x*log(x) + 2*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 166, "integrand": "-2*log(x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ x*cos(2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "Integral(x*cos(2*x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 167, "integrand": "x*cos(2*x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -5*sin(5*x + 1)**2*cos(5*x + 1) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-sin(5*x + 1)**3/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 168, "integrand": "-5*sin(5*x + 1)**2*cos(5*x + 1)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -3*x*sin(3*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*Integral(x*sin(3*x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 169, "integrand": "-3*x*sin(3*x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 18*sin(9*x - 3)*cos(9*x - 3) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "sin(9*x - 3)**2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 170, "integrand": "18*sin(9*x - 3)*cos(9*x - 3)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 3*sqrt(7 - x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*(7 - x)**(3/2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 171, "integrand": "3*sqrt(7 - x)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -3*x**2*sin(3*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*Integral(x**2*sin(3*x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 172, "integrand": "-3*x**2*sin(3*x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 3*(2*x + 5)**2 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "4*x**3 + 30*x**2 + 75*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 173, "integrand": "3*(2*x + 5)**2", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -2*sin(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-sin(x)**2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 174, "integrand": "-2*sin(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 3*x**3*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*x**3*sin(x) + 9*x**2*cos(x) - 18*x*sin(x) - 18*cos(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 175, "integrand": "3*x**3*cos(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 2*atan(2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*x*atan(2*x) - log(4*x**2 + 1)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 176, "integrand": "2*atan(2*x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 4*exp(-2*x - 7) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*exp(-2*x - 7) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 177, "integrand": "4*exp(-2*x - 7)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -10*exp(-5*x - 7) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*exp(-5*x - 7) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 178, "integrand": "-10*exp(-5*x - 7)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 15*sqrt(6 - 5*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*(6 - 5*x)**(3/2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 179, "integrand": "15*sqrt(6 - 5*x)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 2*exp(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "exp(x)*sin(x) + exp(x)*cos(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 180, "integrand": "2*exp(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 3*log(x**2) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*x*log(x**2) - 6*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 181, "integrand": "3*log(x**2)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 2*(8*x + 2)**2 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "128*x**3/3 + 32*x**2 + 8*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 182, "integrand": "2*(8*x + 2)**2", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 4*exp(4*x - 3) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "exp(4*x - 3) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 183, "integrand": "4*exp(4*x - 3)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 18*sin(6*x + 9)**4*cos(6*x + 9) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*sin(6*x + 9)**5/5 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 184, "integrand": "18*sin(6*x + 9)**4*cos(6*x + 9)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -4*sin(4*x + 7)*cos(4*x + 7) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-sin(4*x + 7)**2/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 185, "integrand": "-4*sin(4*x + 7)*cos(4*x + 7)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -2*x**3*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*x**3*cos(x) - 6*x**2*sin(x) - 12*x*cos(x) + 12*sin(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 186, "integrand": "-2*x**3*sin(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 3*x**3*sin(2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*Integral(x**3*sin(2*x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 187, "integrand": "3*x**3*sin(2*x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 2*exp(-x - 8) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*exp(-x - 8) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 188, "integrand": "2*exp(-x - 8)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 2*exp(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "exp(x)*sin(x) + exp(x)*cos(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 189, "integrand": "2*exp(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 2*log(x**3) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*x*log(x**3) - 6*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 190, "integrand": "2*log(x**3)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 9*exp(2 - 9*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-exp(2 - 9*x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 191, "integrand": "9*exp(2 - 9*x)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -3*atan(2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*x*atan(2*x) + 3*log(4*x**2 + 1)/4 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 192, "integrand": "-3*atan(2*x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 2*log(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*x*log(x) - 2*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 193, "integrand": "2*log(x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ (-14*x - 10)*exp(7*x**2 + 10*x - 10) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-exp(7*x**2 + 10*x - 10) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 194, "integrand": "(-14*x - 10)*exp(7*x**2 + 10*x - 10)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 3*x*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*Integral(x*sin(x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 195, "integrand": "3*x*sin(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 3*exp(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*exp(x)*sin(x)/2 + 3*exp(x)*cos(x)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 196, "integrand": "3*exp(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -2*(7*x - 2)**2 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-98*x**3/3 + 28*x**2 - 8*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 197, "integrand": "-2*(7*x - 2)**2", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 2*exp(x)*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "exp(x)*sin(x) - exp(x)*cos(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 198, "integrand": "2*exp(x)*sin(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ (24*x + 15)*exp(4*x**2 + 5*x - 6) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*exp(4*x**2 + 5*x - 6) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 199, "integrand": "(24*x + 15)*exp(4*x**2 + 5*x - 6)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 2*atan(3*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*x*atan(3*x) - log(9*x**2 + 1)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 200, "integrand": "2*atan(3*x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -2*x**3*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*x**3*cos(x) - 6*x**2*sin(x) - 12*x*cos(x) + 12*sin(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 201, "integrand": "-2*x**3*sin(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 2*x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(2*x**3 - 6*x**2 + 12*x - 12)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 202, "integrand": "2*x**3*exp(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -24*sqrt(8*x - 10) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*(8*x - 10)**(3/2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 203, "integrand": "-24*sqrt(8*x - 10)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -3*x**3*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*x**3*cos(x) - 9*x**2*sin(x) - 18*x*cos(x) + 18*sin(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 204, "integrand": "-3*x**3*sin(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -sin(x + 3)*cos(x + 3)**4 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "cos(x + 3)**5/5 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 205, "integrand": "-sin(x + 3)*cos(x + 3)**4", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -sin(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-sin(x)**2/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 206, "integrand": "-sin(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -3*atan(3*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*x*atan(3*x) + log(9*x**2 + 1)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 207, "integrand": "-3*atan(3*x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -18*sin(9*x + 3)**3*cos(9*x + 3) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-sin(9*x + 3)**4/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 208, "integrand": "-18*sin(9*x + 3)**3*cos(9*x + 3)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 7*sin(7*x - 2)*cos(7*x - 2)**3 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-cos(7*x - 2)**4/4 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 209, "integrand": "7*sin(7*x - 2)*cos(7*x - 2)**3", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 2*sin(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "sin(x)**2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 210, "integrand": "2*sin(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 3*x**2*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(3*x**2 - 6*x + 6)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 211, "integrand": "3*x**2*exp(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 2*asin(3*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*x*asin(3*x) + 2*sqrt(1 - 9*x**2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 212, "integrand": "2*asin(3*x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -3*(6*x + 10)**4 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3888*x**5/5 - 6480*x**4 - 21600*x**3 - 36000*x**2 - 30000*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 213, "integrand": "-3*(6*x + 10)**4", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -3*sin(x + 7)*cos(x + 7)**2 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "cos(x + 7)**3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 214, "integrand": "-3*sin(x + 7)*cos(x + 7)**2", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 3*asin(3*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*x*asin(3*x) + sqrt(1 - 9*x**2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 215, "integrand": "3*asin(3*x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -12*exp(4 - 4*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*exp(4 - 4*x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 216, "integrand": "-12*exp(4 - 4*x)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 3*(7*x - 10)**4 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "7203*x**5/5 - 10290*x**4 + 29400*x**3 - 42000*x**2 + 30000*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 217, "integrand": "3*(7*x - 10)**4", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 8*sqrt(10 - 4*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-4*(10 - 4*x)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 218, "integrand": "8*sqrt(10 - 4*x)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -18*sin(9*x - 3)**3*cos(9*x - 3) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-sin(9*x - 3)**4/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 219, "integrand": "-18*sin(9*x - 3)**3*cos(9*x - 3)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -2*asin(2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*x*asin(2*x) - sqrt(1 - 4*x**2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 220, "integrand": "-2*asin(2*x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ (10*x - 8)*exp(-5*x**2 + 8*x - 1) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-exp(-5*x**2 + 8*x - 1) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 221, "integrand": "(10*x - 8)*exp(-5*x**2 + 8*x - 1)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 3*x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(3*x**3 - 9*x**2 + 18*x - 18)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 222, "integrand": "3*x**3*exp(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -2*exp(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-exp(x)*sin(x) - exp(x)*cos(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 223, "integrand": "-2*exp(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(-x**3 + 3*x**2 - 6*x + 6)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 224, "integrand": "-x**3*exp(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -4*sqrt(9 - 2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "4*(9 - 2*x)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 225, "integrand": "-4*sqrt(9 - 2*x)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 2*exp(x)*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "exp(x)*sin(x) - exp(x)*cos(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 226, "integrand": "2*exp(x)*sin(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 2*(10*x + 5)**3 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "500*x**4 + 1000*x**3 + 750*x**2 + 250*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 227, "integrand": "2*(10*x + 5)**3", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -3*exp(x)*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*exp(x)*sin(x)/2 + 3*exp(x)*cos(x)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 228, "integrand": "-3*exp(x)*sin(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 18*sin(6*x - 2)*cos(6*x - 2) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*cos(6*x - 2)**2/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 229, "integrand": "18*sin(6*x - 2)*cos(6*x - 2)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -2*x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(-2*x**3 + 6*x**2 - 12*x + 12)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 230, "integrand": "-2*x**3*exp(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -10*sqrt(-10*x - 3) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*(-10*x - 3)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 231, "integrand": "-10*sqrt(-10*x - 3)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 3*sqrt(1 - x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*(1 - x)**(3/2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 232, "integrand": "3*sqrt(1 - x)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -3*sin(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*sin(x)**2/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 233, "integrand": "-3*sin(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 2*asin(2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*x*asin(2*x) + sqrt(1 - 4*x**2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 234, "integrand": "2*asin(2*x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(x**3 - 3*x**2 + 6*x - 6)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 235, "integrand": "x**3*exp(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -2*x**3*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*x**3*cos(x) - 6*x**2*sin(x) - 12*x*cos(x) + 12*sin(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 236, "integrand": "-2*x**3*sin(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -9*sin(3*x - 2)*cos(3*x - 2)**3 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*cos(3*x - 2)**4/4 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 237, "integrand": "-9*sin(3*x - 2)*cos(3*x - 2)**3", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -2*atan(2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*x*atan(2*x) + log(4*x**2 + 1)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 238, "integrand": "-2*atan(2*x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ (2*x - 8)**4 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "16*x**5/5 - 64*x**4 + 512*x**3 - 2048*x**2 + 4096*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 239, "integrand": "(2*x - 8)**4", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ (18*x - 3)*exp(-3*x**2 + x + 6) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*exp(-3*x**2 + x + 6) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 240, "integrand": "(18*x - 3)*exp(-3*x**2 + x + 6)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ (-14*x - 4)*exp(-7*x**2 - 4*x + 10) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "exp(-7*x**2 - 4*x + 10) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 241, "integrand": "(-14*x - 4)*exp(-7*x**2 - 4*x + 10)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 3*(6*x - 2)**3 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "162*x**4 - 216*x**3 + 108*x**2 - 24*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 242, "integrand": "3*(6*x - 2)**3", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -x**3*cos(2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-Integral(x**3*cos(2*x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 243, "integrand": "-x**3*cos(2*x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -21*sin(7*x - 7)**2*cos(7*x - 7) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-sin(7*x - 7)**3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 244, "integrand": "-21*sin(7*x - 7)**2*cos(7*x - 7)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -x**2*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(-x**2 + 2*x - 2)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 245, "integrand": "-x**2*exp(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -2*x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(-2*x**3 + 6*x**2 - 12*x + 12)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 246, "integrand": "-2*x**3*exp(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ sin(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "sin(x)**2/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 247, "integrand": "sin(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ x**2*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "Integral(x**2*cos(x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 248, "integrand": "x**2*cos(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ (12*x + 12)*exp(-2*x**2 - 4*x - 10) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*exp(-2*x**2 - 4*x - 10) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 249, "integrand": "(12*x + 12)*exp(-2*x**2 - 4*x - 10)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -3*exp(x)*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*exp(x)*sin(x)/2 + 3*exp(x)*cos(x)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 250, "integrand": "-3*exp(x)*sin(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -2*sin(2*x + 6)**2*cos(2*x + 6) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-sin(2*x + 6)**3/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 251, "integrand": "-2*sin(2*x + 6)**2*cos(2*x + 6)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -6*sqrt(2*x - 10) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*(2*x - 10)**(3/2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 252, "integrand": "-6*sqrt(2*x - 10)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -2*sin(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-sin(x)**2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 253, "integrand": "-2*sin(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -3*(6*x + 9)**4 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3888*x**5/5 - 5832*x**4 - 17496*x**3 - 26244*x**2 - 19683*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 254, "integrand": "-3*(6*x + 9)**4", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ x*cos(2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "Integral(x*cos(2*x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 255, "integrand": "x*cos(2*x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 12*sqrt(6*x - 8) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "4*(6*x - 8)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 256, "integrand": "12*sqrt(6*x - 8)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 2*log(x**3) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*x*log(x**3) - 6*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 257, "integrand": "2*log(x**3)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -3*x*sin(2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*Integral(x*sin(2*x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 258, "integrand": "-3*x*sin(2*x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -30*sin(10*x - 2)*cos(10*x - 2)**2 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "cos(10*x - 2)**3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 259, "integrand": "-30*sin(10*x - 2)*cos(10*x - 2)**2", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -x**3*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "x**3*cos(x) - 3*x**2*sin(x) - 6*x*cos(x) + 6*sin(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 260, "integrand": "-x**3*sin(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -3*(2*x - 10)**4 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-48*x**5/5 + 240*x**4 - 2400*x**3 + 12000*x**2 - 30000*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 261, "integrand": "-3*(2*x - 10)**4", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -sqrt(5 - x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*(5 - x)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 262, "integrand": "-sqrt(5 - x)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -9*sqrt(10 - 9*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*(10 - 9*x)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 263, "integrand": "-9*sqrt(10 - 9*x)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -21*sin(7*x - 9)*cos(7*x - 9) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*cos(7*x - 9)**2/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 264, "integrand": "-21*sin(7*x - 9)*cos(7*x - 9)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ (42*x + 3)*exp(-7*x**2 - x - 4) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*exp(-7*x**2 - x - 4) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 265, "integrand": "(42*x + 3)*exp(-7*x**2 - x - 4)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 12*sqrt(-6*x - 3) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-4*(-6*x - 3)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 266, "integrand": "12*sqrt(-6*x - 3)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -(3*x + 4)**2 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*x**3 - 12*x**2 - 16*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 267, "integrand": "-(3*x + 4)**2", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -2*x**3*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*Integral(x**3*sin(x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 268, "integrand": "-2*x**3*sin(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -sin(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-sin(x)**2/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 269, "integrand": "-sin(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -12*exp(6*x + 4) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*exp(6*x + 4) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 270, "integrand": "-12*exp(6*x + 