messages listlengths 1 1 | ground_truth stringlengths 1 3.09k | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Compute the indefinite integral for f(x) = 1x^2 - 5x + 1. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | x**3/3 - 5*x**2/2 + x | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = 2x^2 + 4x. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2*x**3/3 + 2*x**2 | MATH |
[
{
"content": "Determine ∫(4x - 3) 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": "Compute the indefinite integral for f(x) = (-1((2(2x^2 + 1x + 2) + 3)/(-1(2x^2 + 1x + 2) + 2)) - 1)/(3((2(2x^2 + 1x + 2) + 3)/(-1(2x^2 + 1x + 2) + 2)) - 2). Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -x/8 - 7*sqrt(5)*atan(2*sqrt(5)*x/5 + sqrt(5)/10)/64 | MATH |
[
{
"content": "Determine ∫((-2x)/(-2x + 1)) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | x + log(2*x - 1)/2 | MATH |
[
{
"content": "Determine ∫((3((1((2x + 1)/(2x - 3)) + 1)/(3((2x + 1)/(2x - 3)) - 2)))/(-3((1((2x + 1)/(2x - 3)) + 1)/(3((2x + 1)/(2x - 3)) - 2)) + 4)) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -3*x - 30*log(2*x - 21) | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = -4(-4(-4x^2 + 4x + 2) - 4)^2 + 5(-4(-4x^2 + 4x + 2) - 4) + 1. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1024*x**5/5 + 512*x**4 + 592*x**3/3 - 808*x**2 - 635*x | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = -2(3x + 2)^2 + 3(3x + 2) + 1. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -6*x**3 - 15*x**2/2 - x | MATH |
[
{
"content": "Determine ∫(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"
}
] | -x**2 + 4*x | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = 1cos(3π(2x - 4) - 1) - 3. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -3*x + sin(3*pi*(2*x - 4) - 1)/(6*pi) | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = -1x^2 + 4x + 4. 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 + 4*x | MATH |
[
{
"content": "Find the indefinite integral of f(x) = -2sin(3π(-1x - 2) + 3) - 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"
}
] | -x - 2*cos(3*pi*(-x - 2) + 3)/(3*pi) | MATH |
[
{
"content": "Find the indefinite integral of f(x) = (1(-3x + 2) - 3)/(-2(-3x + 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": "user"
}
] | -x/2 - 3*log(6*x - 7)/4 | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = -2e^(1(-1x^2 - 1x - 5)) + 2. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2*x - sqrt(pi)*exp(-19/4)*erf(x + 1/2) | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = (-2x + 2)/(1x). Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2*x + 2*log(x) | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = (-2x - 3)/(-3x - 3). Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2*x/3 + log(x + 1)/3 | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = (-1((1(-1x - 2) - 1)/(3(-1x - 2) - 1)) + 3)/(3((1(-1x - 2) - 1)/(3(-1x - 2) - 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}",
"... | 2*x/3 - log(2*x + 5)/6 | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = 2(-4x^2 - 3x - 5) - 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"
}
] | -8*x**3/3 - 3*x**2 - 11*x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = 2x - 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 - 5*x | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = (-2x + 3)/(-1x - 1). Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2*x - 5*log(x + 1) | MATH |
[
{
