Question:
Evaluate the indefinite integral: ∫ -18*exp(5 - 6*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(5 - 6*x) + C


Question:
Evaluate the indefinite integral: ∫ 3*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: (3*x - 3)*exp(x) + C


Question:
Find the indefinite integral: ∫ -3*(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: -4*x**3 + 48*x**2 - 192*x + C


Question:
Find the indefinite integral: ∫ -3*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: -3*x*asin(3*x) - sqrt(1 - 9*x**2) + C


Question:
Evaluate the indefinite integral: ∫ -3*(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: -x**3 + 9*x**2 - 27*x + C


Question:
Evaluate the indefinite integral: ∫ -3*(7*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: -1029*x**4/4 + 147*x**3 - 63*x**2/2 + 3*x + 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:
Evaluate the indefinite integral: ∫ 2*(10*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: 4000*x**5 + 8000*x**4 + 6400*x**3 + 2560*x**2 + 512*x + C


Question:
Calculate the antiderivative: ∫ 21*sin(7*x - 6)*cos(7*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*cos(7*x - 6)**2/2 + C


Question:
Find the indefinite integral: ∫ -12*sin(4*x - 2)*cos(4*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: cos(4*x - 2)**3 + C


Question:
Calculate the antiderivative: ∫ -(4*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: -16*x**3/3 - 12*x**2 - 9*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: ∫ -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: ∫ 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:
Evaluate the indefinite integral: ∫ -5*sin(5*x + 1)**2*cos(5*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(5*x + 1)**3/3 + C


Question:
Evaluate the indefinite integral: ∫ -3*x*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*sin(3*x), x) + C


Question:
Evaluate the indefinite integral: ∫ 18*sin(9*x - 3)*cos(9*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(9*x - 3)**2 + C


Question:
Find the indefinite integral: ∫ 3*sqrt(7 - 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 - x)**(3/2) + C


Question:
Find the indefinite integral: ∫ -3*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: -3*Integral(x**2*sin(3*x), x) + C


Question:
Evaluate the indefinite integral: ∫ 3*(2*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: 4*x**3 + 30*x**2 + 75*x + 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:
Find 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:
Find the indefinite integral: ∫ 2*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: 2*x*atan(2*x) - log(4*x**2 + 1)/2 + C


Question:
Calculate the antiderivative: ∫ 4*exp(-2*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*exp(-2*x - 7) + C


Question:
Evaluate the indefinite integral: ∫ -10*exp(-5*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*exp(-5*x - 7) + C


Question:
Evaluate the indefinite integral: ∫ 15*sqrt(6 - 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*(6 - 5*x)**(3/2) + C


Question:
Find the indefinite integral: ∫ 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*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:
Find the indefinite integral: ∫ 2*(8*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: 128*x**3/3 + 32*x**2 + 8*x + C


Question:
Find the indefinite integral: ∫ 4*exp(4*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: exp(4*x - 3) + C


Question:
Evaluate the indefinite integral: ∫ 18*sin(6*x + 9)**4*cos(6*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(6*x + 9)**5/5 + C


Question:
Find the indefinite integral: ∫ -4*sin(4*x + 7)*cos(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: -sin(4*x + 7)**2/2 + C


Question:
Find 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:
Evaluate the indefinite integral: ∫ 3*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: 3*Integral(x**3*sin(2*x), x) + C


Question:
Evaluate the indefinite integral: ∫ 2*exp(-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*exp(-x - 8) + C


Question:
Find the indefinite integral: ∫ 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:
Calculate the antiderivative: ∫ 2*log(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: 2*x*log(x**3) - 6*x + C


Question:
Find the indefinite integral: ∫ 9*exp(2 - 9*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(2 - 9*x) + C


Question:
Find the indefinite integral: ∫ -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:
Find the indefinite integral: ∫ 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:
Calculate the antiderivative: ∫ (-14*x - 10)*exp(7*x**2 + 10*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(7*x**2 + 10*x - 10) + C


Question:
Evaluate the indefinite integral: ∫ 3*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*Integral(x*sin(x), 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:
Find the indefinite integral: ∫ -2*(7*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: -98*x**3/3 + 28*x**2 - 8*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:
Evaluate the indefinite integral: ∫ (24*x + 15)*exp(4*x**2 + 5*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(4*x**2 + 5*x - 6) + C


Question:
Find the indefinite integral: ∫ 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:
Find 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: ∫ 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: ∫ -24*sqrt(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: -2*(8*x - 10)**(3/2) + 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*x**3*cos(x) - 9*x**2*sin(x) - 18*x*cos(x) + 18*sin(x) + C


Question:
Find the indefinite integral: ∫ -sin(x + 3)*cos(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: cos(x + 3)**5/5 + C


Question:
Evaluate 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:
Evaluate the indefinite integral: ∫ -3*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: -3*x*atan(3*x) + log(9*x**2 + 1)/2 + C


Question:
Calculate the antiderivative: ∫ -18*sin(9*x + 3)**3*cos(9*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(9*x + 3)**4/2 + C


