messages listlengths 1 1 | ground_truth stringlengths 1 118 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "What is the symbolic antiderivative of the function f(x) = -1((-2x + 1)/(1x))^2 - 4((-2x + 1)/(1x)) - 2? Express your answer in terms of x and do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2*x + 1/x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = 3x^2 - 1x - 4? Express your answer in terms of x and do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | x**3 - x**2/2 - 4*x | MATH |
[
{
"content": "Find the indefinite integral of f(x) = 3x - 1 with respect to x. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3*x**2/2 - x | MATH |
[
{
"content": "Determine ∫(4x) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2*x**2 | MATH |
[
{
"content": "Find the indefinite integral of f(x) = 5(-1(-1x^2 - 5x + 1)^2 - 4(-1x^2 - 5x + 1) - 4) + 2 with respect to x. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -x**5 - 25*x**4/2 - 95*x**3/3 + 75*x**2 - 43*x | MATH |
[
{
"content": "Find the indefinite integral of f(x) = (2x - 2)/(-2x - 3) with respect to x. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -x + 5*log(2*x + 3)/2 | MATH |
[
{
"content": "Determine ∫(1((-3(2x^2 + 1x + 1) + 2)/(-1(2x^2 + 1x + 1)))^2) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9*x + (16*x + 4)/(14*x**2 + 7*x + 7) - 136*sqrt(7)*atan(4*sqrt(7)*x/7 + sqrt(7)/7)/49 | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = 4(-5x^2 - 3x - 3) + 4. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -20*x**3/3 - 6*x**2 - 8*x | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = (2(5x))/(-2(5x) + 3). Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -x - 3*log(10*x - 3)/10 | MATH |
[
{
"content": "Determine ∫((-1x - 1)/(2x - 1)) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -x/2 - 3*log(2*x - 1)/4 | MATH |
[
{
"content": "Determine ∫(1x - 4) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | x**2/2 - 4*x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = 5(2x - 4)^2 - 3(2x - 4) - 4? Express your answer in terms of x and do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20*x**3/3 - 43*x**2 + 88*x | MATH |
[
{
"content": "Determine ∫(2(-4(-2x^2 + 1x - 4)^2 + 4(-2x^2 + 1x - 4) + 4)^2 + 2(-4(-2x^2 + 1x - 4)^2 + 4(-2x^2 + 1x - 4) + 4)) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 512*x**9/9 - 128*x**8 + 768*x**7 - 3584*x**6/3 + 18688*x**5/5 - 3944*x**4 + 25544*x**3/3 - 5436*x**2 + 11400*x | MATH |
[
{
"content": "Find the indefinite integral of f(x) = -5x + 5 with respect to x. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -5*x**2/2 + 5*x | MATH |
[
{
"content": "Determine ∫(2(2x - 1) - 1) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2*x**2 - 3*x | MATH |
[
{
"content": "Determine ∫((-2x - 2)/(-3x + 1)) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2*x/3 + 8*log(3*x - 1)/9 | MATH |
[
{
"content": "Find the indefinite integral of f(x) = 2x + 3 with respect to x. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | x**2 + 3*x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = (3(1(-2e^(-1x) + 3) + 2) + 1)/(-1(1(-2e^(-1x) + 3) + 2) - 2)? Express your answer in terms of x and do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -16*x/7 + 5*log(-7/2 + exp(-x))/7 | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = 5(-1e^(1x) + 2) - 5? Express your answer in terms of x and do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5*x - 5*exp(x) | MATH |
[
{
"content": "Determine ∫(5((1((-2x + 2)/(-3x - 1)) - 3)/(1((-2x + 2)/(-3x - 1)))) + 1) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -33*x/2 - 30*log(x - 1) | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = -5(4((2x)/(-3x - 3)) - 4)? Express your answer in terms of x and do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 100*x/3 - 40*log(x + 1)/3 | MATH |
[
{
"content": "Determine ∫((3(1cos(2πx - 1) - 2) - 1)/(-3(1cos(2πx - 1) - 2) + 1)) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -x | MATH |