"content": "Determine ∫((-2x + 2)/(-1x + 3)) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2*x + 4*log(x - 3) | MATH |
[
{
"content": "Find the indefinite integral of f(x) = 2(-2sin(2π(2x - 3) - 1) - 1) + 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"
}
] | 2*x + cos(2*pi*(2*x - 3) - 1)/pi | MATH |
[
{
"content": "Determine ∫(-5x^2 - 3x - 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 - 3*x**2/2 - 4*x | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = -1(5x - 4) + 5. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -5*x**2/2 + 9*x | MATH |
[
{
"content": "Determine ∫(2sin(2π(-3x - 5)) + 3) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3*x + cos(pi*(6*x + 10))/(3*pi) | MATH |
[
{
"content": "Find the indefinite integral of f(x) = (3(3x^2 - 1) - 3)/(-3(3x^2 - 1) - 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"
}
] | -x + sqrt(2)*log(x - sqrt(2)/3)/3 - sqrt(2)*log(x + sqrt(2)/3)/3 | MATH |
[
{
"content": "Determine ∫((2x - 1)/(2x + 3)) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | x - 2*log(2*x + 3) | MATH |
[
{
"content": "Determine ∫(1x^2 - 1x - 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 - x**2/2 - x | MATH |
[
{
"content": "Find the indefinite integral of f(x) = (-2x - 3)/(2x - 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"
}
] | -x - 2*log(2*x - 1) | MATH |
[
{
"content": "Determine ∫(3x^2 + 3x) dx. 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 | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = (-2x - 1)/(1x)? 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 - log(x) | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = -4x + 2. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2*x**2 + 2*x | MATH |
[
{
"content": "Find the indefinite integral of f(x) = (-2(1x^2 - 3x + 3) + 2)/(-1(1x^2 - 3x + 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"
}
] | 2*x + 2*sqrt(5)*log(x - 3/2 - sqrt(5)/2)/5 - 2*sqrt(5)*log(x - 3/2 + sqrt(5)/2)/5 | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = -5x^2 - 3x - 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"
}
] | -5*x**3/3 - 3*x**2/2 - 3*x | MATH |
[
{
"content": "Determine ∫(-1x + 2) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -x**2/2 + 2*x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = 3x + 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**2/2 + 3*x | 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 - log(2*x - 1)/4 | MATH |
[
{
"content": "Determine ∫(-3(4((3x + 3)/(2x + 1)) + 1)^2 - 1(4((3x + 3)/(2x + 1)) + 1) + 3) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -151*x - 129*log(2*x + 1) + 54/(2*x + 1) | 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": "Find the indefinite integral of f(x) = -1(-2e^(-1x))^2 + 5(-2e^(-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"
}
] | x + 10*exp(-x) + 2*exp(-2*x) | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = (-1x)/(3x + 3). 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": "Compute the indefinite integral for f(x) = -1(1x^2 - 1x - 2)^2 - 4(1x^2 - 1x - 2) + 4. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -x**5/5 + x**4/2 - x**3/3 + 8*x | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = 2((-1x - 3)/(-2x - 2))^2 + 2((-1x - 3)/(-2x - 2)) + 5. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 13*x/2 + 4*log(x + 1) - 2/(x + 1) | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = -2e^(-1(-3x + 5)) + 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*exp(3*x - 5)/3 | MATH |