Question:
Calculate the antiderivative: ∫ 7*sin(7*x - 2)*cos(7*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(7*x - 2)**4/4 + 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:
Find the indefinite integral: ∫ 3*x**2*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**2 - 6*x + 6)*exp(x) + C


Question:
Find the indefinite integral: ∫ 2*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: 2*x*asin(3*x) + 2*sqrt(1 - 9*x**2)/3 + C


Question:
Calculate the antiderivative: ∫ -3*(6*x + 10)**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: -3888*x**5/5 - 6480*x**4 - 21600*x**3 - 36000*x**2 - 30000*x + C


Question:
Calculate the antiderivative: ∫ -3*sin(x + 7)*cos(x + 7)**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: cos(x + 7)**3 + C


Question:
Find the indefinite integral: ∫ 3*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: 3*x*asin(3*x) + sqrt(1 - 9*x**2) + C


Question:
Calculate the antiderivative: ∫ -12*exp(4 - 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: 3*exp(4 - 4*x) + C


Question:
Find the indefinite integral: ∫ 3*(7*x - 10)**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 - 10290*x**4 + 29400*x**3 - 42000*x**2 + 30000*x + C


Question:
Find the indefinite integral: ∫ 8*sqrt(10 - 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*(10 - 4*x)**(3/2)/3 + C


Question:
Calculate the antiderivative: ∫ -18*sin(9*x - 3)**3*cos(9*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(9*x - 3)**4/2 + C


Question:
Find the indefinite integral: ∫ -2*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: -2*x*asin(2*x) - sqrt(1 - 4*x**2) + C


Question:
Evaluate the indefinite integral: ∫ (10*x - 8)*exp(-5*x**2 + 8*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: -exp(-5*x**2 + 8*x - 1) + 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*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:
Calculate the antiderivative: ∫ -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: ∫ -4*sqrt(9 - 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: 4*(9 - 2*x)**(3/2)/3 + 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: ∫ 2*(10*x + 5)**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: 500*x**4 + 1000*x**3 + 750*x**2 + 250*x + C


Question:
Find 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:
Find the indefinite integral: ∫ 18*sin(6*x - 2)*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: -3*cos(6*x - 2)**2/2 + 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:
Evaluate the indefinite integral: ∫ -10*sqrt(-10*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: 2*(-10*x - 3)**(3/2)/3 + C


Question:
Find the indefinite integral: ∫ 3*sqrt(1 - 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*(1 - x)**(3/2) + C


Question:
Evaluate the indefinite integral: ∫ -3*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: -3*sin(x)**2/2 + C


Question:
Calculate the antiderivative: ∫ 2*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: 2*x*asin(2*x) + sqrt(1 - 4*x**2) + C


Question:
Calculate the antiderivative: ∫ 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: ∫ -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:
Find the indefinite integral: ∫ -9*sin(3*x - 2)*cos(3*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(3*x - 2)**4/4 + C


Question:
Evaluate the indefinite integral: ∫ -2*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: -2*x*atan(2*x) + log(4*x**2 + 1)/2 + C


Question:
Evaluate the indefinite integral: ∫ (2*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: 16*x**5/5 - 64*x**4 + 512*x**3 - 2048*x**2 + 4096*x + C


Question:
Calculate the antiderivative: ∫ (18*x - 3)*exp(-3*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: -3*exp(-3*x**2 + x + 6) + C


Question:
Evaluate the indefinite integral: ∫ (-14*x - 4)*exp(-7*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(-7*x**2 - 4*x + 10) + C


Question:
Calculate the antiderivative: ∫ 3*(6*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: 162*x**4 - 216*x**3 + 108*x**2 - 24*x + C


Question:
Calculate the antiderivative: ∫ -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: -Integral(x**3*cos(2*x), x) + C


Question:
Evaluate the indefinite integral: ∫ -21*sin(7*x - 7)**2*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: -sin(7*x - 7)**3 + C


Question:
Evaluate the indefinite integral: ∫ -x**2*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**2 + 2*x - 2)*exp(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:
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:
Find the indefinite integral: ∫ x**2*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**2*cos(x), x) + C


Question:
Calculate the antiderivative: ∫ (12*x + 12)*exp(-2*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: -3*exp(-2*x**2 - 4*x - 10) + C


Question:
Find 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:
Calculate the antiderivative: ∫ -2*sin(2*x + 6)**2*cos(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: -sin(2*x + 6)**3/3 + C


Question:
Calculate the antiderivative: ∫ -6*sqrt(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*(2*x - 10)**(3/2) + C


Question:
Evaluate 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:
Find the indefinite integral: ∫ -3*(6*x + 9)**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: -3888*x**5/5 - 5832*x**4 - 17496*x**3 - 26244*x**2 - 19683*x + C


Question:
Find 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: ∫ 12*sqrt(6*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: 4*(6*x - 8)**(3/2)/3 + C


Question:
Evaluate the indefinite integral: ∫ 2*log(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: 2*x*log(x**3) - 6*x + C


