Question:
Find the indefinite integral: ∫ (16*x + 4)*exp(4*x**2 + 2*x + 10) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: 2*exp(4*x**2 + 2*x + 10) + C


Question:
Evaluate the indefinite integral: ∫ -3*(8*x + 6)**3 dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -384*x**4 - 1152*x**3 - 1296*x**2 - 648*x + C


Question:
Find the indefinite integral: ∫ -4*sin(4*x + 1)**2*cos(4*x + 1) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -sin(4*x + 1)**3/3 + C


Question:
Find the indefinite integral: ∫ -2*asin(x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -2*x*asin(x) - 2*sqrt(1 - x**2) + C


Question:
Evaluate the indefinite integral: ∫ 3*x**3*exp(x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: (3*x**3 - 9*x**2 + 18*x - 18)*exp(x) + C


Question:
Calculate the antiderivative: ∫ -3*atan(2*x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -3*x*atan(2*x) + 3*log(4*x**2 + 1)/4 + C


Question:
Evaluate the indefinite integral: ∫ 2*x**3*cos(3*x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: 2*Integral(x**3*cos(3*x), x) + C


Question:
Find the indefinite integral: ∫ -(2*x + 6)**4 dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -16*x**5/5 - 48*x**4 - 288*x**3 - 864*x**2 - 1296*x + C


Question:
Find the indefinite integral: ∫ -8*sin(8*x - 2)*cos(8*x - 2)**3 dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: cos(8*x - 2)**4/4 + C


Question:
Evaluate the indefinite integral: ∫ -12*sqrt(4*x - 7) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -2*(4*x - 7)**(3/2) + C


Question:
Find the indefinite integral: ∫ 2*x**3*cos(x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: 2*x**3*sin(x) + 6*x**2*cos(x) - 12*x*sin(x) - 12*cos(x) + C


Question:
Evaluate the indefinite integral: ∫ -2*x**2*cos(3*x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -2*Integral(x**2*cos(3*x), x) + C


Question:
Calculate the antiderivative: ∫ -2*x**3*exp(x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: (-2*x**3 + 6*x**2 - 12*x + 12)*exp(x) + C


Question:
Find the indefinite integral: ∫ -(3*x + 5)**4 dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -81*x**5/5 - 135*x**4 - 450*x**3 - 750*x**2 - 625*x + C


Question:
Evaluate the indefinite integral: ∫ -3*x**3*exp(x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: (-3*x**3 + 9*x**2 - 18*x + 18)*exp(x) + C


Question:
Evaluate the indefinite integral: ∫ -2*(4*x - 9)**3 dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -32*x**4 + 288*x**3 - 972*x**2 + 1458*x + C


Question:
Calculate the antiderivative: ∫ x**3*cos(x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: Integral(x**3*cos(x), x) + C


Question:
Calculate the antiderivative: ∫ 9*sqrt(3*x - 1) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: 2*(3*x - 1)**(3/2) + C


Question:
Calculate the antiderivative: ∫ -2*asin(x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -2*x*asin(x) - 2*sqrt(1 - x**2) + C


Question:
Calculate the antiderivative: ∫ -12*sin(6*x - 8)*cos(6*x - 8)**3 dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: cos(6*x - 8)**4/2 + C


Question:
Evaluate the indefinite integral: ∫ -2*x**3*sin(x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: 2*x**3*cos(x) - 6*x**2*sin(x) - 12*x*cos(x) + 12*sin(x) + C


Question:
Calculate the antiderivative: ∫ -6*sin(2*x + 2)*cos(2*x + 2) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -3*sin(2*x + 2)**2/2 + C


Question:
Find the indefinite integral: ∫ -10*sin(5*x + 3)*cos(5*x + 3) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -sin(5*x + 3)**2 + C


Question:
Find the indefinite integral: ∫ -24*sin(8*x + 9)**3*cos(8*x + 9) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -3*sin(8*x + 9)**4/4 + C


Question:
Evaluate the indefinite integral: ∫ 3*(4*x - 8)**3 dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: 48*x**4 - 384*x**3 + 1152*x**2 - 1536*x + C