[
{
"content": "Find the indefinite integral of f(x) = -3x + 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"
}
] | -3*x**2/2 + 2*x | MATH |
[
{
"content": "Determine ∫(-5x^2 + 2x - 3) 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 + x**2 - 3*x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = -3x - 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**2/2 - x | MATH |
[
{
"content": "Find the indefinite integral of f(x) = (3(-5(4x + 4)^2 + 5(4x + 4) - 2) - 2)/(3(-5(4x + 4)^2 + 5(4x + 4) - 2) + 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 + 2*sqrt(15)*atan(8*sqrt(15)*x + 7*sqrt(15))/15 | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = (1x + 3)/(-3x + 2). Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -x/3 - 11*log(3*x - 2)/9 | MATH |
[
{
"content": "Determine ∫(1(-5((1x + 1)/(3x - 1))^2 + 5((1x + 1)/(3x - 1)) + 5) - 2) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 37*x/9 + 20*log(3*x - 1)/27 + 80/(81*x - 27) | MATH |
[
{
"content": "Determine ∫((1(4(2x^2 + 1x + 1)^2 + 3(2x^2 + 1x + 1) + 1) + 3)/(-3(4(2x^2 + 1x + 1)^2 + 3(2x^2 + 1x + 1) + 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 - sqrt(20/549 + 2*sqrt(915)/1647)*log(x**2 + x*(-2*sqrt(10)*sqrt(30 + sqrt(915)) - 119*sqrt(366)*sqrt(30 + sqrt(915))/732 + 1/2 + 3*sqrt(610)*sqrt(30 + sqrt(915))*sqrt(4*sqrt(915) + 121)/122) - 72541*sqrt(15)*sqrt(4*sqrt(915) + 121)/2928 - 2985*sqrt(61)*sqrt(4*sqrt(915) + 121)/244 - sqrt(10)*sqrt(30 + sqrt(915))/2 - 119*sqrt(366)*sqrt(30 + sqrt(915))/2928 + 3*sqrt(610)*sqrt(30 + sqrt(915))*sqrt(4*sqrt(915) + 121)/488 + 1453811/976 + 72121*sqrt(915)/1464) + sqrt(20/549 + 2*sqrt(915)/1647)*log(x**2 + x*(-3*sqrt(610)*sqrt(30 + sqrt(915))*sqrt(4*sqrt(915) + 121)/122 + 1/2 + 119*sqrt(366)*sqrt(30 + sqrt(915))/732 + 2*sqrt(10)*sqrt(30 + sqrt(915))) - 72541*sqrt(15)*sqrt(4*sqrt(915) + 121)/2928 - 2985*sqrt(61)*sqrt(4*sqrt(915) + 121)/244 - 3*sqrt(610)*sqrt(30 + sqrt(915))*sqrt(4*sqrt(915) + 121)/488 + 119*sqrt(366)*sqrt(30 + sqrt(915))/2928 + sqrt(10)*sqrt(30 + sqrt(915))/2 + 1453811/976 + 72121*sqrt(915)/1464) - 2*sqrt(-4*sqrt(15)*sqrt(4*sqrt(915) + 121)/1647 + 20/549 + 2*sqrt(915)/549)*atan(12*sqrt(122)*x/(sqrt(3)*sqrt(-2*sqrt(15)*sqrt(4*sqrt(915) + 121) + 30 + 3*sqrt(915)) + 6*sqrt(5)*sqrt(4*sqrt(915) + 121)*sqrt(-2*sqrt(15)*sqrt(4*sqrt(915) + 121) + 30 + 3*sqrt(915))) - 24*sqrt(305)*sqrt(30 + sqrt(915))/(sqrt(3)*sqrt(-2*sqrt(15)*sqrt(4*sqrt(915) + 121) + 30 + 3*sqrt(915)) + 6*sqrt(5)*sqrt(4*sqrt(915) + 121)*sqrt(-2*sqrt(15)*sqrt(4*sqrt(915) + 121) + 30 + 3*sqrt(915))) - 119*sqrt(3)*sqrt(30 + sqrt(915))/(sqrt(3)*sqrt(-2*sqrt(15)*sqrt(4*sqrt(915) + 121) + 30 + 3*sqrt(915)) + 6*sqrt(5)*sqrt(4*sqrt(915) + 121)*sqrt(-2*sqrt(15)*sqrt(4*sqrt(915) + 121) + 30 + 3*sqrt(915))) + 3*sqrt(122)/(sqrt(3)*sqrt(-2*sqrt(15)*sqrt(4*sqrt(915) + 121) + 30 + 3*sqrt(915)) + 6*sqrt(5)*sqrt(4*sqrt(915) + 121)*sqrt(-2*sqrt(15)*sqrt(4*sqrt(915) + 121) + 30 + 3*sqrt(915))) + 18*sqrt(5)*sqrt(30 + sqrt(915))*sqrt(4*sqrt(915) + 121)/(sqrt(3)*sqrt(-2*sqrt(15)*sqrt(4*sqrt(915) + 121) + 30 + 3*sqrt(915)) + 6*sqrt(5)*sqrt(4*sqrt(915) + 121)*sqrt(-2*sqrt(15)*sqrt(4*sqrt(915) + 121) + 30 + 3*sqrt(915)))) - 2*sqrt(-4*sqrt(15)*sqrt(4*sqrt(915) + 121)/1647 + 20/549 + 2*sqrt(915)/549)*atan(12*sqrt(122)*x/(sqrt(3)*sqrt(-2*sqrt(15)*sqrt(4*sqrt(915) + 121) + 30 + 3*sqrt(915)) + 6*sqrt(5)*sqrt(4*sqrt(915) + 121)*sqrt(-2*sqrt(15)*sqrt(4*sqrt(915) + 121) + 