[
{
"content": "Find the indefinite integral of f(x) = -5((2x)/(1x))^2 - 1((2x)/(1x)) + 1 with respect to x. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -21*x | MATH |
[
{
"content": "Determine ∫(1(-3x) + 5) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -3*x**2/2 + 5*x | MATH |
[
{
"content": "Determine ∫(-5x^2 - 5x - 4) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -5*x**3/3 - 5*x**2/2 - 4*x | MATH |
[
{
"content": "Determine ∫(-2((3x + 3)/(3x - 1)) - 1) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -3*x - 8*log(3*x - 1)/3 | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = 1x - 5? Express your answer in terms of x and do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | x**2/2 - 5*x | MATH |
[
{
"content": "Determine ∫(-5(1sin(1π(-4x) + 2) - 1) + 5) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10*x - 5*cos(4*pi*x - 2)/(4*pi) | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = -1(1(-4x - 5)^2 - 4(-4x - 5))^2 - 2(1(-4x - 5)^2 - 4(-4x - 5)) + 2. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -256*x**5/5 - 448*x**4 - 1536*x**3 - 2576*x**2 - 2113*x | MATH |
[
{
"content": "Find the indefinite integral of f(x) = 4(3(1e^(1x) + 1)^2 - 1(1e^(1x) + 1) - 3)^2 + 5(3(1e^(1x) + 1)^2 - 1(1e^(1x) + 1) - 3) + 2 with respect to x. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | x + 9*exp(4*x) + 40*exp(3*x) + 91*exp(2*x)/2 - 15*exp(x) | MATH |
[
{
"content": "Find the indefinite integral of f(x) = 5(-3e^(1x) + 2)^2 + 5(-3e^(1x) + 2) - 4 with respect to x. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 26*x + 45*exp(2*x)/2 - 75*exp(x) | MATH |
[
{
"content": "Find the indefinite integral of f(x) = -2(4(1x - 1)^2 + 1(1x - 1) + 1)^2 + 2(4(1x - 1)^2 + 1(1x - 1) + 1) - 3 with respect to x. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -32*x**5/5 + 28*x**4 - 154*x**3/3 + 49*x**2 - 27*x | MATH |
[
{
"content": "Find the indefinite integral of f(x) = 2(-1x^2 - 1x)^2 + 1(-1x^2 - 1x) + 2 with respect to x. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2*x**5/5 + x**4 + x**3/3 - x**2/2 + 2*x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = -5(-1(-5x - 4) - 3)^2 - 1(-1(-5x - 4) - 3)? Express your answer in terms of x and do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -125*x**3/3 - 55*x**2/2 - 6*x | MATH |
[
{
"content": "Determine ∫((3x + 2)/(-2x - 3)) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -3*x/2 + 5*log(2*x + 3)/4 | MATH |
[
{
"content": "Determine ∫(-2((1(-1x + 3) + 1)/(2(-1x + 3))) + 4) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3*x + log(x - 3) | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = (3(4(-4x + 3) - 3) - 2)/(-2(4(-4x + 3) - 3) + 3). Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -3*x/2 + 5*log(32*x - 15)/64 | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = (-1(1x^2 - 1x + 2) + 2)/(2(1x^2 - 1x + 2) - 1). Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -x/2 + 3*sqrt(5)*atan(2*sqrt(5)*x/5 - sqrt(5)/5)/10 | MATH |
[
{
"content": "Find the indefinite integral of f(x) = (3x + 2)/(1x + 1) with respect to x. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3*x - log(x + 1) | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = (1(-3e^(1(4x - 2)) + 3) - 1)/(-1(-3e^(1(4x - 2)) + 3) - 1)? Express your answer in terms of x and do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -x/2 - log(exp(4*x - 2) - 4/3)/8 | MATH |
[
{
"content": "Find the indefinite integral of f(x) = (-2(-3((2x + 3)/(1x))^2 + 3((2x + 3)/(1x))) + 2)/(1(-3((2x + 3)/(1x))^2 + 3((2x + 3)/(1x))) - 3) with respect to x. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -14*x/9 - 2*log(x**2 + 3*x + 3)/3 + 4*sqrt(3)*atan(2*sqrt(3)*x/3 + sqrt(3))/9 | MATH |
[
{
"content": "Determine ∫((-3(-3(3e^(1x) - 1)^2 - 2(3e^(1x) - 1) + 5))/(2(-3(3e^(1x) - 1)^2 - 2(3e^(1x) - 1) + 5) - 1)) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -12*x/7 + RootSum(3248*_z**2 - 696*_z + 27, Lambda(_i, _i*log(203*_i/27 + exp(x) - 37/36))) | MATH |