Question:
Evaluate the indefinite integral: ∫ -2*(8*x - 7)**4 dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -8192*x**5/5 + 7168*x**4 - 12544*x**3 + 10976*x**2 - 4802*x + C


Question:
Find the indefinite integral: ∫ 16*exp(-8*x - 6) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -2*exp(-8*x - 6) + C


Question:
Calculate the antiderivative: ∫ -30*exp(10*x - 6) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -3*exp(10*x - 6) + C


Question:
Find the indefinite integral: ∫ -x**3*cos(x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -x**3*sin(x) - 3*x**2*cos(x) + 6*x*sin(x) + 6*cos(x) + C


Question:
Find the indefinite integral: ∫ -asin(x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -x*asin(x) - sqrt(1 - x**2) + C


Question:
Evaluate the indefinite integral: ∫ 3*(6*x - 9)**3 dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: 162*x**4 - 972*x**3 + 2187*x**2 - 2187*x + C


Question:
Evaluate the indefinite integral: ∫ -2*atan(x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -2*x*atan(x) + log(x**2 + 1) + C


Question:
Find the indefinite integral: ∫ -exp(x)*cos(x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -exp(x)*sin(x)/2 - exp(x)*cos(x)/2 + C


Question:
Find the indefinite integral: ∫ 27*sin(9*x - 6)*cos(9*x - 6) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: 3*sin(9*x - 6)**2/2 + C


Question:
Calculate the antiderivative: ∫ -log(x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -x*log(x) + x + C


Question:
Find the indefinite integral: ∫ exp(x)*sin(x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: exp(x)*sin(x)/2 - exp(x)*cos(x)/2 + C


Question:
Evaluate the indefinite integral: ∫ -3*exp(x)*cos(x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -3*exp(x)*sin(x)/2 - 3*exp(x)*cos(x)/2 + C


Question:
Calculate the antiderivative: ∫ 4*sqrt(4*x + 8) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: 2*(4*x + 8)**(3/2)/3 + C


Question:
Calculate the antiderivative: ∫ -3*asin(2*x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -3*x*asin(2*x) - 3*sqrt(1 - 4*x**2)/2 + C


Question:
Find the indefinite integral: ∫ -2*x**2*cos(3*x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -2*Integral(x**2*cos(3*x), x) + C


Question:
Calculate the antiderivative: ∫ -3*sqrt(5 - 3*x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: 2*(5 - 3*x)**(3/2)/3 + C


Question:
Calculate the antiderivative: ∫ 7*sin(7*x + 1)**2*cos(7*x + 1) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: sin(7*x + 1)**3/3 + C


Question:
Evaluate the indefinite integral: ∫ (12 - 54*x)*exp(9*x**2 - 4*x - 8) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -3*exp(9*x**2 - 4*x - 8) + C


Question:
Evaluate the indefinite integral: ∫ -8*sqrt(8 - 4*x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: 4*(8 - 4*x)**(3/2)/3 + C


Question:
Find the indefinite integral: ∫ 2*sin(x)*cos(x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: sin(x)**2 + C


Question:
Evaluate the indefinite integral: ∫ -15*sqrt(5*x - 9) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -2*(5*x - 9)**(3/2) + C


Question:
Find the indefinite integral: ∫ -sin(x + 6)*cos(x + 6)**4 dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: cos(x + 6)**5/5 + C


Question:
Find the indefinite integral: ∫ -2*(3*x + 6)**2 dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -6*x**3 - 36*x**2 - 72*x + C


Question:
Calculate the antiderivative: ∫ 20*sqrt(-10*x - 6) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -4*(-10*x - 6)**(3/2)/3 + C


Question:
Calculate the antiderivative: ∫ -2*(3*x - 7)**4 dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -162*x**5/5 + 378*x**4 - 1764*x**3 + 4116*x**2 - 4802*x + C


Question:
Find the indefinite integral: ∫ 3*sin(3*x - 10)**3*cos(3*x - 10) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: sin(3*x - 10)**4/4 + C


Question:
Find the indefinite integral: ∫ -x**3*sin(x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: x**3*cos(x) - 3*x**2*sin(x) - 6*x*cos(x) + 6*sin(x) + C