30 + 3*sqrt(915))) - 18*sqrt(5)*sqrt(30 + sqrt(915))*sqrt(4*sqrt(915) + 121)/(sqrt(3)*sqrt(-2*sqrt(15)*sqrt(4*sqrt(915) + 121) + 30 + 3*sqrt(915)) + 6*sqrt(5)*sqrt(4*sqrt(915) + 121)*sqrt(-2*sqrt(15)*sqrt(4*sqrt(915) + 121) + 30 + 3*sqrt(915))) + 3*sqrt(122)/(sqrt(3)*sqrt(-2*sqrt(15)*sqrt(4*sqrt(915) + 121) + 30 + 3*sqrt(915)) + 6*sqrt(5)*sqrt(4*sqrt(915) + 121)*sqrt(-2*sqrt(15)*sqrt(4*sqrt(915) + 121) + 30 + 3*sqrt(915))) + 119*sqrt(3)*sqrt(30 + sqrt(915))/(sqrt(3)*sqrt(-2*sqrt(15)*sqrt(4*sqrt(915) + 121) + 30 + 3*sqrt(915)) + 6*sqrt(5)*sqrt(4*sqrt(915) + 121)*sqrt(-2*sqrt(15)*sqrt(4*sqrt(915) + 121) + 30 + 3*sqrt(915))) + 24*sqrt(305)*sqrt(30 + sqrt(915))/(sqrt(3)*sqrt(-2*sqrt(15)*sqrt(4*sqrt(915) + 121) + 30 + 3*sqrt(915)) + 6*sqrt(5)*sqrt(4*sqrt(915) + 121)*sqrt(-2*sqrt(15)*sqrt(4*sqrt(915) + 121) + 30 + 3*sqrt(915)))) | MATH |
[
{
"content": "Find the indefinite integral of f(x) = -2sin(3π(-1x + 1) - 1) - 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"
}
] | -x - 2*cos(3*pi*(1 - x) - 1)/(3*pi) | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = -3(1x - 5) + 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**2/2 + 16*x | MATH |
[
{
"content": "Find the indefinite integral of f(x) = (-2x)/(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"
}
] | -2*x - 6*log(x - 3) | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = -3(5x^2 - 5x + 3)^2 - 2(5x^2 - 5x + 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"
}
] | -15*x**5 + 75*x**4/2 - 175*x**3/3 + 50*x**2 - 36*x | MATH |
[
{
"content": "Determine ∫((1(-2x^2 - 5x + 4))/(1(-2x^2 - 5x + 4))) 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 ∫(-4x + 2) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2*x**2 + 2*x | MATH |
[
{
"content": "Find the indefinite integral of f(x) = (2(-1e^(-1x)) + 1)/(3(-1e^(-1x))) 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 - exp(x)/3 | MATH |
[
{
"content": "Determine ∫((-3(4(-3x^2 - 1)^2 - 2(-3x^2 - 1) - 5) + 3)/(-3(4(-3x^2 - 1)^2 - 2(-3x^2 - 1) - 5) + 1)) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | x + 2*sqrt(5/1608 - sqrt(201)/4824)*atan(12*sqrt(2)*x/(sqrt(67)*sqrt(15 - sqrt(201)) + 5*sqrt(3)*sqrt(15 - sqrt(201)))) - 2*sqrt(sqrt(201)/4824 + 5/1608)*atan(12*sqrt(2)*x/(-sqrt(67)*sqrt(sqrt(201) + 15) + 5*sqrt(3)*sqrt(sqrt(201) + 15))) | MATH |
[
{
"content": "Determine ∫(-3(-1e^(-1x) - 1) + 1) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4*x - 3*exp(-x) | MATH |
[
{
"content": "Find the indefinite integral of f(x) = (2(-5(3e^(1x))) - 3)/(3(-5(3e^(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"
}
] | 3*x/2 - 5*log(exp(x) + 2/45)/6 | MATH |
[
{
"content": "Determine ∫(1x^2 - 1x) dx. 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 | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = -4x - 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**2 - 2*x | MATH |
[
{
"content": "Determine ∫(-2((3(4x - 4))/(1(4x - 4) + 1)) + 3) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -3*x + 3*log(4*x - 3)/2 | MATH |
[
{
"content": "Determine ∫(-2(-5(-5x^2 - 1x - 2)^2 + 1(-5x^2 - 1x - 2) + 2)^2 - 4(-5(-5x^2 - 1x - 2)^2 + 1(-5x^2 - 1x - 2) + 2) - 5) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -31250*x**9/9 - 3125*x**8 - 60000*x**7/7 - 16250*x**6/3 - 7580*x**5 - 3260*x**4 - 9242*x**3/3 - 798*x**2 - 725*x | MATH |
[
{
"content": "Find the indefinite integral of f(x) = -1e^(1(3x - 3)) + 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"