Question:
Evaluate the indefinite integral: ∫ -3*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: -3*Integral(x*sin(2*x), x) + C


Question:
Find the indefinite integral: ∫ -30*sin(10*x - 2)*cos(10*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: cos(10*x - 2)**3 + 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: ∫ -3*(2*x - 10)**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 + 240*x**4 - 2400*x**3 + 12000*x**2 - 30000*x + C


Question:
Find the indefinite integral: ∫ -sqrt(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*(5 - x)**(3/2)/3 + C


Question:
Calculate the antiderivative: ∫ -9*sqrt(10 - 9*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*(10 - 9*x)**(3/2)/3 + C


Question:
Calculate the antiderivative: ∫ -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*cos(7*x - 9)**2/2 + C


Question:
Find the indefinite integral: ∫ (42*x + 3)*exp(-7*x**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: -3*exp(-7*x**2 - x - 4) + C


Question:
Evaluate the indefinite integral: ∫ 12*sqrt(-6*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: -4*(-6*x - 3)**(3/2)/3 + C


Question:
Find the indefinite integral: ∫ -(3*x + 4)**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**3 - 12*x**2 - 16*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*Integral(x**3*sin(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:
Find the indefinite integral: ∫ -12*exp(6*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*exp(6*x + 4) + C


Question:
Find the indefinite integral: ∫ x**2*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**2 - 2*x + 2)*exp(x) + C


Question:
Calculate the antiderivative: ∫ 2*sqrt(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: 4*(x - 4)**(3/2)/3 + C


Question:
Find the indefinite integral: ∫ 18*sin(6*x + 2)*cos(6*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: -cos(6*x + 2)**3 + C


Question:
Calculate the antiderivative: ∫ 2*(6*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: 24*x**3 + 12*x**2 + 2*x + C


Question:
Calculate the antiderivative: ∫ -12*sin(4*x - 8)**4*cos(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*sin(4*x - 8)**5/5 + C


Question:
Calculate the antiderivative: ∫ (42*x - 30)*exp(-7*x**2 + 10*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*exp(-7*x**2 + 10*x - 7) + C


Question:
Find the indefinite integral: ∫ 30*sqrt(4 - 10*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*(4 - 10*x)**(3/2) + C


Question:
Evaluate the indefinite integral: ∫ 6*sin(2*x + 5)*cos(2*x + 5) 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(2*x + 5)**2/2 + C


Question:
Evaluate the indefinite integral: ∫ -2*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: -2*x*asin(3*x) - 2*sqrt(1 - 9*x**2)/3 + 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:
Calculate the antiderivative: ∫ 2*exp(-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(-x - 6) + C


Question:
Find the indefinite integral: ∫ 2*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: 2*Integral(x*cos(2*x), x) + C


Question:
Find 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: ∫ 3*(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: x**3 - 24*x**2 + 192*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:
Evaluate the indefinite integral: ∫ (12*x + 24)*exp(-2*x**2 - 8*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: -3*exp(-2*x**2 - 8*x - 4) + C


Question:
Calculate the antiderivative: ∫ 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:
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:
Evaluate 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:
Find the indefinite integral: ∫ -9*sqrt(4 - 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*(4 - 3*x)**(3/2) + C


Question:
Calculate the antiderivative: ∫ -2*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: -2*Integral(x*sin(x), 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:
Evaluate the indefinite integral: ∫ 2*sqrt(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: -4*(3 - x)**(3/2)/3 + C


Question:
Evaluate the indefinite integral: ∫ -(3*x - 9)**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 + 243*x**4 - 1458*x**3 + 4374*x**2 - 6561*x + C


Question:
Calculate the antiderivative: ∫ 18*sqrt(9*x - 5) 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 - 5)**(3/2)/3 + C


Question:
Evaluate the indefinite integral: ∫ 3*(8*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: 12288*x**5/5 + 12288*x**4 + 24576*x**3 + 24576*x**2 + 12288*x + C


Question:
Find the indefinite integral: ∫ 2*sqrt(10 - 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*(10 - x)**(3/2)/3 + C


Question:
Evaluate the indefinite integral: ∫ 6*sin(3*x + 4)**3*cos(3*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: sin(3*x + 4)**4/2 + C


Question:
Evaluate the indefinite integral: ∫ -3*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: (3 - 3*x)*exp(x) + C


Question:
Evaluate the indefinite integral: ∫ -3*(2*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: -4*x**3 + 12*x**2 - 12*x + C


Question:
Find the indefinite integral: ∫ 20*sqrt(9 - 10*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*(9 - 10*x)**(3/2)/3 + C


Question:
Calculate the antiderivative: ∫ 10*sin(5*x + 7)*cos(5*x + 7)**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(5*x + 7)**4/2 + 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: ∫ -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:
Evaluate the indefinite integral: ∫ 2*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: 2*x*atan(2*x) - log(4*x**2 + 1)/2 + 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:
Calculate the antiderivative: ∫ -20*sin(10*x + 10)*cos(10*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: cos(10*x + 10)**4/2 + C