4)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ x**2*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(x**2 - 2*x + 2)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 271, "integrand": "x**2*exp(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 2*sqrt(x - 4) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "4*(x - 4)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 272, "integrand": "2*sqrt(x - 4)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 18*sin(6*x + 2)*cos(6*x + 2)**2 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-cos(6*x + 2)**3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 273, "integrand": "18*sin(6*x + 2)*cos(6*x + 2)**2", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 2*(6*x + 1)**2 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "24*x**3 + 12*x**2 + 2*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 274, "integrand": "2*(6*x + 1)**2", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -12*sin(4*x - 8)**4*cos(4*x - 8) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*sin(4*x - 8)**5/5 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 275, "integrand": "-12*sin(4*x - 8)**4*cos(4*x - 8)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ (42*x - 30)*exp(-7*x**2 + 10*x - 7) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*exp(-7*x**2 + 10*x - 7) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 276, "integrand": "(42*x - 30)*exp(-7*x**2 + 10*x - 7)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 30*sqrt(4 - 10*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*(4 - 10*x)**(3/2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 277, "integrand": "30*sqrt(4 - 10*x)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 6*sin(2*x + 5)*cos(2*x + 5) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*cos(2*x + 5)**2/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 278, "integrand": "6*sin(2*x + 5)*cos(2*x + 5)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -2*asin(3*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*x*asin(3*x) - 2*sqrt(1 - 9*x**2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 279, "integrand": "-2*asin(3*x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ exp(x)*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "exp(x)*sin(x)/2 - exp(x)*cos(x)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 280, "integrand": "exp(x)*sin(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 2*exp(-x - 6) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*exp(-x - 6) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 281, "integrand": "2*exp(-x - 6)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 2*x*cos(2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*Integral(x*cos(2*x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 282, "integrand": "2*x*cos(2*x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 3*x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(3*x**3 - 9*x**2 + 18*x - 18)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 283, "integrand": "3*x**3*exp(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 3*(x - 8)**2 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "x**3 - 24*x**2 + 192*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 284, "integrand": "3*(x - 8)**2", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 3*exp(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*exp(x)*sin(x)/2 + 3*exp(x)*cos(x)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 285, "integrand": "3*exp(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ (12*x + 24)*exp(-2*x**2 - 8*x - 4) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*exp(-2*x**2 - 8*x - 4) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 286, "integrand": "(12*x + 24)*exp(-2*x**2 - 8*x - 4)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 2*sin(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "sin(x)**2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 287, "integrand": "2*sin(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 3*x**3*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*x**3*sin(x) + 9*x**2*cos(x) - 18*x*sin(x) - 18*cos(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 288, "integrand": "3*x**3*cos(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ exp(x)*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "exp(x)*sin(x)/2 - exp(x)*cos(x)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 289, "integrand": "exp(x)*sin(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -9*sqrt(4 - 3*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*(4 - 3*x)**(3/2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 290, "integrand": "-9*sqrt(4 - 3*x)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -2*x*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*Integral(x*sin(x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 291, "integrand": "-2*x*sin(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -2*x**3*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*x**3*cos(x) - 6*x**2*sin(x) - 12*x*cos(x) + 12*sin(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 292, "integrand": "-2*x**3*sin(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 2*sqrt(3 - x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-4*(3 - x)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 293, "integrand": "2*sqrt(3 - x)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -(3*x - 9)**4 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-81*x**5/5 + 243*x**4 - 1458*x**3 + 4374*x**2 - 6561*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 294, "integrand": "-(3*x - 9)**4", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 18*sqrt(9*x - 5) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "4*(9*x - 5)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 295, "integrand": "18*sqrt(9*x - 5)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 3*(8*x + 8)**4 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "12288*x**5/5 + 12288*x**4 + 24576*x**3 + 24576*x**2 + 12288*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 296, "integrand": "3*(8*x + 8)**4", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 2*sqrt(10 - x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-4*(10 - x)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 297, "integrand": "2*sqrt(10 - x)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 6*sin(3*x + 4)**3*cos(3*x + 4) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "sin(3*x + 4)**4/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 298, "integrand": "6*sin(3*x + 4)**3*cos(3*x + 4)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -3*x*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(3 - 3*x)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 299, "integrand": "-3*x*exp(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -3*(2*x - 2)**2 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-4*x**3 + 12*x**2 - 12*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 300, "integrand": "-3*(2*x - 2)**2", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 20*sqrt(9 - 10*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-4*(9 - 10*x)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 301, "integrand": "20*sqrt(9 - 10*x)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 10*sin(5*x + 7)*cos(5*x + 7)**3 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-cos(5*x + 7)**4/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 302, "integrand": "10*sin(5*x + 7)*cos(5*x + 7)**3", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 2*exp(x)*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "exp(x)*sin(x) - exp(x)*cos(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 303, "integrand": "2*exp(x)*sin(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -3*x**3*sin(3*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*Integral(x**3*sin(3*x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 304, "integrand": "-3*x**3*sin(3*x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 2*atan(2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*x*atan(2*x) - log(4*x**2 + 1)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 305, "integrand": "2*atan(2*x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -exp(x)*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-exp(x)*sin(x)/2 + exp(x)*cos(x)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 306, "integrand": "-exp(x)*sin(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -20*sin(10*x + 10)*cos(10*x + 10)**3 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "cos(10*x + 10)**4/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 307, "integrand": "-20*sin(10*x + 10)*cos(10*x + 10)**3", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -2*x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(-2*x**3 + 6*x**2 - 12*x + 12)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 308, "integrand": "-2*x**3*exp(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -3*exp(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*exp(x)*sin(x)/2 - 3*exp(x)*cos(x)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 309, "integrand": "-3*exp(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 2*x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(2*x**3 - 6*x**2 + 12*x - 12)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 310, "integrand": "2*x**3*exp(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 3*(2*x - 10)**3 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "6*x**4 - 120*x**3 + 900*x**2 - 3000*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 311, "integrand": "3*(2*x - 10)**3", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 6*sqrt(3*x + 2) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "4*(3*x + 2)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 312, "integrand": "6*sqrt(3*x + 2)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -3*sqrt(9 - x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*(9 - x)**(3/2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 313, "integrand": "-3*sqrt(9 - x)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ (42*x + 27)*exp(-7*x**2 - 9*x - 4) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*exp(-7*x**2 - 9*x - 4) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 314, "integrand": "(42*x + 27)*exp(-7*x**2 - 9*x - 4)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 12*sqrt(4*x - 3) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*(4*x - 3)**(3/2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 315, "integrand": "12*sqrt(4*x - 3)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -2*exp(x)*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-exp(x)*sin(x) + exp(x)*cos(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 316, "integrand": "-2*exp(x)*sin(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ (10*x - 8)**3 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "250*x**4 - 800*x**3 + 960*x**2 - 512*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 317, "integrand": "(10*x - 8)**3", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(x**3 - 3*x**2 + 6*x - 6)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 318, "integrand": "x**3*exp(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 2*x**3*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*x**3*sin(x) + 6*x**2*cos(x) - 12*x*sin(x) - 12*cos(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 319, "integrand": "2*x**3*cos(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -3*exp(x)*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*exp(x)*sin(x)/2 + 3*exp(x)*cos(x)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 320, "integrand": "-3*exp(x)*sin(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -sin(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-sin(x)**2/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 321, "integrand": "-sin(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ exp(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "exp(x)*sin(x)/2 + exp(x)*cos(x)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 322, "integrand": "exp(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ (18*x - 10)*exp(9*x**2 - 10*x - 9) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "exp(9*x**2 - 10*x - 9) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 323, "integrand": "(18*x - 10)*exp(9*x**2 - 10*x - 9)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -2*(3*x - 9)**4 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-162*x**5/5 + 486*x**4 - 2916*x**3 + 8748*x**2 - 13122*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 324, "integrand": "-2*(3*x - 9)**4", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -3*(x + 6)**2 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-x**3 - 18*x**2 - 108*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 325, "integrand": "-3*(x + 6)**2", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -x**3*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "x**3*cos(x) - 3*x**2*sin(x) - 6*x*cos(x) + 6*sin(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 326, "integrand": "-x**3*sin(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ sin(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "sin(x)**2/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 327, "integrand": "sin(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -(10*x - 9)**4 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2000*x**5 + 9000*x**4 - 16200*x**3 + 14580*x**2 - 6561*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 328, "integrand": "-(10*x - 9)**4", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ asin(3*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "x*asin(3*x) + sqrt(1 - 9*x**2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 329, "integrand": "asin(3*x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -2*(4*x + 2)**4 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-512*x**5/5 - 256*x**4 - 256*x**3 - 128*x**2 - 32*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 330, "integrand": "-2*(4*x + 2)**4", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -2*(4*x - 4)**3 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-32*x**4 + 128*x**3 - 192*x**2 + 128*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 331, "integrand": "-2*(4*x - 4)**3", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 3*log(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*x*log(x) - 3*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 332, "integrand": "3*log(x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 9*sqrt(-3*x - 3) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*(-3*x - 3)**(3/2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 333, "integrand": "9*sqrt(-3*x - 3)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ (21 - 18*x)*exp(-3*x**2 + 7*x - 3) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*exp(-3*x**2 + 7*x - 3) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 334, "integrand": "(21 - 18*x)*exp(-3*x**2 + 7*x - 3)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -2*sqrt(2*x + 8) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*(2*x + 8)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 335, "integrand": "-2*sqrt(2*x + 8)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ (8*x - 3)**3 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "128*x**4 - 192*x**3 + 108*x**2 - 27*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 336, "integrand": "(8*x - 3)**3", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -2*(10*x - 6)**4 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-4000*x**5 + 12000*x**4 - 14400*x**3 + 8640*x**2 - 2592*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 337, "integrand": "-2*(10*x - 6)**4", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 2*x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(2*x**3 - 6*x**2 + 12*x - 12)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 338, "integrand": "2*x**3*exp(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 15*sin(5*x + 9)**3*cos(5*x + 9) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*sin(5*x + 9)**4/4 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 339, "integrand": "15*sin(5*x + 9)**3*cos(5*x + 9)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -3*(6*x + 4)**3 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-162*x**4 - 432*x**3 - 432*x**2 - 192*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 340, "integrand": "-3*(6*x + 4)**3", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 2*x*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(2*x - 2)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 341, "integrand": "2*x*exp(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 6*exp(6*x + 8) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "exp(6*x + 8) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 342, "integrand": "6*exp(6*x + 8)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 2*x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(2*x**3 - 6*x**2 + 12*x - 12)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 343, "integrand": "2*x**3*exp(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ x**3*sin(2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "Integral(x**3*sin(2*x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 344, "integrand": "x**3*sin(2*x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 12*sin(4*x - 5)*cos(4*x - 5) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*cos(4*x - 5)**2/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 345, "integrand": "12*sin(4*x - 5)*cos(4*x - 5)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 2*exp(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "exp(x)*sin(x) + exp(x)*cos(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 346, "integrand": "2*exp(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ (8*x - 7)*exp(4*x**2 - 7*x + 7) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "exp(4*x**2 - 7*x + 7) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 347, "integrand": "(8*x - 7)*exp(4*x**2 - 7*x + 7)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -3*x**3*cos(3*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*Integral(x**3*cos(3*x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 348, "integrand": "-3*x**3*cos(3*x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 8*sin(8*x + 8)*cos(8*x + 8) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-cos(8*x + 8)**2/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 349, "integrand": "8*sin(8*x + 8)*cos(8*x + 8)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 3*x**2*cos(3*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*Integral(x**2*cos(3*x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 350, "integrand": "3*x**2*cos(3*x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ log(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "x*log(x) - x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 351, "integrand": "log(x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(-x**3 + 3*x**2 - 6*x + 6)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 352, "integrand": "-x**3*exp(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 3*log(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*x*log(x) - 3*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 353, "integrand": "3*log(x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -(9*x - 3)**3 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-729*x**4/4 + 243*x**3 - 243*x**2/2 + 27*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 354, "integrand": "-(9*x - 3)**3", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ (8*x - 1)**4 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "4096*x**5/5 - 512*x**4 + 128*x**3 - 16*x**2 + x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 355, "integrand": "(8*x - 1)**4", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -2*x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(-2*x**3 + 6*x**2 - 12*x + 12)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 356, "integrand": "-2*x**3*exp(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 3*(10*x + 4)**2 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "100*x**3 + 120*x**2 + 48*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 357, "integrand": "3*(10*x + 4)**2", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -2*log(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*x*log(x) + 2*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 358, "integrand": "-2*log(x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 24*sin(8*x + 3)*cos(8*x + 3)**3 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*cos(8*x + 3)**4/4 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 359, "integrand": "24*sin(8*x + 3)*cos(8*x + 3)**3", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -3*sin(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*sin(x)**2/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 360, "integrand": "-3*sin(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -3*sqrt(3*x - 8) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*(3*x - 8)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 361, "integrand": "-3*sqrt(3*x - 8)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 3*(x + 9)**4 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*x**5/5 + 27*x**4 + 486*x**3 + 4374*x**2 + 19683*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 362, "integrand": "3*(x + 9)**4", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -2*(2*x + 10)**4 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-32*x**5/5 - 160*x**4 - 1600*x**3 - 8000*x**2 - 20000*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 363, "integrand": "-2*(2*x + 10)**4", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 2*sin(2*x - 1)*cos(2*x - 1) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-cos(2*x - 1)**2/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 364, "integrand": "2*sin(2*x - 1)*cos(2*x - 1)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ (24*x + 18)*exp(-6*x**2 - 9*x - 2) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*exp(-6*x**2 - 9*x - 2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 365, "integrand": "(24*x + 18)*exp(-6*x**2 - 9*x - 2)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 3*exp(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*exp(x)*sin(x)/2 + 3*exp(x)*cos(x)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 366, "integrand": "3*exp(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -3*exp(x)*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*exp(x)*sin(x)/2 + 3*exp(x)*cos(x)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 367, "integrand": "-3*exp(x)*sin(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -18*sqrt(6*x + 5) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*(6*x + 5)**(3/2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 368, "integrand": "-18*sqrt(6*x + 5)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -20*sqrt(10*x + 4) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-4*(10*x + 4)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 369, "integrand": "-20*sqrt(10*x + 4)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ log(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "x*log(x) - x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 370, "integrand": "log(x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -exp(x)*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-exp(x)*sin(x)/2 + exp(x)*cos(x)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 371, "integrand": "-exp(x)*sin(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 15*sin(5*x - 5)**2*cos(5*x - 5) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "sin(5*x - 5)**3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 372, "integrand": "15*sin(5*x - 5)**2*cos(5*x - 5)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ exp(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "exp(x)*sin(x)/2 + exp(x)*cos(x)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 373, "integrand": "exp(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -3*atan(3*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*x*atan(3*x) + log(9*x**2 + 1)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 