[
{
"content": "Find the indefinite integral of f(x) = 1(1x^2 + 2x - 1) + 2 with respect to x. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | x**3/3 + x**2 + x | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = -1e^(2(-3x^2 - 3x - 4)) - 3. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -3*x - sqrt(6)*sqrt(pi)*exp(-13/2)*erf(sqrt(6)*(12*x + 6)/12)/12 | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = (-1((2x + 1)/(-2x - 2)) + 3)/(-1((2x + 1)/(-2x - 2)) - 1). Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -4*x**2 - 7*x | MATH |
[
{
"content": "Determine ∫(1x - 1) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | x**2/2 - x | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = (-1(-4((-1x + 1)/(3x))^2 + 4((-1x + 1)/(3x)) + 1) - 3)/(1(-4((-1x + 1)/(3x))^2 + 4((-1x + 1)/(3x)) + 1)). Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20*x/7 + (270/49 + 387*sqrt(2)/98)*log(x - 10/7 - 6*sqrt(2)/7) + (270/49 - 387*sqrt(2)/98)*log(x - 10/7 + 6*sqrt(2)/7) | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = (-3((3(-2e^(-1x) + 1) + 3)/(-2(-2e^(-1x) + 1) + 3)) + 2)/(2((3(-2e^(-1x) + 1) + 3)/(-2(-2e^(-1x) + 1) + 3)) + 1)? Express your answer in terms of x and do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\... | -16*x/13 + 105*log(-13/8 + exp(-x))/52 | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = 3e^(2(1(-1x))) + 2? Express your answer in terms of x and do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2*x - 3*exp(-2*x)/2 | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = 5(3e^(2(-1x^2 - 3)))^2 - 4(3e^(2(-1x^2 - 3))) + 2? Express your answer in terms of x and do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2*x + 45*sqrt(pi)*exp(-12)*erf(2*x)/4 - 3*sqrt(2)*sqrt(pi)*exp(-6)*erf(sqrt(2)*x) | MATH |
[
{
"content": "Find the indefinite integral of f(x) = 1x^2 - 4x + 2 with respect to x. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | x**3/3 - 2*x**2 + 2*x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = (1(-1x + 3))/(-1(-1x + 3) + 3)? Express your answer in terms of x and do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -x + 3*log(x) | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = 2sin(2π(-1x - 1) - 1) - 2? Express your answer in terms of x and do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2*x + cos(2*pi*(-x - 1) - 1)/pi | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = 1(-3cos(1π(2x - 5)) - 2) - 1? Express your answer in terms of x and do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -3*x - 3*sin(pi*(2*x - 5))/(2*pi) | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = -3sin(2π(3(-5x + 1)) - 2) + 1? Express your answer in terms of x and do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | x - cos(2*pi*(3 - 15*x) - 2)/(10*pi) | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = -1cos(2π(3x - 4) - 2) - 3. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -3*x - sin(2*pi*(3*x - 4) - 2)/(6*pi) | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = 3cos(1π(4x - 2) + 2) + 3? Express your answer in terms of x and do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3*x + 3*sin(pi*(4*x - 2) + 2)/(4*pi) | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = -2sin(3π(3(3x - 4) + 5) - 1) + 3? Express your answer in terms of x and do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3*x + 2*cos(3*pi*(9*x - 7) - 1)/(27*pi) | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = -1(-1sin(1π(-4x - 2) - 1) - 2) + 4? Express your answer in terms of x and do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6*x + cos(pi*(-4*x - 2) - 1)/(4*pi) | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = 2sin(1π(3x + 3)) + 2. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2*x - 2*cos(pi*(3*x + 3))/(3*pi) | MATH |
[
{
"content": "Determine ∫(5(-1cos(2π(5x + 4)) + 1) + 4) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9*x - sin(pi*(10*x + 8))/(2*pi) | MATH |