Question:
Calculate the antiderivative: ∫ -x**2*sin(2*x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -Integral(x**2*sin(2*x), x) + C


Question:
Find the indefinite integral: ∫ exp(x)*cos(x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: exp(x)*sin(x)/2 + exp(x)*cos(x)/2 + C


Question:
Find the indefinite integral: ∫ 3*log(x**2) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: 3*x*log(x**2) - 6*x + C


Question:
Evaluate the indefinite integral: ∫ 10*sqrt(10*x + 9) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: 2*(10*x + 9)**(3/2)/3 + C


Question:
Calculate the antiderivative: ∫ -asin(2*x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -x*asin(2*x) - sqrt(1 - 4*x**2)/2 + C


Question:
Evaluate the indefinite integral: ∫ -12*sin(4*x + 2)**3*cos(4*x + 2) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -3*sin(4*x + 2)**4/4 + C


Question:
Evaluate the indefinite integral: ∫ 21*sqrt(7*x - 7) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: 2*(7*x - 7)**(3/2) + C


Question:
Evaluate the indefinite integral: ∫ x**3*sin(2*x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: Integral(x**3*sin(2*x), x) + C


Question:
Evaluate the indefinite integral: ∫ -18*sqrt(9*x + 7) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -4*(9*x + 7)**(3/2)/3 + C


Question:
Evaluate the indefinite integral: ∫ x**3*exp(x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: (x**3 - 3*x**2 + 6*x - 6)*exp(x) + C


Question:
Evaluate the indefinite integral: ∫ 2*x**3*cos(x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: 2*x**3*sin(x) + 6*x**2*cos(x) - 12*x*sin(x) - 12*cos(x) + C


Question:
Calculate the antiderivative: ∫ -2*x**3*sin(x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: 2*x**3*cos(x) - 6*x**2*sin(x) - 12*x*cos(x) + 12*sin(x) + C


Question:
Calculate the antiderivative: ∫ exp(-x - 2) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -exp(-x - 2) + C


Question:
Calculate the antiderivative: ∫ -15*sqrt(7 - 5*x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: 2*(7 - 5*x)**(3/2) + C


Question:
Find the indefinite integral: ∫ 5*sqrt(-5*x - 4) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -2*(-5*x - 4)**(3/2)/3 + C


Question:
Find the indefinite integral: ∫ asin(3*x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: x*asin(3*x) + sqrt(1 - 9*x**2)/3 + C


Question:
Evaluate the indefinite integral: ∫ -2*x**3*cos(x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -2*x**3*sin(x) - 6*x**2*cos(x) + 12*x*sin(x) + 12*cos(x) + C


Question:
Calculate the antiderivative: ∫ 2*exp(x)*cos(x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: exp(x)*sin(x) + exp(x)*cos(x) + C


Question:
Evaluate the indefinite integral: ∫ 3*sin(3*x + 4)*cos(3*x + 4)**4 dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -cos(3*x + 4)**5/5 + C


Question:
Find the indefinite integral: ∫ 2*(x - 8)**2 dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: 2*x**3/3 - 16*x**2 + 128*x + C


Question:
Evaluate the indefinite integral: ∫ 12*sqrt(3 - 4*x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -2*(3 - 4*x)**(3/2) + C


Question:
Evaluate the indefinite integral: ∫ -x**3*exp(x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: (-x**3 + 3*x**2 - 6*x + 6)*exp(x) + C


Question:
Evaluate the indefinite integral: ∫ 3*exp(x)*sin(x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: 3*exp(x)*sin(x)/2 - 3*exp(x)*cos(x)/2 + C


Question:
Evaluate the indefinite integral: ∫ 14*sqrt(7*x + 9) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: 4*(7*x + 9)**(3/2)/3 + C


Question:
Evaluate the indefinite integral: ∫ (1 - 12*x)*exp(6*x**2 - x - 6) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -exp(6*x**2 - x - 6) + C


Question:
Evaluate the indefinite integral: ∫ -x**3*sin(x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: x**3*cos(x) - 3*x**2*sin(x) - 6*x*cos(x) + 6*sin(x) + C


Question:
Find the indefinite integral: ∫ -3*x**3*cos(3*x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -3*Integral(x**3*cos(3*x), x) + C