374, "integrand": "-3*atan(3*x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -2*x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(-2*x**3 + 6*x**2 - 12*x + 12)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 375, "integrand": "-2*x**3*exp(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 2*asin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*x*asin(x) + 2*sqrt(1 - x**2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 376, "integrand": "2*asin(x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 3*x*sin(2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*Integral(x*sin(2*x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 377, "integrand": "3*x*sin(2*x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 3*(5*x + 7)**4 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "375*x**5 + 2625*x**4 + 7350*x**3 + 10290*x**2 + 7203*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 378, "integrand": "3*(5*x + 7)**4", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ (-30*x - 27)*exp(-5*x**2 - 9*x - 7) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*exp(-5*x**2 - 9*x - 7) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 379, "integrand": "(-30*x - 27)*exp(-5*x**2 - 9*x - 7)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 20*sin(10*x + 5)*cos(10*x + 5) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "sin(10*x + 5)**2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 380, "integrand": "20*sin(10*x + 5)*cos(10*x + 5)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -3*log(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*x*log(x) + 3*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 381, "integrand": "-3*log(x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 2*x*cos(3*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*Integral(x*cos(3*x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 382, "integrand": "2*x*cos(3*x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 30*sin(10*x + 10)*cos(10*x + 10)**2 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-cos(10*x + 10)**3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 383, "integrand": "30*sin(10*x + 10)*cos(10*x + 10)**2", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -8*sqrt(4*x + 5) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-4*(4*x + 5)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 384, "integrand": "-8*sqrt(4*x + 5)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -sqrt(5 - x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*(5 - x)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 385, "integrand": "-sqrt(5 - x)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -atan(2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-x*atan(2*x) + log(4*x**2 + 1)/4 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 386, "integrand": "-atan(2*x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -x*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-Integral(x*sin(x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 387, "integrand": "-x*sin(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -2*log(x**3) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*x*log(x**3) + 6*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 388, "integrand": "-2*log(x**3)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -3*x**3*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*x**3*cos(x) - 9*x**2*sin(x) - 18*x*cos(x) + 18*sin(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 389, "integrand": "-3*x**3*sin(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 3*x*sin(2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*Integral(x*sin(2*x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 390, "integrand": "3*x*sin(2*x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -2*sqrt(x - 10) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-4*(x - 10)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 391, "integrand": "-2*sqrt(x - 10)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 2*asin(3*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*x*asin(3*x) + 2*sqrt(1 - 9*x**2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 392, "integrand": "2*asin(3*x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -x**3*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-x**3*sin(x) - 3*x**2*cos(x) + 6*x*sin(x) + 6*cos(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 393, "integrand": "-x**3*cos(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 12*sin(6*x + 9)*cos(6*x + 9) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-cos(6*x + 9)**2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 394, "integrand": "12*sin(6*x + 9)*cos(6*x + 9)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -x*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(1 - x)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 395, "integrand": "-x*exp(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -27*sqrt(-9*x - 1) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*(-9*x - 1)**(3/2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 396, "integrand": "-27*sqrt(-9*x - 1)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 18*sin(9*x + 5)*cos(9*x + 5)**4 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*cos(9*x + 5)**5/5 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 397, "integrand": "18*sin(9*x + 5)*cos(9*x + 5)**4", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ (5*x + 5)**2 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "25*x**3/3 + 25*x**2 + 25*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 398, "integrand": "(5*x + 5)**2", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -24*sqrt(8*x + 8) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*(8*x + 8)**(3/2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 399, "integrand": "-24*sqrt(8*x + 8)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -2*atan(2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*x*atan(2*x) + log(4*x**2 + 1)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 400, "integrand": "-2*atan(2*x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -3*sin(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*sin(x)**2/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 401, "integrand": "-3*sin(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -2*asin(2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*x*asin(2*x) - sqrt(1 - 4*x**2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 402, "integrand": "-2*asin(2*x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -2*x*sin(3*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*Integral(x*sin(3*x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 403, "integrand": "-2*x*sin(3*x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -exp(x)*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-exp(x)*sin(x)/2 + exp(x)*cos(x)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 404, "integrand": "-exp(x)*sin(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -6*sin(3*x + 7)*cos(3*x + 7) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "cos(3*x + 7)**2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 405, "integrand": "-6*sin(3*x + 7)*cos(3*x + 7)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -asin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-x*asin(x) - sqrt(1 - x**2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 406, "integrand": "-asin(x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 2*sqrt(8 - 2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*(8 - 2*x)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 407, "integrand": "2*sqrt(8 - 2*x)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 2*(7*x + 1)**4 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "4802*x**5/5 + 686*x**4 + 196*x**3 + 28*x**2 + 2*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 408, "integrand": "2*(7*x + 1)**4", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -(8*x + 6)**2 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-64*x**3/3 - 48*x**2 - 36*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 409, "integrand": "-(8*x + 6)**2", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 2*asin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*x*asin(x) + 2*sqrt(1 - x**2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 410, "integrand": "2*asin(x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 27*sqrt(-9*x - 4) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*(-9*x - 4)**(3/2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 411, "integrand": "27*sqrt(-9*x - 4)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 2*atan(2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*x*atan(2*x) - log(4*x**2 + 1)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 412, "integrand": "2*atan(2*x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 3*x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(3*x**3 - 9*x**2 + 18*x - 18)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 413, "integrand": "3*x**3*exp(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ (2*x - 6)*exp(-x**2 + 6*x - 2) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-exp(-x**2 + 6*x - 2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 414, "integrand": "(2*x - 6)*exp(-x**2 + 6*x - 2)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -2*sin(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-sin(x)**2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 415, "integrand": "-2*sin(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -3*(2*x - 2)**4 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-48*x**5/5 + 48*x**4 - 96*x**3 + 96*x**2 - 48*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 416, "integrand": "-3*(2*x - 2)**4", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(x**3 - 3*x**2 + 6*x - 6)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 417, "integrand": "x**3*exp(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -2*atan(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*x*atan(x) + log(x**2 + 1) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 418, "integrand": "-2*atan(x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ (5 - 4*x)*exp(2*x**2 - 5*x - 4) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-exp(2*x**2 - 5*x - 4) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 419, "integrand": "(5 - 4*x)*exp(2*x**2 - 5*x - 4)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ x**2*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "Integral(x**2*cos(x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 420, "integrand": "x**2*cos(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -12*sqrt(4*x + 3) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*(4*x + 3)**(3/2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 421, "integrand": "-12*sqrt(4*x + 3)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 2*log(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*x*log(x) - 2*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 422, "integrand": "2*log(x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 3*sqrt(x + 4) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*(x + 4)**(3/2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 423, "integrand": "3*sqrt(x + 4)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ x**3*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-x**3*cos(x) + 3*x**2*sin(x) + 6*x*cos(x) - 6*sin(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 424, "integrand": "x**3*sin(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -log(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-x*log(x) + x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 425, "integrand": "-log(x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(x**3 - 3*x**2 + 6*x - 6)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 426, "integrand": "x**3*exp(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -2*atan(2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*x*atan(2*x) + log(4*x**2 + 1)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 427, "integrand": "-2*atan(2*x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -(3*x - 3)**4 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-81*x**5/5 + 81*x**4 - 162*x**3 + 162*x**2 - 81*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 428, "integrand": "-(3*x - 3)**4", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -2*x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(-2*x**3 + 6*x**2 - 12*x + 12)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 429, "integrand": "-2*x**3*exp(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 3*x**3*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*x**3*cos(x) + 9*x**2*sin(x) + 18*x*cos(x) - 18*sin(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 430, "integrand": "3*x**3*sin(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -3*log(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*x*log(x) + 3*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 431, "integrand": "-3*log(x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 2*(7*x - 3)**3 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "343*x**4/2 - 294*x**3 + 189*x**2 - 54*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 432, "integrand": "2*(7*x - 3)**3", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -3*x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(-3*x**3 + 9*x**2 - 18*x + 18)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 433, "integrand": "-3*x**3*exp(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -8*sin(8*x + 4)*cos(8*x + 4)**4 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "cos(8*x + 4)**5/5 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 434, "integrand": "-8*sin(8*x + 4)*cos(8*x + 4)**4", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -3*x**2*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*Integral(x**2*cos(x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 435, "integrand": "-3*x**2*cos(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(-x**3 + 3*x**2 - 6*x + 6)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 436, "integrand": "-x**3*exp(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(x**3 - 3*x**2 + 6*x - 6)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 437, "integrand": "x**3*exp(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -5*sin(5*x + 4)*cos(5*x + 4)**2 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "cos(5*x + 4)**3/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 438, "integrand": "-5*sin(5*x + 4)*cos(5*x + 4)**2", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ (16 - 32*x)*exp(8*x**2 - 8*x + 2) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*exp(8*x**2 - 8*x + 2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 439, "integrand": "(16 - 32*x)*exp(8*x**2 - 8*x + 2)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 3*x**2*cos(3*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*Integral(x**2*cos(3*x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 440, "integrand": "3*x**2*cos(3*x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ x**2*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(x**2 - 2*x + 2)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 441, "integrand": "x**2*exp(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 3*x**2*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(3*x**2 - 6*x + 6)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 442, "integrand": "3*x**2*exp(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 12*sqrt(-6*x - 7) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-4*(-6*x - 7)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 443, "integrand": "12*sqrt(-6*x - 7)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 6*sqrt(8 - 3*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-4*(8 - 3*x)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 444, "integrand": "6*sqrt(8 - 3*x)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ exp(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "exp(x)*sin(x)/2 + exp(x)*cos(x)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 445, "integrand": "exp(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -3*(9*x - 9)**3 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2187*x**4/4 + 2187*x**3 - 6561*x**2/2 + 2187*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 446, "integrand": "-3*(9*x - 9)**3", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(-x**3 + 3*x**2 - 6*x + 6)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 447, "integrand": "-x**3*exp(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 3*x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(3*x**3 - 9*x**2 + 18*x - 18)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 448, "integrand": "3*x**3*exp(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 3*sin(3*x + 4)*cos(3*x + 4)**4 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-cos(3*x + 4)**5/5 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 449, "integrand": "3*sin(3*x + 4)*cos(3*x + 4)**4", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 2*exp(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "exp(x)*sin(x) + exp(x)*cos(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 450, "integrand": "2*exp(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -3*x**3*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*x**3*sin(x) - 9*x**2*cos(x) + 18*x*sin(x) + 18*cos(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 451, "integrand": "-3*x**3*cos(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -16*exp(8*x - 7) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*exp(8*x - 7) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 452, "integrand": "-16*exp(8*x - 7)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 6*exp(6*x - 6) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "exp(6*x - 6) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 453, "integrand": "6*exp(6*x - 6)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ (36*x + 27)*exp(6*x**2 + 9*x + 10) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*exp(6*x**2 + 9*x + 10) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 454, "integrand": "(36*x + 27)*exp(6*x**2 + 9*x + 10)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 2*asin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*x*asin(x) + 2*sqrt(1 - x**2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 455, "integrand": "2*asin(x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 21*sin(7*x - 10)**4*cos(7*x - 10) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*sin(7*x - 10)**5/5 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 456, "integrand": "21*sin(7*x - 10)**4*cos(7*x - 10)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 3*(5*x - 10)**3 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "375*x**4/4 - 750*x**3 + 2250*x**2 - 3000*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 457, "integrand": "3*(5*x - 10)**3", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -3*exp(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*exp(x)*sin(x)/2 - 3*exp(x)*cos(x)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 458, "integrand": "-3*exp(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 18*exp(-6*x - 3) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*exp(-6*x - 3) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 459, "integrand": "18*exp(-6*x - 3)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 3*x**3*sin(3*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*Integral(x**3*sin(3*x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 460, "integrand": "3*x**3*sin(3*x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 21*sqrt(7*x - 3) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*(7*x - 3)**(3/2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 461, "integrand": "21*sqrt(7*x - 3)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -3*sin(x + 3)**3*cos(x + 3) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*sin(x + 3)**4/4 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 462, "integrand": "-3*sin(x + 3)**3*cos(x + 3)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 18*sqrt(-6*x - 5) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*(-6*x - 5)**(3/2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 463, "integrand": "18*sqrt(-6*x - 5)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -2*exp(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-exp(x)*sin(x) - exp(x)*cos(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 464, "integrand": "-2*exp(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -24*sin(8*x - 2)*cos(8*x - 2)**3 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*cos(8*x - 2)**4/4 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 465, "integrand": "-24*sin(8*x - 2)*cos(8*x - 2)**3", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -x**2*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(-x**2 + 2*x - 2)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 466, "integrand": "-x**2*exp(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -6*exp(3*x + 10) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*exp(3*x + 10) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 467, "integrand": "-6*exp(3*x + 10)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ (9 - 12*x)*exp(-2*x**2 + 3*x - 3) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*exp(-2*x**2 + 3*x - 3) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 468, "integrand": "(9 - 12*x)*exp(-2*x**2 + 3*x - 3)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 3*(3*x - 4)**4 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "243*x**5/5 - 324*x**4 + 864*x**3 - 1152*x**2 + 768*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 469, "integrand": "3*(3*x - 4)**4", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -3*(3*x - 6)**3 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-81*x**4/4 + 162*x**3 - 486*x**2 + 648*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 470, "integrand": "-3*(3*x - 6)**3", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -2*(10*x - 3)**4 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-4000*x**5 + 6000*x**4 - 3600*x**3 + 1080*x**2 - 162*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 471, "integrand": "-2*(10*x - 3)**4", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -2*log(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*x*log(x) + 2*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 472, "integrand": "-2*log(x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 4*sqrt(2*x + 8) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "4*(2*x + 8)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 473, "integrand": "4*sqrt(2*x + 8)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 3*sin(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*sin(x)**2/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 474, "integrand": "3*sin(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 2*exp(x)*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "exp(x)*sin(x) - exp(x)*cos(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 475, "integrand": "2*exp(x)*sin(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -3*x**3*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*x**3*sin(x) - 9*x**2*cos(x) + 18*x*sin(x) + 18*cos(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 476, "integrand": "-3*x**3*cos(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -x**2*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(-x**2 + 2*x - 2)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 477, "integrand": "-x**2*exp(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -x**3*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-x**3*sin(x) - 3*x**2*cos(x) + 6*x*sin(x) + 6*cos(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 478, "integrand": "-x**3*cos(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 2*(5*x + 7)**3 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "125*x**4/2 + 350*x**3 + 735*x**2 + 686*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 479, "integrand": "2*(5*x + 7)**3", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ (10*x + 1)**4 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2000*x**5 + 1000*x**4 + 200*x**3 + 20*x**2 + x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 480, "integrand": "(10*x + 1)**4", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 2*x**3*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*x**3*cos(x) + 6*x**2*sin(x) + 12*x*cos(x) - 12*sin(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 481, "integrand": "2*x**3*sin(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 24*sqrt(-8*x - 2) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*(-8*x - 2)**(3/2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 482, "integrand": "24*sqrt(-8*x - 2)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ exp(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "exp(x)*sin(x)/2 + exp(x)*cos(x)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 483, "integrand": "exp(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -2*x**3*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*x**3*cos(x) - 6*x**2*sin(x) - 12*x*cos(x) + 12*sin(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 484, "integrand": "-2*x**3*sin(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 3*x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(3*x**3 - 9*x**2 + 18*x - 18)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 485, "integrand": "3*x**3*exp(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -2*exp(x)*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-exp(x)*sin(x) + exp(x)*cos(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 486, "integrand": "-2*exp(x)*sin(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 12*exp(-4*x - 4) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*exp(-4*x - 4) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 487, "integrand": "12*exp(-4*x - 4)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 2*x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(2*x**3 - 6*x**2 + 12*x - 12)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 488, "integrand": "2*x**3*exp(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -2*x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(-2*x**3 + 6*x**2 - 12*x + 12)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 489, "integrand": "-2*x**3*exp(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 24*sqrt(8*x - 1) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*(8*x - 1)**(3/2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 490, "integrand": "24*sqrt(8*x - 1)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ sin(x + 6)*cos(x + 6)**3 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-cos(x + 6)**4/4 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 491, "integrand": "sin(x + 6)*cos(x + 6)**3", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -5*sin(5*x - 7)*cos(5*x - 7) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "cos(5*x - 7)**2/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 492, "integrand": "-5*sin(5*x - 7)*cos(5*x - 7)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -10*sqrt(-10*x - 3) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*(-10*x - 3)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 493, "integrand": "-10*sqrt(-10*x - 3)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ (-28*x - 6)*exp(-7*x**2 - 3*x - 6) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*exp(-7*x**2 - 3*x - 6) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 494, "integrand": "(-28*x - 6)*exp(-7*x**2 - 3*x - 6)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -24*exp(8*x - 3) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*exp(8*x - 3) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 495, "integrand": "-24*exp(8*x - 3)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -asin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-x*asin(x) - sqrt(1 - x**2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 496, "integrand": "-asin(x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ log(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "x*log(x) - x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 497, "integrand": "log(x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -3*x*sin(2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*Integral(x*sin(2*x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 498, "integrand": "-3*x*sin(2*x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -asin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-x*asin(x) - sqrt(1 - x**2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 499, "integrand": "-asin(x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 3*sin(3*x - 10)*cos(3*x - 10)**3 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-cos(3*x - 10)**4/4 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 500, "integrand": "3*sin(3*x - 10)*cos(3*x - 10)**3", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 2*exp(x)*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "exp(x)*sin(x) - exp(x)*cos(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 501, "integrand": "2*exp(x)*sin(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -30*exp(-10*x - 2) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*exp(-10*x - 2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 502, "integrand": "-30*exp(-10*x - 2)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -16*sqrt(8*x + 7) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-4*(8*x + 7)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 503, "integrand": "-16*sqrt(8*x + 7)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 3*(7*x - 1)**3 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "1029*x**4/4 - 147*x**3 + 63*x**2/2 - 3*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 504, "integrand": "3*(7*x - 1)**3", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 2*(6*x + 8)**3 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "108*x**4 + 576*x**3 + 1152*x**2 + 1024*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 505, "integrand": "2*(6*x + 8)**3", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 2*x**3*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*x**3*cos(x) + 6*x**2*sin(x) + 12*x*cos(x) - 12*sin(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 506, "integrand": "2*x**3*sin(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -3*x**3*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*x**3*cos(x) - 9*x**2*sin(x) - 18*x*cos(x) + 18*sin(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 507, "integrand": "-3*x**3*sin(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -3*exp(x)*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*exp(x)*sin(x)/2 + 3*exp(x)*cos(x)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 508, "integrand": "-3*exp(x)*sin(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -x*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(1 - x)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 509, "integrand": "-x*exp(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -(9*x + 7)**4 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-6561*x**5/5 - 5103*x**4 - 7938*x**3 - 6174*x**2 - 2401*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 510, "integrand": "-(9*x + 7)**4", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -sin(x + 7)**4*cos(x + 7) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-sin(x + 7)**5/5 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 511, "integrand": "-sin(x + 7)**4*cos(x + 7)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 2*x**2*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(2*x**2 - 4*x + 4)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 512, "integrand": "2*x**2*exp(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -18*sqrt(9*x + 3) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-4*(9*x + 3)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 513, "integrand": "-18*sqrt(9*x + 3)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ (21 - 6*x)*exp(-x**2 + 7*x + 9) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*exp(-x**2 + 7*x + 9) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 514, "integrand": "(21 - 6*x)*exp(-x**2 + 7*x + 9)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 3*(9*x - 10)**3 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2187*x**4/4 - 2430*x**3 + 4050*x**2 - 3000*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 515, "integrand": "3*(9*x - 10)**3", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 3*x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(3*x**3 - 9*x**2 + 18*x - 18)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 516, "integrand": "3*x**3*exp(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -3*(6*x + 6)**2 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-36*x**3 - 108*x**2 - 108*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 517, "integrand": "-3*(6*x + 6)**2", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -3*exp(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*exp(x)*sin(x)/2 - 3*exp(x)*cos(x)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 518, "integrand": "-3*exp(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ x*cos(2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "Integral(x*cos(2*x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 519, "integrand": "x*cos(2*x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -4*exp(2*x - 3) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*exp(2*x - 3) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 520, "integrand": "-4*exp(2*x - 3)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(x**3 - 3*x**2 + 6*x - 6)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 521, "integrand": "x**3*exp(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -2*x**3*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*x**3*cos(x) - 6*x**2*sin(x) - 12*x*cos(x) + 12*sin(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 522, "integrand": "-2*x**3*sin(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -3*x**3*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*x**3*sin(x) - 9*x**2*cos(x) + 18*x*sin(x) + 18*cos(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 523, "integrand": "-3*x**3*cos(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 2*sin(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "sin(x)**2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 524, "integrand": "2*sin(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 20*sqrt(10*x - 8) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "4*(10*x - 8)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 525, "integrand": "20*sqrt(10*x - 8)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -(5*x + 7)**4 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-125*x**5 - 875*x**4 - 2450*x**3 - 3430*x**2 - 2401*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 526, "integrand": "-(5*x + 7)**4", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -2*x**2*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(-2*x**2 + 4*x - 4)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 527, "integrand": "-2*x**2*exp(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 2*(6*x + 1)**3 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "108*x**4 + 72*x**3 + 18*x**2 + 2*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 528, "integrand": "2*(6*x + 1)**3", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -3*sqrt(1 - x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*(1 - x)**(3/2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 529, "integrand": "-3*sqrt(1 - x)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -3*x**3*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*x**3*sin(x) - 9*x**2*cos(x) + 18*x*sin(x) + 18*cos(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 530, "integrand": "-3*x**3*cos(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 21*exp(7*x - 3) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*exp(7*x - 3) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 531, "integrand": "21*exp(7*x - 3)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -2*asin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*x*asin(x) - 2*sqrt(1 - x**2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 532, "integrand": "-2*asin(x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -2*asin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*x*asin(x) - 2*sqrt(1 - x**2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 533, "integrand": "-2*asin(x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -exp(x)*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-exp(x)*sin(x)/2 + exp(x)*cos(x)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 534, "integrand": "-exp(x)*sin(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -14*sin(7*x - 9)*cos(7*x - 9)**4 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*cos(7*x - 9)**5/5 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 535, "integrand": "-14*sin(7*x - 9)*cos(7*x - 9)**4", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -3*sin(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*sin(x)**2/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 536, "integrand": "-3*sin(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -asin(3*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-x*asin(3*x) - sqrt(1 - 9*x**2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 537, "integrand": "-asin(3*x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 2*x*cos(3*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*Integral(x*cos(3*x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 538, "integrand": "2*x*cos(3*x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ (20 - 28*x)*exp(-7*x**2 + 10*x - 5) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*exp(-7*x**2 + 10*x - 5) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 539, "integrand": "(20 - 28*x)*exp(-7*x**2 + 10*x - 5)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 8*sqrt(8*x + 7) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*(8*x + 7)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 540, "integrand": "8*sqrt(8*x + 7)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -3*x**2*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*Integral(x**2*cos(x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 541, "integrand": "-3*x**2*cos(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -2*x*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(2 - 2*x)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 542, "integrand": "-2*x*exp(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -3*(8*x - 10)**3 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-384*x**4 + 1920*x**3 - 3600*x**2 + 3000*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 543, "integrand": "-3*(8*x - 10)**3", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ (-48*x - 30)*exp(8*x**2 + 10*x + 7) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*exp(8*x**2 + 10*x + 7) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 544, "integrand": "(-48*x - 30)*exp(8*x**2 + 10*x + 7)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -3*x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(-3*x**3 + 9*x**2 - 18*x + 18)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 545, "integrand": "-3*x**3*exp(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ (6*x - 27)*exp(x**2 - 9*x + 6) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*exp(x**2 - 9*x + 6) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 546, "integrand": "(6*x - 27)*exp(x**2 - 9*x + 6)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 2*(5*x + 7)**2 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "50*x**3/3 + 70*x**2 + 98*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 547, "integrand": "2*(5*x + 7)**2", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -3*(9*x - 8)**3 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2187*x**4/4 + 1944*x**3 - 2592*x**2 + 1536*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 548, "integrand": "-3*(9*x - 8)**3", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ x**2*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(x**2 - 2*x + 2)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 549, "integrand": "x**2*exp(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 2*(2*x + 3)**4 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "32*x**5/5 + 48*x**4 + 144*x**3 + 216*x**2 + 162*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 550, "integrand": "2*(2*x + 3)**4", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(-x**3 + 3*x**2 - 6*x + 6)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 551, "integrand": "-x**3*exp(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -2*sqrt(10 - x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "4*(10 - x)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 552, "integrand": "-2*sqrt(10 - x)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -3*x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(-3*x**3 + 9*x**2 - 18*x + 18)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 553, "integrand": "-3*x**3*exp(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 4*sin(4*x + 7)**2*cos(4*x + 7) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "sin(4*x + 7)**3/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 554, "integrand": "4*sin(4*x + 7)**2*cos(4*x + 7)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -2*(5*x + 7)**4 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-250*x**5 - 1750*x**4 - 4900*x**3 - 6860*x**2 - 4802*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 555, "integrand": "-2*(5*x + 7)**4", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -3*sin(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*sin(x)**2/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 556, "integrand": "-3*sin(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -2*exp(-x - 3) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*exp(-x - 3) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 557, "integrand": "-2*exp(-x - 3)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 3*x**3*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*x**3*cos(x) + 9*x**2*sin(x) + 18*x*cos(x) - 18*sin(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 558, "integrand": "3*x**3*sin(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 8*sqrt(8*x - 8) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*(8*x - 8)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 559, "integrand": "8*sqrt(8*x - 8)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -30*sin(10*x + 7)*cos(10*x + 7) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*sin(10*x + 7)**2/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 560, "integrand": "-30*sin(10*x + 7)*cos(10*x + 7)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -2*sqrt(2 - x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "4*(2 - x)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 561, "integrand": "-2*sqrt(2 - x)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -2*(6*x - 10)**4 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2592*x**5/5 + 4320*x**4 - 14400*x**3 + 24000*x**2 - 20000*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 562, "integrand": "-2*(6*x - 10)**4", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 2*sqrt(6 - 2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*(6 - 2*x)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 563, "integrand": "2*sqrt(6 - 2*x)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ (8 - 12*x)*exp(-6*x**2 + 8*x - 8) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "exp(-6*x**2 + 8*x - 8) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 564, "integrand": "(8 - 12*x)*exp(-6*x**2 + 8*x - 8)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -exp(9 - x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "exp(9 - x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 565, "integrand": "-exp(9 - x)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -20*sqrt(-10*x - 9) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "4*(-10*x - 9)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 566, "integrand": "-20*sqrt(-10*x - 9)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 8*exp(4*x + 3) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*exp(4*x + 3) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 567, "integrand": "8*exp(4*x + 3)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -6*sin(6*x - 6)*cos(6*x - 6) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "cos(6*x - 6)**2/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 568, "integrand": "-6*sin(6*x - 6)*cos(6*x - 6)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -3*x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(-3*x**3 + 9*x**2 - 18*x + 18)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 569, "integrand": "-3*x**3*exp(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 3*exp(x)*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*exp(x)*sin(x)/2 - 3*exp(x)*cos(x)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 570, "integrand": "3*exp(x)*sin(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -2*atan(2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*x*atan(2*x) + log(4*x**2 + 1)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 571, "integrand": "-2*atan(2*x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ log(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "x*log(x) - x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 572, "integrand": "log(x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 6*sqrt(3*x - 6) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "4*(3*x - 6)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 573, "integrand": "6*sqrt(3*x - 6)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 3*(9*x + 9)**3 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2187*x**4/4 + 2187*x**3 + 6561*x**2/2 + 2187*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 574, "integrand": "3*(9*x + 9)**3", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ (-12*x - 3)*exp(-2*x**2 - x - 8) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*exp(-2*x**2 - x - 8) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 575, "integrand": "(-12*x - 3)*exp(-2*x**2 - x - 8)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 6*sin(6*x + 2)*cos(6*x + 2) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-cos(6*x + 2)**2/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 576, "integrand": "6*sin(6*x + 2)*cos(6*x + 2)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 2*x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(2*x**3 - 6*x**2 + 12*x - 12)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 577, "integrand": "2*x**3*exp(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 8*sqrt(8*x + 5) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*(8*x + 5)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 578, "integrand": "8*sqrt(8*x + 5)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -3*asin(2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*x*asin(2*x) - 3*sqrt(1 - 4*x**2)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 579, "integrand": "-3*asin(2*x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -atan(2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-x*atan(2*x) + log(4*x**2 + 1)/4 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 580, "integrand": "-atan(2*x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -(2*x + 7)**2 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-4*x**3/3 - 14*x**2 - 49*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 581, "integrand": "-(2*x + 7)**2", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -8*sqrt(4*x - 10) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-4*(4*x - 10)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 582, "integrand": "-8*sqrt(4*x - 10)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -2*x**3*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*x**3*sin(x) - 6*x**2*cos(x) + 12*x*sin(x) + 12*cos(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 583, "integrand": "-2*x**3*cos(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -3*log(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*x*log(x) + 3*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 584, "integrand": "-3*log(x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ x**3*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-x**3*cos(x) + 3*x**2*sin(x) + 6*x*cos(x) - 6*sin(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 585, "integrand": "x**3*sin(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ x**3*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "x**3*sin(x) + 3*x**2*cos(x) - 6*x*sin(x) - 6*cos(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 586, "integrand": "x**3*cos(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -3*(10*x - 1)**2 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-100*x**3 + 30*x**2 - 3*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 587, "integrand": "-3*(10*x - 1)**2", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 2*x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(2*x**3 - 6*x**2 + 12*x - 12)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 588, "integrand": "2*x**3*exp(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ exp(x)*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "exp(x)*sin(x)/2 - exp(x)*cos(x)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 589, "integrand": "exp(x)*sin(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -log(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-x*log(x) + x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 590, "integrand": "-log(x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 2*(6*x + 1)**2 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "24*x**3 + 12*x**2 + 2*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 591, "integrand": "2*(6*x + 1)**2", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -9*sqrt(9 - 9*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*(9 - 9*x)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 592, "integrand": "-9*sqrt(9 - 9*x)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 3*asin(2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*x*asin(2*x) + 3*sqrt(1 - 4*x**2)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 593, "integrand": "3*asin(2*x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -18*sqrt(9*x - 7) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-4*(9*x - 7)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 594, "integrand": "-18*sqrt(9*x - 7)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 24*sin(8*x - 2)**2*cos(8*x - 2) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "sin(8*x - 2)**3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 595, "integrand": "24*sin(8*x - 2)**2*cos(8*x - 2)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ (12*x - 18)*exp(-2*x**2 + 6*x - 1) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*exp(-2*x**2 + 6*x - 1) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 596, "integrand": "(12*x - 18)*exp(-2*x**2 + 6*x - 1)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ exp(-x - 3) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-exp(-x - 3) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 597, "integrand": "exp(-x - 3)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 3*(3*x - 1)**2 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "9*x**3 - 9*x**2 + 3*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 598, "integrand": "3*(3*x - 1)**2", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 12*sin(6*x + 1)**4*cos(6*x + 1) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*sin(6*x + 1)**5/5 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 599, "integrand": "12*sin(6*x + 1)**4*cos(6*x + 1)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ (12*x + 21)*exp(-2*x**2 - 7*x - 9) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*exp(-2*x**2 - 7*x - 9) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 600, "integrand": "(12*x + 21)*exp(-2*x**2 - 7*x - 9)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ x**3*sin(3*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "Integral(x**3*sin(3*x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 601, "integrand": "x**3*sin(3*x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -20*sin(10*x - 4)*cos(10*x - 4) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "cos(10*x - 4)**2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 602, "integrand": "-20*sin(10*x - 4)*cos(10*x - 4)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -4*sqrt(-2*x - 1) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "4*(-2*x - 1)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 603, "integrand": "-4*sqrt(-2*x - 1)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -x**3*cos(3*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-Integral(x**3*cos(3*x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 604, "integrand": "-x**3*cos(3*x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -2*x**3*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*x**3*sin(x) - 6*x**2*cos(x) + 12*x*sin(x) + 12*cos(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 605, "integrand": "-2*x**3*cos(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -21*exp(7*x - 8) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*exp(7*x - 8) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 606, "integrand": "-21*exp(7*x - 8)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 3*asin(2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*x*asin(2*x) + 3*sqrt(1 - 4*x**2)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 607, "integrand": "3*asin(2*x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -2*asin(2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*x*asin(2*x) - sqrt(1 - 4*x**2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 608, "integrand": "-2*asin(2*x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -(x + 2)**2 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-x**3/3 - 2*x**2 - 4*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 609, "integrand": "-(x + 2)**2", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 2*sqrt(4 - 2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*(4 - 2*x)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 610, "integrand": "2*sqrt(4 - 2*x)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 10*exp(-5*x - 7) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*exp(-5*x - 7) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 611, "integrand": "10*exp(-5*x - 7)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ (16 - 40*x)*exp(10*x**2 - 8*x - 3) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*exp(10*x**2 - 8*x - 3) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 612, "integrand": "(16 - 40*x)*exp(10*x**2 - 8*x - 3)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ exp(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "exp(x)*sin(x)/2 + exp(x)*cos(x)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 613, "integrand": "exp(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 27*exp(9*x - 2) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*exp(9*x - 2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 614, "integrand": "27*exp(9*x - 2)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -2*x**2*sin(3*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*Integral(x**2*sin(3*x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 615, "integrand": "-2*x**2*sin(3*x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -sqrt(-x - 8) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*(-x - 8)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 616, "integrand": "-sqrt(-x - 8)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -6*exp(3*x + 10) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*exp(3*x + 10) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 617, "integrand": "-6*exp(3*x + 10)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 3*(5*x + 2)**2 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "25*x**3 + 30*x**2 + 12*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 618, "integrand": "3*(5*x + 2)**2", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 3*x**3*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*x**3*cos(x) + 9*x**2*sin(x) + 18*x*cos(x) - 18*sin(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 619, "integrand": "3*x**3*sin(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -15*exp(-5*x - 8) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*exp(-5*x - 8) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 620, "integrand": "-15*exp(-5*x - 8)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -3*x**3*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*x**3*cos(x) - 9*x**2*sin(x) - 18*x*cos(x) + 18*sin(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 621, "integrand": "-3*x**3*sin(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 3*sin(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*sin(x)**2/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 622, "integrand": "3*sin(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -x**3*sin(2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-Integral(x**3*sin(2*x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 623, "integrand": "-x**3*sin(2*x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -9*sin(9*x - 9)*cos(9*x - 9)**3 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "cos(9*x - 9)**4/4 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 624, "integrand": "-9*sin(9*x - 9)*cos(9*x - 9)**3", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ (7*x - 6)**3 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "343*x**4/4 - 294*x**3 + 378*x**2 - 216*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 625, "integrand": "(7*x - 6)**3", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -3*sin(x + 9)*cos(x + 9) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*sin(x + 9)**2/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 626, "integrand": "-3*sin(x + 9)*cos(x + 9)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -2*atan(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*x*atan(x) + log(x**2 + 1) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 627, "integrand": "-2*atan(x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -2*x**2*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(-2*x**2 + 4*x - 4)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 628, "integrand": "-2*x**2*exp(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -3*exp(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*exp(x)*sin(x)/2 - 3*exp(x)*cos(x)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 629, "integrand": "-3*exp(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ (3*x - 9)**2 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*x**3 - 27*x**2 + 81*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 630, "integrand": "(3*x - 9)**2", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -x**2*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(-x**2 + 2*x - 2)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 631, "integrand": "-x**2*exp(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 10*sin(5*x - 2)**2*cos(5*x - 2) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*sin(5*x - 2)**3/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 632, "integrand": "10*sin(5*x - 2)**2*cos(5*x - 2)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 10*sqrt(-5*x - 5) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-4*(-5*x - 5)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 633, "integrand": "10*sqrt(-5*x - 5)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -2*(9*x - 9)**4 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-13122*x**5/5 + 13122*x**4 - 26244*x**3 + 26244*x**2 - 13122*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 634, "integrand": "-2*(9*x - 9)**4", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -20*exp(-10*x - 2) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*exp(-10*x - 2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 635, "integrand": "-20*exp(-10*x - 2)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 2*(x + 6)**2 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*x**3/3 + 12*x**2 + 72*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 636, "integrand": "2*(x + 6)**2", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 3*x**3*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*x**3*cos(x) + 9*x**2*sin(x) + 18*x*cos(x) - 18*sin(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 637, "integrand": "3*x**3*sin(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -2*x**3*cos(2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*Integral(x**3*cos(2*x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 638, "integrand": "-2*x**3*cos(2*x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 7*sin(7*x - 8)**3*cos(7*x - 8) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "sin(7*x - 8)**4/4 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 639, "integrand": "7*sin(7*x - 8)**3*cos(7*x - 8)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -2*x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(-2*x**3 + 6*x**2 - 12*x + 12)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 640, "integrand": "-2*x**3*exp(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -3*sin(3*x + 9)*cos(3*x + 9) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "cos(3*x + 9)**2/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 641, "integrand": "-3*sin(3*x + 9)*cos(3*x + 9)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 16*sin(8*x + 4)*cos(8*x + 4)**2 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*cos(8*x + 4)**3/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 642, "integrand": "16*sin(8*x + 4)*cos(8*x + 4)**2", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ log(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "x*log(x) - x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 643, "integrand": "log(x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(-x**3 + 3*x**2 - 6*x + 6)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 644, "integrand": "-x**3*exp(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 4*sin(2*x + 1)*cos(2*x + 1)**4 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*cos(2*x + 1)**5/5 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 645, "integrand": "4*sin(2*x + 1)*cos(2*x + 1)**4", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 2*exp(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "exp(x)*sin(x) + exp(x)*cos(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 646, "integrand": "2*exp(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -3*x*sin(3*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*Integral(x*sin(3*x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 647, "integrand": "-3*x*sin(3*x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ log(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "x*log(x) - x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 648, "integrand": "log(x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 15*exp(-5*x - 4) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*exp(-5*x - 4) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 649, "integrand": "15*exp(-5*x - 4)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 2*sin(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "sin(x)**2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 650, "integrand": "2*sin(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -sin(x - 1)*cos(x - 1) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-sin(x - 1)**2/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 651, "integrand": "-sin(x - 1)*cos(x - 1)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -7*exp(-7*x - 5) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "exp(-7*x - 5) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 652, "integrand": "-7*exp(-7*x - 5)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -3*atan(2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*x*atan(2*x) + 3*log(4*x**2 + 1)/4 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 653, "integrand": "-3*atan(2*x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 20*sqrt(-10*x - 4) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-4*(-10*x - 4)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 654, "integrand": "20*sqrt(-10*x - 4)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -4*sqrt(-2*x - 8) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "4*(-2*x - 8)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 655, "integrand": "-4*sqrt(-2*x - 8)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -2*exp(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-exp(x)*sin(x) - exp(x)*cos(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 656, "integrand": "-2*exp(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ atan(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "x*atan(x) - log(x**2 + 1)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 657, "integrand": "atan(x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -12*sqrt(-4*x - 1) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*(-4*x - 1)**(3/2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 658, "integrand": "-12*sqrt(-4*x - 1)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -9*exp(9*x + 9) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-exp(9*x + 9) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 659, "integrand": "-9*exp(9*x + 9)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -exp(x)*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-exp(x)*sin(x)/2 + exp(x)*cos(x)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 660, "integrand": "-exp(x)*sin(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 2*(8*x - 4)**2 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "128*x**3/3 - 64*x**2 + 32*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 661, "integrand": "2*(8*x - 4)**2", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -3*sin(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*sin(x)**2/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 662, "integrand": "-3*sin(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -2*exp(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-exp(x)*sin(x) - exp(x)*cos(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 663, "integrand": "-2*exp(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -3*x**3*cos(3*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*Integral(x**3*cos(3*x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 664, "integrand": "-3*x**3*cos(3*x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -(9*x - 9)**4 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-6561*x**5/5 + 6561*x**4 - 13122*x**3 + 13122*x**2 - 6561*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 665, "integrand": "-(9*x - 9)**4", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -2*(5*x - 3)**4 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-250*x**5 + 750*x**4 - 900*x**3 + 540*x**2 - 162*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 666, "integrand": "-2*(5*x - 3)**4", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ x*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(x - 1)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 667, "integrand": "x*exp(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -15*sin(5*x - 6)**3*cos(5*x - 6) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*sin(5*x - 6)**4/4 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 668, "integrand": "-15*sin(5*x - 6)**3*cos(5*x - 6)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -x**3*sin(2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-Integral(x**3*sin(2*x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 669, "integrand": "-x**3*sin(2*x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -3*asin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*x*asin(x) - 3*sqrt(1 - x**2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 670, "integrand": "-3*asin(x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -14*sin(7*x - 5)*cos(7*x - 5)**4 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*cos(7*x - 5)**5/5 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 671, "integrand": "-14*sin(7*x - 5)*cos(7*x - 5)**4", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -exp(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-exp(x)*sin(x)/2 - exp(x)*cos(x)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 672, "integrand": "-exp(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ x*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(x - 1)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 673, "integrand": "x*exp(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -6*sqrt(2*x - 3) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*(2*x - 3)**(3/2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 674, "integrand": "-6*sqrt(2*x - 3)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -8*sqrt(8*x + 2) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*(8*x + 2)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 675, "integrand": "-8*sqrt(8*x + 2)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -asin(2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-x*asin(2*x) - sqrt(1 - 4*x**2)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 676, "integrand": "-asin(2*x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -3*atan(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*x*atan(x) + 3*log(x**2 + 1)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 677, "integrand": "-3*atan(x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 16*exp(8*x - 2) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*exp(8*x - 2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 678, "integrand": "16*exp(8*x - 2)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -18*sqrt(6*x - 7) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*(6*x - 7)**(3/2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 679, "integrand": "-18*sqrt(6*x - 7)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -2*x*sin(3*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*Integral(x*sin(3*x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 680, "integrand": "-2*x*sin(3*x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -3*x**2*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(-3*x**2 + 6*x - 6)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 681, "integrand": "-3*x**2*exp(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(-x**3 + 3*x**2 - 6*x + 6)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 682, "integrand": "-x**3*exp(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ (x - 9)**4 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "x**5/5 - 9*x**4 + 162*x**3 - 1458*x**2 + 6561*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 683, "integrand": "(x - 9)**4", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 2*asin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*x*asin(x) + 2*sqrt(1 - x**2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 684, "integrand": "2*asin(x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -3*x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(-3*x**3 + 9*x**2 - 18*x + 18)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 685, "integrand": "-3*x**3*exp(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(-x**3 + 3*x**2 - 6*x + 6)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 686, "integrand": "-x**3*exp(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ (-40*x - 12)*exp(10*x**2 + 6*x + 2) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*exp(10*x**2 + 6*x + 2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 687, "integrand": "(-40*x - 12)*exp(10*x**2 + 6*x + 2)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -3*atan(3*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*x*atan(3*x) + log(9*x**2 + 1)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 688, "integrand": "-3*atan(3*x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 16*exp(9 - 8*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*exp(9 - 8*x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 689, "integrand": "16*exp(9 - 8*x)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 6*exp(2*x - 3) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*exp(2*x - 3) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 690, "integrand": "6*exp(2*x - 3)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 8*sin(8*x + 4)**3*cos(8*x + 4) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "sin(8*x + 4)**4/4 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 691, "integrand": "8*sin(8*x + 4)**3*cos(8*x + 4)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ (2 - 2*x)*exp(x**2 - 2*x + 3) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-exp(x**2 - 2*x + 3) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 692, "integrand": "(2 - 2*x)*exp(x**2 - 2*x + 3)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 6*sin(2*x - 1)**3*cos(2*x - 1) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*sin(2*x - 1)**4/4 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 693, "integrand": "6*sin(2*x - 1)**3*cos(2*x - 1)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 3*log(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*x*log(x) - 3*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 694, "integrand": "3*log(x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -3*(x + 4)**3 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*x**4/4 - 12*x**3 - 72*x**2 - 192*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 695, "integrand": "-3*(x + 4)**3", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 3*exp(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*exp(x)*sin(x)/2 + 3*exp(x)*cos(x)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 696, "integrand": "3*exp(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 3*sqrt(1 - 3*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*(1 - 3*x)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 697, "integrand": "3*sqrt(1 - 3*x)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ x**2*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(x**2 - 2*x + 2)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 698, "integrand": "x**2*exp(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -8*sqrt(-8*x - 2) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*(-8*x - 2)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 699, "integrand": "-8*sqrt(-8*x - 2)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -20*sin(10*x + 7)**2*cos(10*x + 7) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*sin(10*x + 7)**3/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 700, "integrand": "-20*sin(10*x + 7)**2*cos(10*x + 7)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -7*exp(7*x - 6) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-exp(7*x - 6) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 701, "integrand": "-7*exp(7*x - 6)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -atan(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-x*atan(x) + log(x**2 + 1)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 702, "integrand": "-atan(x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -2*sqrt(x - 9) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-4*(x - 9)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 703, "integrand": "-2*sqrt(x - 9)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 30*sin(10*x - 4)*cos(10*x - 4)**2 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-cos(10*x - 4)**3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 704, "integrand": "30*sin(10*x - 4)*cos(10*x - 4)**2", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -2*asin(2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*x*asin(2*x) - sqrt(1 - 4*x**2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 705, "integrand": "-2*asin(2*x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -2*(5*x + 7)**3 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-125*x**4/2 - 350*x**3 - 735*x**2 - 686*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 706, "integrand": "-2*(5*x + 7)**3", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -sin(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-sin(x)**2/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 707, "integrand": "-sin(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ log(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "x*log(x) - x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 708, "integrand": "log(x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -2*exp(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-exp(x)*sin(x) - exp(x)*cos(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 709, "integrand": "-2*exp(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -3*x**2*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*Integral(x**2*sin(x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 710, "integrand": "-3*x**2*sin(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 3*exp(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*exp(x)*sin(x)/2 + 3*exp(x)*cos(x)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 711, "integrand": "3*exp(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 3*sqrt(3*x + 2) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*(3*x + 2)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 712, "integrand": "3*sqrt(3*x + 2)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 2*exp(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "exp(x)*sin(x) + exp(x)*cos(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 713, "integrand": "2*exp(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 4*sin(2*x + 9)*cos(2*x + 9)**2 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*cos(2*x + 9)**3/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 714, "integrand": "4*sin(2*x + 9)*cos(2*x + 9)**2", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 16*sin(8*x - 7)*cos(8*x - 7)**2 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*cos(8*x - 7)**3/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 715, "integrand": "16*sin(8*x - 7)*cos(8*x - 7)**2", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -3*atan(2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*x*atan(2*x) + 3*log(4*x**2 + 1)/4 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 716, "integrand": "-3*atan(2*x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 2*(6*x - 4)**2 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "24*x**3 - 48*x**2 + 32*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 717, "integrand": "2*(6*x - 4)**2", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -12*sqrt(4*x + 7) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*(4*x + 7)**(3/2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 718, "integrand": "-12*sqrt(4*x + 7)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 30*sqrt(-10*x - 2) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*(-10*x - 2)**(3/2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 719, "integrand": "30*sqrt(-10*x - 2)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ x**3*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "x**3*sin(x) + 3*x**2*cos(x) - 6*x*sin(x) - 6*cos(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 720, "integrand": "x**3*cos(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 3*x*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(3*x - 3)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 721, "integrand": "3*x*exp(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -3*x**3*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*x**3*sin(x) - 9*x**2*cos(x) + 18*x*sin(x) + 18*cos(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 722, "integrand": "-3*x**3*cos(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ (7*x + 5)**2 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "49*x**3/3 + 35*x**2 + 25*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 723, "integrand": "(7*x + 5)**2", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 2*asin(2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*x*asin(2*x) + sqrt(1 - 4*x**2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 724, "integrand": "2*asin(2*x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -3*exp(x)*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*exp(x)*sin(x)/2 + 3*exp(x)*cos(x)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 725, "integrand": "-3*exp(x)*sin(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 3*(5*x - 4)**2 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "25*x**3 - 60*x**2 + 48*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 726, "integrand": "3*(5*x - 4)**2", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 3*(9*x + 6)**4 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "19683*x**5/5 + 13122*x**4 + 17496*x**3 + 11664*x**2 + 3888*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 727, "integrand": "3*(9*x + 6)**4", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -12*sin(6*x + 10)**2*cos(6*x + 10) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*sin(6*x + 10)**3/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 728, "integrand": "-12*sin(6*x + 10)**2*cos(6*x + 10)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 2*x**3*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*x**3*sin(x) + 6*x**2*cos(x) - 12*x*sin(x) - 12*cos(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 729, "integrand": "2*x**3*cos(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -2*(x + 4)**3 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-x**4/2 - 8*x**3 - 48*x**2 - 128*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 730, "integrand": "-2*(x + 4)**3", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -27*sqrt(-9*x - 8) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*(-9*x - 8)**(3/2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 731, "integrand": "-27*sqrt(-9*x - 8)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 2*atan(2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*x*atan(2*x) - log(4*x**2 + 1)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 732, "integrand": "2*atan(2*x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 21*sin(7*x - 1)**2*cos(7*x - 1) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "sin(7*x - 1)**3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 733, "integrand": "21*sin(7*x - 1)**2*cos(7*x - 1)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 3*sin(x + 7)*cos(x + 7) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*sin(x + 7)**2/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 734, "integrand": "3*sin(x + 7)*cos(x + 7)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -30*sqrt(-10*x - 6) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*(-10*x - 6)**(3/2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 735, "integrand": "-30*sqrt(-10*x - 6)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -2*(6*x - 4)**4 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2592*x**5/5 + 1728*x**4 - 2304*x**3 + 1536*x**2 - 512*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 736, "integrand": "-2*(6*x - 4)**4", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -x**2*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-Integral(x**2*cos(x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 737, "integrand": "-x**2*cos(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 16*sqrt(8*x + 7) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "4*(8*x + 7)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 738, "integrand": "16*sqrt(8*x + 7)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 12*sqrt(6*x - 2) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "4*(6*x - 2)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 739, "integrand": "12*sqrt(6*x - 2)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ (32*x + 10)*exp(-8*x**2 - 5*x - 5) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*exp(-8*x**2 - 5*x - 5) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 740, "integrand": "(32*x + 10)*exp(-8*x**2 - 5*x - 5)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 2*x*sin(2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*Integral(x*sin(2*x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 741, "integrand": "2*x*sin(2*x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 10*sin(5*x - 6)*cos(5*x - 6)**4 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*cos(5*x - 6)**5/5 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 742, "integrand": "10*sin(5*x - 6)*cos(5*x - 6)**4", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -x**2*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-Integral(x**2*cos(x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 743, "integrand": "-x**2*cos(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 2*sin(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "sin(x)**2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 744, "integrand": "2*sin(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -2*log(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*x*log(x) + 2*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 745, "integrand": "-2*log(x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 3*x**2*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(3*x**2 - 6*x + 6)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 746, "integrand": "3*x**2*exp(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -21*sin(7*x - 9)*cos(7*x - 9)**3 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*cos(7*x - 9)**4/4 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 747, "integrand": "-21*sin(7*x - 9)*cos(7*x - 9)**3", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ (32*x + 10)*exp(8*x**2 + 5*x + 5) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*exp(8*x**2 + 5*x + 5) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 748, "integrand": "(32*x + 10)*exp(8*x**2 + 5*x + 5)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -3*exp(3*x - 9) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-exp(3*x - 9) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 749, "integrand": "-3*exp(3*x - 9)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 2*x**3*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*Integral(x**3*cos(x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 750, "integrand": "2*x**3*cos(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 3*exp(x)*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*exp(x)*sin(x)/2 - 3*exp(x)*cos(x)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 751, "integrand": "3*exp(x)*sin(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 2*asin(2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*x*asin(2*x) + sqrt(1 - 4*x**2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 752, "integrand": "2*asin(2*x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -5*sin(5*x - 4)*cos(5*x - 4)**3 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "cos(5*x - 4)**4/4 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 753, "integrand": "-5*sin(5*x - 4)*cos(5*x - 4)**3", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -2*x**3*cos(2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*Integral(x**3*cos(2*x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 754, "integrand": "-2*x**3*cos(2*x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -2*x**3*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*x**3*cos(x) - 6*x**2*sin(x) - 12*x*cos(x) + 12*sin(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 755, "integrand": "-2*x**3*sin(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -12*sin(4*x + 8)*cos(4*x + 8) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*cos(4*x + 8)**2/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 756, "integrand": "-12*sin(4*x + 8)*cos(4*x + 8)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ exp(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "exp(x)*sin(x)/2 + exp(x)*cos(x)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 757, "integrand": "exp(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ (-54*x - 3)*exp(-9*x**2 - x - 4) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*exp(-9*x**2 - x - 4) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 758, "integrand": "(-54*x - 3)*exp(-9*x**2 - x - 4)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 3*(2*x + 8)**3 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "6*x**4 + 96*x**3 + 576*x**2 + 1536*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 759, "integrand": "3*(2*x + 8)**3", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -3*x**2*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*Integral(x**2*sin(x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 760, "integrand": "-3*x**2*sin(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 3*(9*x + 7)**2 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "81*x**3 + 189*x**2 + 147*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 761, "integrand": "3*(9*x + 7)**2", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -2*sin(x - 4)**2*cos(x - 4) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*sin(x - 4)**3/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 762, "integrand": "-2*sin(x - 4)**2*cos(x - 4)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 24*sin(8*x - 10)*cos(8*x - 10)**3 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*cos(8*x - 10)**4/4 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 763, "integrand": "24*sin(8*x - 10)*cos(8*x - 10)**3", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -2*x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(-2*x**3 + 6*x**2 - 12*x + 12)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 764, "integrand": "-2*x**3*exp(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 3*log(x**2) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*x*log(x**2) - 6*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 765, "integrand": "3*log(x**2)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 2*atan(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*x*atan(x) - log(x**2 + 1) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 766, "integrand": "2*atan(x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 2*(3*x - 10)**4 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "162*x**5/5 - 540*x**4 + 3600*x**3 - 12000*x**2 + 20000*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 767, "integrand": "2*(3*x - 10)**4", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 5*exp(5*x + 7) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "exp(5*x + 7) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 768, "integrand": "5*exp(5*x + 7)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -3*(x + 4)**2 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-x**3 - 12*x**2 - 48*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 769, "integrand": "-3*(x + 4)**2", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -(6*x + 5)**2 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-12*x**3 - 30*x**2 - 25*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 770, "integrand": "-(6*x + 5)**2", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 2*x**3*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*x**3*sin(x) + 6*x**2*cos(x) - 12*x*sin(x) - 12*cos(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 771, "integrand": "2*x**3*cos(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 2*x*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*Integral(x*cos(x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 772, "integrand": "2*x*cos(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -2*x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(-2*x**3 + 6*x**2 - 12*x + 12)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 773, "integrand": "-2*x**3*exp(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 16*sqrt(1 - 8*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-4*(1 - 8*x)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 774, "integrand": "16*sqrt(1 - 8*x)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 12*sqrt(-4*x - 10) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*(-4*x - 10)**(3/2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 775, "integrand": "12*sqrt(-4*x - 10)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -18*sin(9*x - 1)*cos(9*x - 1)**4 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*cos(9*x - 1)**5/5 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 776, "integrand": "-18*sin(9*x - 1)*cos(9*x - 1)**4", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -3*log(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*x*log(x) + 3*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 777, "integrand": "-3*log(x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 12*sqrt(4*x + 5) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*(4*x + 5)**(3/2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 778, "integrand": "12*sqrt(4*x + 5)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ x**2*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "Integral(x**2*sin(x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 779, "integrand": "x**2*sin(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -3*x**3*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*x**3*cos(x) - 9*x**2*sin(x) - 18*x*cos(x) + 18*sin(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 780, "integrand": "-3*x**3*sin(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -3*log(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*x*log(x) + 3*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 781, "integrand": "-3*log(x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ (18*x + 3)*exp(3*x**2 + x + 4) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*exp(3*x**2 + x + 4) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 782, "integrand": "(18*x + 3)*exp(3*x**2 + x + 4)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 3*atan(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*x*atan(x) - 3*log(x**2 + 1)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 783, "integrand": "3*atan(x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ x**2*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "Integral(x**2*sin(x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 784, "integrand": "x**2*sin(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -asin(3*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-x*asin(3*x) - sqrt(1 - 9*x**2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 785, "integrand": "-asin(3*x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -30*sqrt(10*x + 6) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*(10*x + 6)**(3/2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 786, "integrand": "-30*sqrt(10*x + 6)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 30*sqrt(10*x + 5) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*(10*x + 5)**(3/2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 787, "integrand": "30*sqrt(10*x + 5)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 3*(5*x - 5)**4 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "375*x**5 - 1875*x**4 + 3750*x**3 - 3750*x**2 + 1875*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 788, "integrand": "3*(5*x - 5)**4", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 3*sqrt(x + 4) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*(x + 4)**(3/2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 789, "integrand": "3*sqrt(x + 4)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 10*exp(-10*x - 2) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-exp(-10*x - 2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 790, "integrand": "10*exp(-10*x - 2)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -x**2*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-Integral(x**2*cos(x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 791, "integrand": "-x**2*cos(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 3*log(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*x*log(x) - 3*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 792, "integrand": "3*log(x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -3*x**2*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(-3*x**2 + 6*x - 6)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 793, "integrand": "-3*x**2*exp(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -2*sin(2*x - 7)**2*cos(2*x - 7) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-sin(2*x - 7)**3/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 794, "integrand": "-2*sin(2*x - 7)**2*cos(2*x - 7)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 3*x*cos(2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*Integral(x*cos(2*x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 795, "integrand": "3*x*cos(2*x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -x**3*cos(2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-Integral(x**3*cos(2*x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 796, "integrand": "-x**3*cos(2*x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -x**2*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-Integral(x**2*cos(x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 797, "integrand": "-x**2*cos(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -18*sqrt(-9*x - 8) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "4*(-9*x - 8)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 798, "integrand": "-18*sqrt(-9*x - 8)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -3*x*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*Integral(x*cos(x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 799, "integrand": "-3*x*cos(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(-x**3 + 3*x**2 - 6*x + 6)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 800, "integrand": "-x**3*exp(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ (-6*x - 5)*exp(-3*x**2 - 5*x - 7) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "exp(-3*x**2 - 5*x - 7) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 801, "integrand": "(-6*x - 5)*exp(-3*x**2 - 5*x - 7)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 27*exp(-9*x - 6) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*exp(-9*x - 6) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 802, "integrand": "27*exp(-9*x - 6)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -(9*x + 3)**2 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-27*x**3 - 27*x**2 - 9*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 803, "integrand": "-(9*x + 3)**2", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -(3*x - 3)**2 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*x**3 + 9*x**2 - 9*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 804, "integrand": "-(3*x - 3)**2", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -4*sin(2*x - 10)**3*cos(2*x - 10) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-sin(2*x - 10)**4/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 805, "integrand": "-4*sin(2*x - 10)**3*cos(2*x - 10)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -exp(x)*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-exp(x)*sin(x)/2 + exp(x)*cos(x)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 806, "integrand": "-exp(x)*sin(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 2*(5*x + 6)**2 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "50*x**3/3 + 60*x**2 + 72*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 807, "integrand": "2*(5*x + 6)**2", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -exp(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-exp(x)*sin(x)/2 - exp(x)*cos(x)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 808, "integrand": "-exp(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 3*x**2*sin(2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*Integral(x**2*sin(2*x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 809, "integrand": "3*x**2*sin(2*x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -2*exp(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-exp(x)*sin(x) - exp(x)*cos(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 810, "integrand": "-2*exp(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -6*sin(2*x - 2)*cos(2*x - 2)**4 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*cos(2*x - 2)**5/5 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 811, "integrand": "-6*sin(2*x - 2)*cos(2*x - 2)**4", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -3*x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(-3*x**3 + 9*x**2 - 18*x + 18)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 812, "integrand": "-3*x**3*exp(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -18*sqrt(9*x + 2) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-4*(9*x + 2)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 813, "integrand": "-18*sqrt(9*x + 2)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -30*sqrt(10*x + 5) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*(10*x + 5)**(3/2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 814, "integrand": "-30*sqrt(10*x + 5)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 2*x**3*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*x**3*sin(x) + 6*x**2*cos(x) - 12*x*sin(x) - 12*cos(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 815, "integrand": "2*x**3*cos(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 2*x**2*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(2*x**2 - 4*x + 4)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 816, "integrand": "2*x**2*exp(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 3*x*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(3*x - 3)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 817, "integrand": "3*x*exp(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -27*sqrt(9*x - 9) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*(9*x - 9)**(3/2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 818, "integrand": "-27*sqrt(9*x - 9)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ sin(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "sin(x)**2/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 819, "integrand": "sin(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ x**3*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "Integral(x**3*cos(x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 820, "integrand": "x**3*cos(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -3*x**3*cos(2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*Integral(x**3*cos(2*x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 821, "integrand": "-3*x**3*cos(2*x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ log(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "x*log(x) - x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 822, "integrand": "log(x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 15*sin(5*x + 8)*cos(5*x + 8)**2 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-cos(5*x + 8)**3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 823, "integrand": "15*sin(5*x + 8)*cos(5*x + 8)**2", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 2*x**3*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*x**3*cos(x) + 6*x**2*sin(x) + 12*x*cos(x) - 12*sin(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 824, "integrand": "2*x**3*sin(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -2*sin(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-sin(x)**2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 825, "integrand": "-2*sin(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 12*sin(4*x - 4)*cos(4*x - 4) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*cos(4*x - 4)**2/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 826, "integrand": "12*sin(4*x - 4)*cos(4*x - 4)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -8*sin(8*x + 3)*cos(8*x + 3) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-sin(8*x + 3)**2/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 827, "integrand": "-8*sin(8*x + 3)*cos(8*x + 3)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -12*sqrt(6*x - 10) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-4*(6*x - 10)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 828, "integrand": "-12*sqrt(6*x - 10)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -asin(3*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-x*asin(3*x) - sqrt(1 - 9*x**2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 829, "integrand": "-asin(3*x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 2*x*sin(2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*Integral(x*sin(2*x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 830, "integrand": "2*x*sin(2*x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 18*sqrt(6 - 6*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*(6 - 6*x)**(3/2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 831, "integrand": "18*sqrt(6 - 6*x)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ x**2*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(x**2 - 2*x + 2)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 832, "integrand": "x**2*exp(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -3*x**2*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*Integral(x**2*cos(x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 833, "integrand": "-3*x**2*cos(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ (6*x - 6)*exp(-x**2 + 2*x + 4) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*exp(-x**2 + 2*x + 4) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 834, "integrand": "(6*x - 6)*exp(-x**2 + 2*x + 4)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 24*sqrt(8*x - 10) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*(8*x - 10)**(3/2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 835, "integrand": "24*sqrt(8*x - 10)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -2*exp(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-exp(x)*sin(x) - exp(x)*cos(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 836, "integrand": "-2*exp(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 2*(3*x + 1)**2 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "6*x**3 + 6*x**2 + 2*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 837, "integrand": "2*(3*x + 1)**2", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 3*x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(3*x**3 - 9*x**2 + 18*x - 18)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 838, "integrand": "3*x**3*exp(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ (18*x - 9)*exp(9*x**2 - 9*x - 1) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "exp(9*x**2 - 9*x - 1) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 839, "integrand": "(18*x - 9)*exp(9*x**2 - 9*x - 1)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -3*x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(-3*x**3 + 9*x**2 - 18*x + 18)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 840, "integrand": "-3*x**3*exp(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -x**2*cos(3*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-Integral(x**2*cos(3*x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 841, "integrand": "-x**2*cos(3*x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 2*sin(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "sin(x)**2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 842, "integrand": "2*sin(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -asin(2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-x*asin(2*x) - sqrt(1 - 4*x**2)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 843, "integrand": "-asin(2*x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 8*sqrt(4*x - 3) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "4*(4*x - 3)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 844, "integrand": "8*sqrt(4*x - 3)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -18*sin(6*x + 8)**3*cos(6*x + 8) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*sin(6*x + 8)**4/4 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 845, "integrand": "-18*sin(6*x + 8)**3*cos(6*x + 8)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 2*(8*x - 7)**4 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "8192*x**5/5 - 7168*x**4 + 12544*x**3 - 10976*x**2 + 4802*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 846, "integrand": "2*(8*x - 7)**4", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 27*exp(9*x + 4) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*exp(9*x + 4) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 847, "integrand": "27*exp(9*x + 4)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -(5*x + 5)**3 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-125*x**4/4 - 125*x**3 - 375*x**2/2 - 125*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 848, "integrand": "-(5*x + 5)**3", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(x**3 - 3*x**2 + 6*x - 6)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 849, "integrand": "x**3*exp(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 8*sqrt(8*x - 4) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*(8*x - 4)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 850, "integrand": "8*sqrt(8*x - 4)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 2*x*cos(2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*Integral(x*cos(2*x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 851, "integrand": "2*x*cos(2*x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -3*sin(x - 10)*cos(x - 10) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*sin(x - 10)**2/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 852, "integrand": "-3*sin(x - 10)*cos(x - 10)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ (-36*x - 8)*exp(9*x**2 + 4*x - 5) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*exp(9*x**2 + 4*x - 5) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 853, "integrand": "(-36*x - 8)*exp(9*x**2 + 4*x - 5)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -12*sqrt(6*x - 2) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-4*(6*x - 2)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 854, "integrand": "-12*sqrt(6*x - 2)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -(5*x - 7)**3 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-125*x**4/4 + 175*x**3 - 735*x**2/2 + 343*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 855, "integrand": "-(5*x - 7)**3", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 24*sin(8*x + 1)*cos(8*x + 1)**2 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-cos(8*x + 1)**3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 856, "integrand": "24*sin(8*x + 1)*cos(8*x + 1)**2", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 3*sin(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*sin(x)**2/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 857, "integrand": "3*sin(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 3*x**3*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*x**3*cos(x) + 9*x**2*sin(x) + 18*x*cos(x) - 18*sin(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 858, "integrand": "3*x**3*sin(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -21*sin(7*x - 5)**3*cos(7*x - 5) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*sin(7*x - 5)**4/4 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 859, "integrand": "-21*sin(7*x - 5)**3*cos(7*x - 5)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 3*x**3*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*x**3*cos(x) + 9*x**2*sin(x) + 18*x*cos(x) - 18*sin(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 860, "integrand": "3*x**3*sin(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ (5*x + 8)**4 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "125*x**5 + 1000*x**4 + 3200*x**3 + 5120*x**2 + 4096*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 861, "integrand": "(5*x + 8)**4", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ (9 - 14*x)*exp(7*x**2 - 9*x + 8) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-exp(7*x**2 - 9*x + 8) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 862, "integrand": "(9 - 14*x)*exp(7*x**2 - 9*x + 8)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ (6 - 12*x)*exp(3*x**2 - 3*x + 9) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*exp(3*x**2 - 3*x + 9) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 863, "integrand": "(6 - 12*x)*exp(3*x**2 - 3*x + 9)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -2*(2*x - 5)**3 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-4*x**4 + 40*x**3 - 150*x**2 + 250*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 864, "integrand": "-2*(2*x - 5)**3", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -15*exp(-5*x - 3) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*exp(-5*x - 3) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 865, "integrand": "-15*exp(-5*x - 3)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 10*exp(5*x - 8) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*exp(5*x - 8) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 866, "integrand": "10*exp(5*x - 8)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -8*sqrt(4*x + 10) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-4*(4*x + 10)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 867, "integrand": "-8*sqrt(4*x + 10)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -3*x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(-3*x**3 + 9*x**2 - 18*x + 18)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 868, "integrand": "-3*x**3*exp(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -9*sin(9*x + 8)**2*cos(9*x + 8) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-sin(9*x + 8)**3/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 869, "integrand": "-9*sin(9*x + 8)**2*cos(9*x + 8)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 3*x*cos(2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*Integral(x*cos(2*x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 870, "integrand": "3*x*cos(2*x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 2*(10*x - 6)**3 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "500*x**4 - 1200*x**3 + 1080*x**2 - 432*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 871, "integrand": "2*(10*x - 6)**3", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -(10*x - 3)**2 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-100*x**3/3 + 30*x**2 - 9*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 872, "integrand": "-(10*x - 3)**2", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -2*sqrt(-x - 7) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "4*(-x - 7)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 873, "integrand": "-2*sqrt(-x - 7)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 9*exp(-3*x - 6) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*exp(-3*x - 6) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 874, "integrand": "9*exp(-3*x - 6)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -exp(x)*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-exp(x)*sin(x)/2 + exp(x)*cos(x)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 875, "integrand": "-exp(x)*sin(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ sin(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "sin(x)**2/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 876, "integrand": "sin(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ (-18*x - 3)*exp(9*x**2 + 3*x + 9) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-exp(9*x**2 + 3*x + 9) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 877, "integrand": "(-18*x - 3)*exp(9*x**2 + 3*x + 9)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 2*x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(2*x**3 - 6*x**2 + 12*x - 12)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 878, "integrand": "2*x**3*exp(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ x**3*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "x**3*sin(x) + 3*x**2*cos(x) - 6*x*sin(x) - 6*cos(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 879, "integrand": "x**3*cos(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -(4*x + 4)**4 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-256*x**5/5 - 256*x**4 - 512*x**3 - 512*x**2 - 256*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 880, "integrand": "-(4*x + 4)**4", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 2*sin(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "sin(x)**2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 881, "integrand": "2*sin(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -3*x**2*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(-3*x**2 + 6*x - 6)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 882, "integrand": "-3*x**2*exp(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -2*x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(-2*x**3 + 6*x**2 - 12*x + 12)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 883, "integrand": "-2*x**3*exp(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ (-40*x - 18)*exp(10*x**2 + 9*x + 10) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*exp(10*x**2 + 9*x + 10) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 884, "integrand": "(-40*x - 18)*exp(10*x**2 + 9*x + 10)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 8*exp(4*x - 7) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*exp(4*x - 7) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 885, "integrand": "8*exp(4*x - 7)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 2*log(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*x*log(x) - 2*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 886, "integrand": "2*log(x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 6*sqrt(-2*x - 10) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*(-2*x - 10)**(3/2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 887, "integrand": "6*sqrt(-2*x - 10)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -3*x**3*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*x**3*sin(x) - 9*x**2*cos(x) + 18*x*sin(x) + 18*cos(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 888, "integrand": "-3*x**3*cos(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -3*sin(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*sin(x)**2/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 889, "integrand": "-3*sin(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -3*x**3*cos(3*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*Integral(x**3*cos(3*x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 890, "integrand": "-3*x**3*cos(3*x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 3*x**3*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*Integral(x**3*cos(x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 891, "integrand": "3*x**3*cos(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 5*sin(5*x + 6)**3*cos(5*x + 6) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "sin(5*x + 6)**4/4 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 892, "integrand": "5*sin(5*x + 6)**3*cos(5*x + 6)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -exp(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-exp(x)*sin(x)/2 - exp(x)*cos(x)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 893, "integrand": "-exp(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 2*sqrt(x + 2) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "4*(x + 2)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 894, "integrand": "2*sqrt(x + 2)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -x**3*sin(3*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-Integral(x**3*sin(3*x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 895, "integrand": "-x**3*sin(3*x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 18*sin(6*x + 2)*cos(6*x + 2) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*cos(6*x + 2)**2/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 896, "integrand": "18*sin(6*x + 2)*cos(6*x + 2)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 2*x**3*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*x**3*cos(x) + 6*x**2*sin(x) + 12*x*cos(x) - 12*sin(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 897, "integrand": "2*x**3*sin(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 3*log(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*x*log(x) - 3*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 898, "integrand": "3*log(x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -3*atan(3*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*x*atan(3*x) + log(9*x**2 + 1)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 