[
{
"content": "Determine ∫((-3((-2(3x^2 - 1x + 4) - 1)/(-2(3x^2 - 1x + 4))) - 3)/(-3((-2(3x^2 - 1x + 4) - 1)/(-2(3x^2 - 1x + 4))) + 4)) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -6*x - 21*sqrt(29)*atan(6*sqrt(29)*x/29 - sqrt(29)/29)/29 | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = (-2(-1e^(1(1x - 5)) + 1))/(-2(-1e^(1(1x - 5)) + 1) - 2). Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | x/2 + log(exp(x - 5) - 2)/2 | MATH |
[
{
"content": "Determine ∫(1x^2 + 4x - 1) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | x**3/3 + 2*x**2 - x | MATH |
[
{
"content": "Find the indefinite integral of f(x) = 3x^2 - 3x + 4 with respect to x. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | x**3 - 3*x**2/2 + 4*x | MATH |
[
{
"content": "Find the indefinite integral of f(x) = (-2(2(-1x + 5) - 5))/(-3(2(-1x + 5) - 5) - 2) with respect to x. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2*x/3 + 2*log(6*x - 17)/9 | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = -5(-1sin(3π(-1x - 3) - 2) + 3) - 5? Express your answer in terms of x and do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -20*x + 5*cos(3*pi*(-x - 3) - 2)/(3*pi) | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = 5x^2 + 5x - 2. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5*x**3/3 + 5*x**2/2 - 2*x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = (3(1x + 5) - 2)/(1(1x + 5) - 2)? Express your answer in terms of x and do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3*x + 4*log(x + 3) | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = -4(-5((3x)/(3x + 3))^2 - 3((3x)/(3x + 3)))^2 + 4(-5((3x)/(3x + 3))^2 - 3((3x)/(3x + 3))) - 5. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -293*x - (-3048*x**2 - 5316*x - 2368)/(3*x**3 + 9*x**2 + 9*x + 3) + 884*log(x + 1) | MATH |
[
{
"content": "Determine ∫(3((2((-2x + 1)/(-2x - 1)) + 3)/(-1((-2x + 1)/(-2x - 1)) + 2))^2 + 3((2((-2x + 1)/(-2x - 1)) + 3)/(-1((-2x + 1)/(-2x - 1)) + 2)) - 3) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 87*x - 231*log(2*x + 3) - 294/(2*x + 3) | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = 4(-5(2x^2 - 1x + 5) + 2)^2 + 5? Express your answer in terms of x and do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 80*x**5 - 100*x**4 + 1940*x**3/3 - 460*x**2 + 2121*x | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = 3e^(1(-2x^2 + 3x + 2)) - 3. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -3*x + 3*sqrt(2)*sqrt(pi)*exp(25/8)*erf(sqrt(2)*(4*x - 3)/4)/4 | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = -4(-3e^(1(-1x + 5)) + 2)^2 - 1(-3e^(1(-1x + 5)) + 2) - 1? Express your answer in terms of x and do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -19*x - 51*exp(5 - x) + 18*exp(10 - 2*x) | MATH |
[
{
"content": "Determine ∫((-1x - 2)/(3x + 3)) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -x/3 - log(x + 1)/3 | MATH |
[
{
"content": "Find the indefinite integral of f(x) = 1(-5((2x + 1)/(3x - 2))^2 - 4((2x + 1)/(3x - 2)) + 2)^2 - 4(-5((2x + 1)/(3x - 2))^2 - 4((2x + 1)/(3x - 2)) + 2) + 3 with respect to x. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "use... | 1855*x/81 + (-1936872*x**2 + 2088576*x - 591577)/(19683*x**3 - 39366*x**2 + 26244*x - 5832) + 19712*log(3*x - 2)/243 | MATH |
[
{
"content": "Determine ∫(-1(4((1x - 2)/(-3x - 1)) - 1)^2 + 5(4((1x - 2)/(-3x - 1)) - 1) - 2) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -172*x/9 + 812*log(3*x + 1)/27 + 784/(81*x + 27) | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = (3x + 1)/(2x + 2)? Express your answer in terms of x and do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3*x/2 - log(x + 1) | MATH |
[
{
"content": "Find the indefinite integral of f(x) = (1x + 1)/(-1x - 2) with respect to x. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -x + log(x + 2) | MATH |
[
{