Question:
Evaluate the indefinite integral: ∫ 2*(3*x + 10)**3 dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: 27*x**4/2 + 180*x**3 + 900*x**2 + 2000*x + C


Question:
Evaluate the indefinite integral: ∫ -x*cos(2*x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -Integral(x*cos(2*x), x) + C


Question:
Calculate the antiderivative: ∫ -2*(7*x + 5)**2 dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -98*x**3/3 - 70*x**2 - 50*x + C


Question:
Calculate the antiderivative: ∫ -2*x**3*sin(x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: 2*x**3*cos(x) - 6*x**2*sin(x) - 12*x*cos(x) + 12*sin(x) + C


Question:
Calculate the antiderivative: ∫ 3*x**3*exp(x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: (3*x**3 - 9*x**2 + 18*x - 18)*exp(x) + C


Question:
Find the indefinite integral: ∫ -2*x*cos(x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -2*Integral(x*cos(x), x) + C


Question:
Calculate the antiderivative: ∫ 2*(x - 1)**2 dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: 2*x**3/3 - 2*x**2 + 2*x + C


Question:
Calculate the antiderivative: ∫ 2*x**3*exp(x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: (2*x**3 - 6*x**2 + 12*x - 12)*exp(x) + C


Question:
Calculate the antiderivative: ∫ 3*x*cos(2*x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: 3*Integral(x*cos(2*x), x) + C


Question:
Find the indefinite integral: ∫ -3*x**3*cos(2*x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -3*Integral(x**3*cos(2*x), x) + C


Question:
Find the indefinite integral: ∫ -asin(2*x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -x*asin(2*x) - sqrt(1 - 4*x**2)/2 + C


Question:
Calculate the antiderivative: ∫ -sin(x - 2)*cos(x - 2) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -sin(x - 2)**2/2 + C


Question:
Calculate the antiderivative: ∫ 27*sin(9*x - 2)*cos(9*x - 2)**3 dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -3*cos(9*x - 2)**4/4 + C


Question:
Evaluate the indefinite integral: ∫ 16*sin(8*x + 7)**2*cos(8*x + 7) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: 2*sin(8*x + 7)**3/3 + C


Question:
Evaluate the indefinite integral: ∫ (4*x + 5)*exp(-2*x**2 - 5*x + 10) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -exp(-2*x**2 - 5*x + 10) + C


Question:
Find the indefinite integral: ∫ 2*x**2*sin(x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: 2*Integral(x**2*sin(x), x) + C


Question:
Calculate the antiderivative: ∫ 2*(6*x + 4)**3 dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: 108*x**4 + 288*x**3 + 288*x**2 + 128*x + C


Question:
Calculate the antiderivative: ∫ -4*sqrt(-4*x - 4) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: 2*(-4*x - 4)**(3/2)/3 + C


Question:
Evaluate the indefinite integral: ∫ 2*(9*x - 1)**3 dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: 729*x**4/2 - 162*x**3 + 27*x**2 - 2*x + C


Question:
Evaluate the indefinite integral: ∫ 2*exp(x)*sin(x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: exp(x)*sin(x) - exp(x)*cos(x) + C


Question:
Find the indefinite integral: ∫ -3*x**3*sin(x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -3*Integral(x**3*sin(x), x) + C


Question:
Calculate the antiderivative: ∫ -2*x*sin(2*x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -2*Integral(x*sin(2*x), x) + C


Question:
Find the indefinite integral: ∫ x**3*sin(x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -x**3*cos(x) + 3*x**2*sin(x) + 6*x*cos(x) - 6*sin(x) + C


Question:
Calculate the antiderivative: ∫ 21*sin(7*x + 7)**4*cos(7*x + 7) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: 3*sin(7*x + 7)**5/5 + C


Question:
Find the indefinite integral: ∫ -sin(x)*cos(x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -sin(x)**2/2 + C


Question:
Find the indefinite integral: ∫ 6*sqrt(3*x - 2) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: 4*(3*x - 2)**(3/2)/3 + C


Question:
Evaluate the indefinite integral: ∫ 2*x**2*sin(3*x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: 2*Integral(x**2*sin(3*x), x) + C