899, "integrand": "-3*atan(3*x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -2*x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(-2*x**3 + 6*x**2 - 12*x + 12)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 900, "integrand": "-2*x**3*exp(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -2*x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(-2*x**3 + 6*x**2 - 12*x + 12)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 901, "integrand": "-2*x**3*exp(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 3*(x - 6)**4 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*x**5/5 - 18*x**4 + 216*x**3 - 1296*x**2 + 3888*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 902, "integrand": "3*(x - 6)**4", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 6*sin(3*x - 8)**4*cos(3*x - 8) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*sin(3*x - 8)**5/5 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 903, "integrand": "6*sin(3*x - 8)**4*cos(3*x - 8)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ (8*x - 5)**2 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "64*x**3/3 - 40*x**2 + 25*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 904, "integrand": "(8*x - 5)**2", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 18*sqrt(3 - 9*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-4*(3 - 9*x)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 905, "integrand": "18*sqrt(3 - 9*x)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(-x**3 + 3*x**2 - 6*x + 6)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 906, "integrand": "-x**3*exp(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -2*atan(2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*x*atan(2*x) + log(4*x**2 + 1)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 907, "integrand": "-2*atan(2*x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 8*sqrt(8*x + 6) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*(8*x + 6)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 908, "integrand": "8*sqrt(8*x + 6)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -2*exp(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-exp(x)*sin(x) - exp(x)*cos(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 909, "integrand": "-2*exp(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ (8*x + 4)**2 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "64*x**3/3 + 32*x**2 + 16*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 910, "integrand": "(8*x + 4)**2", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -(5*x + 7)**2 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-25*x**3/3 - 35*x**2 - 49*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 911, "integrand": "-(5*x + 7)**2", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 27*sqrt(9*x - 5) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*(9*x - 5)**(3/2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 912, "integrand": "27*sqrt(9*x - 5)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ (-12*x - 12)*exp(-3*x**2 - 6*x + 9) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*exp(-3*x**2 - 6*x + 9) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 913, "integrand": "(-12*x - 12)*exp(-3*x**2 - 6*x + 9)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ (12*x + 15)*exp(-2*x**2 - 5*x - 8) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*exp(-2*x**2 - 5*x - 8) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 914, "integrand": "(12*x + 15)*exp(-2*x**2 - 5*x - 8)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -7*sin(7*x - 4)*cos(7*x - 4)**4 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "cos(7*x - 4)**5/5 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 915, "integrand": "-7*sin(7*x - 4)*cos(7*x - 4)**4", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ log(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "x*log(x) - x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 916, "integrand": "log(x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -8*sin(4*x - 9)*cos(4*x - 9) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "cos(4*x - 9)**2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 917, "integrand": "-8*sin(4*x - 9)*cos(4*x - 9)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 18*sin(9*x + 5)**4*cos(9*x + 5) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*sin(9*x + 5)**5/5 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 918, "integrand": "18*sin(9*x + 5)**4*cos(9*x + 5)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 18*exp(-9*x - 3) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*exp(-9*x - 3) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 919, "integrand": "18*exp(-9*x - 3)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 2*asin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*x*asin(x) + 2*sqrt(1 - x**2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 920, "integrand": "2*asin(x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 3*x**3*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*x**3*cos(x) + 9*x**2*sin(x) + 18*x*cos(x) - 18*sin(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 921, "integrand": "3*x**3*sin(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 3*sin(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*sin(x)**2/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 922, "integrand": "3*sin(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 5*sqrt(-5*x - 7) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*(-5*x - 7)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 923, "integrand": "5*sqrt(-5*x - 7)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -3*(6*x - 8)**3 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-162*x**4 + 864*x**3 - 1728*x**2 + 1536*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 924, "integrand": "-3*(6*x - 8)**3", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 3*x**3*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*x**3*sin(x) + 9*x**2*cos(x) - 18*x*sin(x) - 18*cos(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 925, "integrand": "3*x**3*cos(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 3*sin(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*sin(x)**2/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 926, "integrand": "3*sin(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -14*sin(7*x + 4)*cos(7*x + 4)**4 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*cos(7*x + 4)**5/5 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 927, "integrand": "-14*sin(7*x + 4)*cos(7*x + 4)**4", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 3*exp(x)*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*exp(x)*sin(x)/2 - 3*exp(x)*cos(x)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 928, "integrand": "3*exp(x)*sin(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ log(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "x*log(x) - x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 929, "integrand": "log(x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 7*exp(-7*x - 10) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-exp(-7*x - 10) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 930, "integrand": "7*exp(-7*x - 10)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 5*sqrt(-5*x - 10) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*(-5*x - 10)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 931, "integrand": "5*sqrt(-5*x - 10)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -2*x**3*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*x**3*sin(x) - 6*x**2*cos(x) + 12*x*sin(x) + 12*cos(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 932, "integrand": "-2*x**3*cos(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 6*sin(2*x + 9)*cos(2*x + 9) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*sin(2*x + 9)**2/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 933, "integrand": "6*sin(2*x + 9)*cos(2*x + 9)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -sin(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-sin(x)**2/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 934, "integrand": "-sin(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ (20*x - 4)*exp(-10*x**2 + 4*x - 4) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-exp(-10*x**2 + 4*x - 4) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 935, "integrand": "(20*x - 4)*exp(-10*x**2 + 4*x - 4)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -x**3*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-x**3*sin(x) - 3*x**2*cos(x) + 6*x*sin(x) + 6*cos(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 936, "integrand": "-x**3*cos(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -9*sin(3*x - 2)**2*cos(3*x - 2) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-sin(3*x - 2)**3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 937, "integrand": "-9*sin(3*x - 2)**2*cos(3*x - 2)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 5*sin(5*x + 5)**3*cos(5*x + 5) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "sin(5*x + 5)**4/4 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 938, "integrand": "5*sin(5*x + 5)**3*cos(5*x + 5)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -2*x**3*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*x**3*sin(x) - 6*x**2*cos(x) + 12*x*sin(x) + 12*cos(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 939, "integrand": "-2*x**3*cos(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -x*sin(2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-Integral(x*sin(2*x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 940, "integrand": "-x*sin(2*x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ (18*x + 5)*exp(9*x**2 + 5*x - 3) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "exp(9*x**2 + 5*x - 3) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 941, "integrand": "(18*x + 5)*exp(9*x**2 + 5*x - 3)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ exp(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "exp(x)*sin(x)/2 + exp(x)*cos(x)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 942, "integrand": "exp(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -2*asin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*x*asin(x) - 2*sqrt(1 - x**2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 943, "integrand": "-2*asin(x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -2*(6*x + 3)**4 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2592*x**5/5 - 1296*x**4 - 1296*x**3 - 648*x**2 - 162*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 944, "integrand": "-2*(6*x + 3)**4", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 2*x*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(2*x - 2)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 945, "integrand": "2*x*exp(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -x**3*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "x**3*cos(x) - 3*x**2*sin(x) - 6*x*cos(x) + 6*sin(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 946, "integrand": "-x**3*sin(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -3*exp(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*exp(x)*sin(x)/2 - 3*exp(x)*cos(x)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 947, "integrand": "-3*exp(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -2*sin(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-sin(x)**2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 948, "integrand": "-2*sin(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -10*sqrt(3 - 5*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "4*(3 - 5*x)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 949, "integrand": "-10*sqrt(3 - 5*x)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -2*x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(-2*x**3 + 6*x**2 - 12*x + 12)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 950, "integrand": "-2*x**3*exp(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 3*(3*x - 9)**4 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "243*x**5/5 - 729*x**4 + 4374*x**3 - 13122*x**2 + 19683*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 951, "integrand": "3*(3*x - 9)**4", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 3*x**3*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*x**3*cos(x) + 9*x**2*sin(x) + 18*x*cos(x) - 18*sin(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 952, "integrand": "3*x**3*sin(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -21*sqrt(7*x - 2) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*(7*x - 2)**(3/2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 953, "integrand": "-21*sqrt(7*x - 2)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ x**3*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-x**3*cos(x) + 3*x**2*sin(x) + 6*x*cos(x) - 6*sin(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 954, "integrand": "x**3*sin(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -18*sin(6*x + 6)*cos(6*x + 6)**2 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "cos(6*x + 6)**3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 955, "integrand": "-18*sin(6*x + 6)*cos(6*x + 6)**2", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 12*sqrt(4*x - 3) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*(4*x - 3)**(3/2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 956, "integrand": "12*sqrt(4*x - 3)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -3*sin(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*sin(x)**2/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 957, "integrand": "-3*sin(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 2*exp(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "exp(x)*sin(x) + exp(x)*cos(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 958, "integrand": "2*exp(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -exp(x)*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-exp(x)*sin(x)/2 + exp(x)*cos(x)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 959, "integrand": "-exp(x)*sin(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -x*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(1 - x)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 960, "integrand": "-x*exp(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -24*sin(8*x + 7)*cos(8*x + 7) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*sin(8*x + 7)**2/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 961, "integrand": "-24*sin(8*x + 7)*cos(8*x + 7)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ sin(x - 10)**3*cos(x - 10) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "sin(x - 10)**4/4 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 962, "integrand": "sin(x - 10)**3*cos(x - 10)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 18*sin(6*x - 8)*cos(6*x - 8) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*sin(6*x - 8)**2/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 963, "integrand": "18*sin(6*x - 8)*cos(6*x - 8)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -asin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-x*asin(x) - sqrt(1 - x**2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 964, "integrand": "-asin(x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 3*exp(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*exp(x)*sin(x)/2 + 3*exp(x)*cos(x)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 965, "integrand": "3*exp(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 3*x**2*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(3*x**2 - 6*x + 6)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 966, "integrand": "3*x**2*exp(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 27*sqrt(9*x - 3) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*(9*x - 3)**(3/2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 967, "integrand": "27*sqrt(9*x - 3)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 7*exp(-7*x - 3) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-exp(-7*x - 3) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 968, "integrand": "7*exp(-7*x - 3)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -3*asin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*x*asin(x) - 3*sqrt(1 - x**2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 969, "integrand": "-3*asin(x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 3*asin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*x*asin(x) + 3*sqrt(1 - x**2) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 970, "integrand": "3*asin(x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 3*x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(3*x**3 - 9*x**2 + 18*x - 18)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 971, "integrand": "3*x**3*exp(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -2*x**2*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(-2*x**2 + 4*x - 4)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 972, "integrand": "-2*x**2*exp(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -2*(8*x - 9)**3 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-256*x**4 + 1152*x**3 - 1944*x**2 + 1458*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 973, "integrand": "-2*(8*x - 9)**3", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 3*atan(2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*x*atan(2*x) - 3*log(4*x**2 + 1)/4 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 974, "integrand": "3*atan(2*x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 12*sin(6*x - 2)**3*cos(6*x - 2) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "sin(6*x - 2)**4/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 975, "integrand": "12*sin(6*x - 2)**3*cos(6*x - 2)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -30*sin(10*x - 4)**2*cos(10*x - 4) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-sin(10*x - 4)**3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 976, "integrand": "-30*sin(10*x - 4)**2*cos(10*x - 4)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 3*(2*x - 4)**4 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "48*x**5/5 - 96*x**4 + 384*x**3 - 768*x**2 + 768*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 977, "integrand": "3*(2*x - 4)**4", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -(7*x + 10)**3 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-343*x**4/4 - 490*x**3 - 1050*x**2 - 1000*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 978, "integrand": "-(7*x + 10)**3", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -2*x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(-2*x**3 + 6*x**2 - 12*x + 12)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 979, "integrand": "-2*x**3*exp(x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -7*sqrt(7*x + 6) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*(7*x + 6)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 980, "integrand": "-7*sqrt(7*x + 6)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 14*sin(7*x - 1)*cos(7*x - 1)**4 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-2*cos(7*x - 1)**5/5 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 981, "integrand": "14*sin(7*x - 1)*cos(7*x - 1)**4", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 2*exp(x)*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "exp(x)*sin(x) + exp(x)*cos(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 982, "integrand": "2*exp(x)*cos(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -12*sqrt(6*x + 4) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-4*(6*x + 4)**(3/2)/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 983, "integrand": "-12*sqrt(6*x + 4)", "problem_type": "radical", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -3*(5*x - 7)**2 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-25*x**3 + 105*x**2 - 147*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 984, "integrand": "-3*(5*x - 7)**2", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -3*(9*x + 8)**2 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-81*x**3 - 216*x**2 - 192*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 985, "integrand": "-3*(9*x + 8)**2", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -8*sin(8*x - 9)*cos(8*x - 9)**4 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "cos(8*x - 9)**5/5 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 986, "integrand": "-8*sin(8*x - 9)*cos(8*x - 9)**4", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -3*x**3*cos(3*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*Integral(x**3*cos(3*x), x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 987, "integrand": "-3*x**3*cos(3*x)", "problem_type": "polynomial_exp_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -x**3*exp(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "(-x**3 + 3*x**2 - 6*x + 6)*exp(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 988, "integrand": "-x**3*exp(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 18*exp(6 - 6*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-3*exp(6 - 6*x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 989, "integrand": "18*exp(6 - 6*x)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 4*sin(4*x + 5)**2*cos(4*x + 5) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "sin(4*x + 5)**3/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 990, "integrand": "4*sin(4*x + 5)**2*cos(4*x + 5)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ x**3*cos(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "x**3*sin(x) + 3*x**2*cos(x) - 6*x*sin(x) - 6*cos(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 991, "integrand": "x**3*cos(x)", "problem_type": "repeated_parts", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ -exp(x)*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-exp(x)*sin(x)/2 + exp(x)*cos(x)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 992, "integrand": "-exp(x)*sin(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ 2*exp(x)*sin(x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "exp(x)*sin(x) - exp(x)*cos(x) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 993, "integrand": "2*exp(x)*sin(x)", "problem_type": "cyclic", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ -2*sin(2*x - 8)**2*cos(2*x - 8) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-sin(2*x - 8)**3/3 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 994, "integrand": "-2*sin(2*x - 8)**2*cos(2*x - 8)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -3*(2*x + 1)**3 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-6*x**4 - 12*x**3 - 9*x**2 - 3*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 995, "integrand": "-3*(2*x + 1)**3", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ -(3*x - 2)**3 dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "-27*x**4/4 + 18*x**3 - 18*x**2 + 8*x + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 996, "integrand": "-(3*x - 2)**3", "problem_type": "linear", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Find the indefinite integral: ∫ exp(x + 7) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "exp(x + 7) + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 997, "integrand": "exp(x + 7)", "problem_type": "exponential", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Calculate the antiderivative: ∫ 2*atan(2*x) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "2*x*atan(2*x) - log(4*x**2 + 1)/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 998, "integrand": "2*atan(2*x)", "problem_type": "log_inverse_trig", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}
{"question": "Evaluate the indefinite integral: ∫ 12*sin(4*x + 4)*cos(4*x + 4) dx\nWhen performing calculations, please follow these guidelines:\nUse same variable symbols as given in the question\n1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.\n2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.\n3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).\n", "answer": "3*sin(4*x + 4)**2/2 + C", "metadata": {"source_dataset": "intermediate_integration", "source_index": 999, "integrand": "12*sin(4*x + 4)*cos(4*x + 4)", "problem_type": "trigonometric", "variable": "x", "difficulty": {"problem_type_weights": [0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125]}}}