"content": "Determine ∫(1cos(3π(-1x + 1) + 1) - 2) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2*x - sin(3*pi*(1 - x) + 1)/(3*pi) | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = 4(-2e^(-2(-4x - 1)) - 1)^2 - 2(-2e^(-2(-4x - 1)) - 1)? Express your answer in terms of x and do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6*x + 5*exp(8*x + 2)/2 + exp(16*x + 4) | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = -2(1e^(-2(-1x - 5)) - 1)^2 + 2(1e^(-2(-1x - 5)) - 1) + 2? Express your answer in terms of x and do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2*x + 3*exp(2*x + 10) - exp(4*x + 20)/2 | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = 5(1(2x^2 - 3x)) + 5? Express your answer in terms of x and do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 10*x**3/3 - 15*x**2/2 + 5*x | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = (-2x)/(-3x - 2). Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2*x/3 - 4*log(3*x + 2)/9 | MATH |
[
{
"content": "Determine ∫(-4((2(2x - 5) + 2)/(-1(2x - 5) - 1)) - 1) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7*x | MATH |
[
{
"content": "Determine ∫((1(5x^2 + 3x - 1) + 3)/(-3(5x^2 + 3x - 1) - 1)) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -x/3 + 8*sqrt(201)*log(x + 3/10 + sqrt(201)/30)/603 - 8*sqrt(201)*log(x - sqrt(201)/30 + 3/10)/603 | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = (1(2(-1x^2 + 1x - 5) + 4) - 2)/(2(2(-1x^2 + 1x - 5) + 4))? Express your answer in terms of x and do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | x/2 + sqrt(11)*atan(2*sqrt(11)*x/11 - sqrt(11)/11)/11 | MATH |
[
{
"content": "Find the indefinite integral of f(x) = -2((1x + 3)/(1x + 3)) + 5 with respect to x. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3*x | MATH |
[
{
"content": "Determine ∫((1(-5x + 2) + 1)/(-1(-5x + 2) - 1)) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -x | MATH |
[
{
"content": "Determine ∫(-2(-4(-5x - 1)) - 5) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -20*x**2 - 13*x | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = -4((-3x + 1)/(2x + 1))^2 - 1((-3x + 1)/(2x + 1)) + 2. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -11*x/2 + 55*log(2*x + 1)/4 + 25/(4*x + 2) | MATH |
[
{
"content": "Determine ∫((-1x + 1)/(2x)) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -x/2 + log(x)/2 | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = 4x + 1? Express your answer in terms of x and do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2*x**2 + x | MATH |
[
{
"content": "Determine ∫((-2((-1(-4x - 4) - 1)/(2(-4x - 4) + 2)) - 3)/(3((-1(-4x - 4) - 1)/(2(-4x - 4) + 2)) - 2)) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4*x/7 | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = 5(5(-5x^2 - 2) - 5)^2 - 2(5(-5x^2 - 2) - 5) - 5. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 625*x**5 + 3800*x**3/3 + 1150*x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = (-1(2e^(2x) - 3) - 2)/(-3(2e^(2x) - 3))? Express your answer in terms of x and do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | x/9 + log(exp(2*x) - 3/2)/9 | MATH |
[
{
"content": "Determine ∫(-2((-2(-3x^2 + 3x - 2) - 2)/(-2(-3x^2 + 3x - 2) + 3)) - 4) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -6*x + 10*sqrt(33)*atan(2*sqrt(33)*x/11 - sqrt(33)/11)/33 | MATH |
[
{
"content": "Determine ∫(-1(5x^2 + 5x - 3)^2 + 5(5x^2 + 5x - 3) - 1) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -5*x**5 - 25*x**4/2 + 10*x**3 + 55*x**2/2 - 25*x | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = -4(-2((-1x + 1)/(1x - 3))^2 - 4((-1x + 1)/(1x - 3)) - 2)^2 + 4(-2((-1x + 1)/(1x - 3))^2 - 4((-1x + 1)/(1x - 3)) - 2) + 4. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4*x + (96*x**2 - 576*x + 1120)/(3*x**3 - 27*x**2 + 81*x - 81) | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = -2((1x - 3)/(2x + 1))^2 + 2((1x - 3)/(2x + 1)) - 3. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -5*x/2 + 49/(8*x + 4) | MATH |
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