Question:
Calculate the antiderivative: ∫ -10*sin(5*x + 2)*cos(5*x + 2)**2 dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: 2*cos(5*x + 2)**3/3 + C


Question:
Evaluate the indefinite integral: ∫ (7*x + 3)**2 dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: 49*x**3/3 + 21*x**2 + 9*x + C


Question:
Calculate the antiderivative: ∫ -exp(x)*sin(x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -exp(x)*sin(x)/2 + exp(x)*cos(x)/2 + C


Question:
Find the indefinite integral: ∫ (12*x - 8)*exp(-6*x**2 + 8*x - 10) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -exp(-6*x**2 + 8*x - 10) + C


Question:
Evaluate the indefinite integral: ∫ x**3*cos(x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: x**3*sin(x) + 3*x**2*cos(x) - 6*x*sin(x) - 6*cos(x) + C


Question:
Evaluate the indefinite integral: ∫ -3*x**3*cos(x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -3*x**3*sin(x) - 9*x**2*cos(x) + 18*x*sin(x) + 18*cos(x) + C


Question:
Calculate the antiderivative: ∫ 4*sqrt(-4*x - 9) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -2*(-4*x - 9)**(3/2)/3 + C


Question:
Evaluate the indefinite integral: ∫ -3*x**3*sin(3*x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -3*Integral(x**3*sin(3*x), x) + C


Question:
Find the indefinite integral: ∫ 8*sin(4*x + 3)*cos(4*x + 3)**4 dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -2*cos(4*x + 3)**5/5 + C


Question:
Calculate the antiderivative: ∫ -x*exp(x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: (1 - x)*exp(x) + C


Question:
Find the indefinite integral: ∫ 21*exp(7*x - 8) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: 3*exp(7*x - 8) + C


Question:
Calculate the antiderivative: ∫ 20*sin(10*x + 1)**4*cos(10*x + 1) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: 2*sin(10*x + 1)**5/5 + C


Question:
Evaluate the indefinite integral: ∫ -3*(7*x - 3)**4 dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -7203*x**5/5 + 3087*x**4 - 2646*x**3 + 1134*x**2 - 243*x + C


Question:
Evaluate the indefinite integral: ∫ 2*x*cos(3*x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: 2*Integral(x*cos(3*x), x) + C


Question:
Calculate the antiderivative: ∫ -3*(9*x - 4)**3 dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -2187*x**4/4 + 972*x**3 - 648*x**2 + 192*x + C


Question:
Find the indefinite integral: ∫ -2*x**3*exp(x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: (-2*x**3 + 6*x**2 - 12*x + 12)*exp(x) + C


Question:
Find the indefinite integral: ∫ 2*(5*x - 8)**4 dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: 250*x**5 - 2000*x**4 + 6400*x**3 - 10240*x**2 + 8192*x + C


Question:
Evaluate the indefinite integral: ∫ -2*(2*x + 8)**2 dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -8*x**3/3 - 32*x**2 - 128*x + C


Question:
Calculate the antiderivative: ∫ 2*sqrt(-x - 1) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -4*(-x - 1)**(3/2)/3 + C


Question:
Calculate the antiderivative: ∫ -21*sqrt(-7*x - 2) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: 2*(-7*x - 2)**(3/2) + C


Question:
Find the indefinite integral: ∫ (-8*x - 4)*exp(4*x**2 + 4*x - 10) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -exp(4*x**2 + 4*x - 10) + C


Question:
Evaluate the indefinite integral: ∫ -atan(3*x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -x*atan(3*x) + log(9*x**2 + 1)/6 + C


Question:
Calculate the antiderivative: ∫ exp(x)*cos(x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: exp(x)*sin(x)/2 + exp(x)*cos(x)/2 + C


Question:
Evaluate the indefinite integral: ∫ -exp(x)*cos(x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -exp(x)*sin(x)/2 - exp(x)*cos(x)/2 + C


Question:
Calculate the antiderivative: ∫ 3*asin(2*x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: 3*x*asin(2*x) + 3*sqrt(1 - 4*x**2)/2 + C


Question:
Evaluate the indefinite integral: ∫ -log(x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -x*log(x) + x + C


Question:
Find the indefinite integral: ∫ -2*exp(x)*sin(x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -exp(x)*sin(x) + exp(x)*cos(x) + C


Question:
Calculate the antiderivative: ∫ -20*sin(10*x - 8)**4*cos(10*x - 8) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -2*sin(10*x - 8)**5/5 + C


Question:
Find the indefinite integral: ∫ -3*(2*x - 7)**4 dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -48*x**5/5 + 168*x**4 - 1176*x**3 + 4116*x**2 - 7203*x + C


Question:
Find the indefinite integral: ∫ -x**3*exp(x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: (-x**3 + 3*x**2 - 6*x + 6)*exp(x) + C


Question:
Calculate the antiderivative: ∫ -3*x**3*cos(x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -3*x**3*sin(x) - 9*x**2*cos(x) + 18*x*sin(x) + 18*cos(x) + C


Question:
Calculate the antiderivative: ∫ -x**3*sin(x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: x**3*cos(x) - 3*x**2*sin(x) - 6*x*cos(x) + 6*sin(x) + C


Question:
Find the indefinite integral: ∫ -6*sqrt(-2*x - 4) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: 2*(-2*x - 4)**(3/2) + C


Question:
Calculate the antiderivative: ∫ -x*sin(2*x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -Integral(x*sin(2*x), x) + C


Question:
Evaluate the indefinite integral: ∫ -6*sin(6*x + 2)**3*cos(6*x + 2) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -sin(6*x + 2)**4/4 + C


Question:
Find the indefinite integral: ∫ 3*(6*x + 5)**2 dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: 36*x**3 + 90*x**2 + 75*x + C


Question:
Calculate the antiderivative: ∫ -2*atan(3*x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -2*x*atan(3*x) + log(9*x**2 + 1)/3 + C


Question:
Calculate the antiderivative: ∫ -2*x**3*sin(x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: 2*x**3*cos(x) - 6*x**2*sin(x) - 12*x*cos(x) + 12*sin(x) + C


Question:
Evaluate the indefinite integral: ∫ -atan(2*x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -x*atan(2*x) + log(4*x**2 + 1)/4 + C


Question:
Evaluate the indefinite integral: ∫ 3*atan(x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: 3*x*atan(x) - 3*log(x**2 + 1)/2 + C


Question:
Find the indefinite integral: ∫ exp(x)*cos(x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: exp(x)*sin(x)/2 + exp(x)*cos(x)/2 + C


Question:
Evaluate the indefinite integral: ∫ 21*sin(7*x + 9)*cos(7*x + 9) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: 3*sin(7*x + 9)**2/2 + C


Question:
Find the indefinite integral: ∫ 2*(6*x + 4)**3 dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: 108*x**4 + 288*x**3 + 288*x**2 + 128*x + C


Question:
Find the indefinite integral: ∫ -3*exp(x)*cos(x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -3*exp(x)*sin(x)/2 - 3*exp(x)*cos(x)/2 + C


Question:
Calculate the antiderivative: ∫ -2*log(x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -2*x*log(x) + 2*x + C


Question:
Find the indefinite integral: ∫ 3*x**2*cos(2*x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: 3*Integral(x**2*cos(2*x), x) + C


Question:
Calculate the antiderivative: ∫ -sin(x)*cos(x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: -sin(x)**2/2 + C


Question:
Calculate the antiderivative: ∫ 3*x**3*exp(x) dx
When performing calculations, please follow these guidelines:
Use same variable symbols as given in the question
1. Use ** instead of ^ to represent exponents. For example, write 7*X**2 instead of 7*X^2.
2. Always include the * symbol for all multiplication operations in your reasoning steps. For example, write `-3*X**3*sin(X) - 9*X**2*cos(X) + 18*X*sin(X) + 18*cos(X) + C` instead of `-3x3sin(x) - 9x2cos(x) + 18xsin(x) + 18cos(x) + C`.
3. Use `exp(x)` or `E**(x)` for the exponential function (i.e. use capital E for Euler's number).

Answer: (3*x**3 - 9*x**2 + 18*x - 18)*exp(x) + C