}
] | 3*x - exp(3*x - 3)/3 | MATH |
[
{
"content": "Determine ∫((-2x - 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 | MATH |
[
{
"content": "Determine ∫((-1(-1cos(3πx + 1) - 3) + 3)/(1(-1cos(3πx + 1) - 3) - 3)) 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(-2x^2 + 4x + 5) - 1)/(3(-2x^2 + 4x + 5) + 2)) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2*x/3 - 7*sqrt(138)*log(x - 1 + sqrt(138)/6)/828 + 7*sqrt(138)*log(x - sqrt(138)/6 - 1)/828 | MATH |
[
{
"content": "Find the indefinite integral of f(x) = (2(-5x^2 + 5x - 5) + 2)/(-1(-5x^2 + 5x - 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 - 4*sqrt(35)*atan(2*sqrt(35)*x/7 - sqrt(35)/7)/35 | MATH |
[
{
"content": "Find the indefinite integral of f(x) = -1(1((-1x + 2)/(2x - 3))^2 - 1((-1x + 2)/(2x - 3)) + 3)^2 + 3(1((-1x + 2)/(2x - 3))^2 - 1((-1x + 2)/(2x - 3)) + 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": "... | -13*x/16 - (-408*x**2 + 1248*x - 955)/(768*x**3 - 3456*x**2 + 5184*x - 2592) + 9*log(2*x - 3)/4 | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = (2((-2(1x^2 + 3x - 1) - 2)/(-2(1x^2 + 3x - 1) + 3)) + 3)/(1((-2(1x^2 + 3x - 1) - 2)/(-2(1x^2 + 3x - 1) + 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: \... | -5*x/2 + 15*sqrt(6)*log(x + 3/2 + sqrt(6))/32 - 15*sqrt(6)*log(x - sqrt(6) + 3/2)/32 | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = -1x? 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 | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = -4((-1(3x^2 + 3x + 1) + 3)/(-3(3x^2 + 3x + 1)))^2 + 3((-1(3x^2 + 3x + 1) + 3)/(-3(3x^2 + 3x + 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... | -22*x/9 - (8*x + 4)/(3*x**2 + 3*x + 1) - 50*sqrt(3)*atan(2*sqrt(3)*x + sqrt(3))/9 | MATH |
[
{
"content": "Find the indefinite integral of f(x) = (-1(-5(3x^2 + 4x - 3) - 3) - 2)/(-3(-5(3x^2 + 4x - 3) - 3) - 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/3 + sqrt(295)*log(x + 2/3 + sqrt(295)/15)/1770 - sqrt(295)*log(x - sqrt(295)/15 + 2/3)/1770 | MATH |
[
{
"content": "Find the indefinite integral of f(x) = -1cos(2π(-2x + 5) - 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"
}
] | -2*x + sin(2*pi*(5 - 2*x) - 1)/(4*pi) | MATH |
[
{
"content": "Determine ∫(1cos(3π(-1(5x + 3) + 2)) + 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(pi*(15*x + 3))/(15*pi) | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = 2(-1cos(1π(-3x - 5) + 3) - 2)^2 + 3(-1cos(1π(-3x - 5) + 3) - 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"
}
] | x*sin(3*pi*x - 3)**2 + x*cos(3*pi*x - 3)**2 - 3*x + sin(3*pi*x - 3)*cos(3*pi*x - 3)/(3*pi) - 8*sin(3*pi*x - 3)/(3*pi) + sin(pi*(-3*x - 5) + 3)/pi | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = 1(-3(-2x - 2) - 5) - 3. 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": "Find the indefinite integral of f(x) = -2x^2 - 3x - 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"
}
] | -2*x**3/3 - 3*x**2/2 - 3*x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = (1(-2x + 5) - 2)/(-1(-2x + 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"
}
] | -x - 2*log(2*x - 7) | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = (2(-1(-3e^(-1x))^2 - 5(-3e^(-1x)) - 2) - 1)/(-2(-1(-3e^(-1x))^2 - 5(-3e^(-1x)) - 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}",
... | -5*x/7 + RootSum(77*_z**2 - 22*_z - 2, Lambda(_i, _i*log(77*_i/30 - 6/5 + exp(-x)))) | MATH |
[
{
"content": "Determine ∫((-3(-1x^2 - 2x + 4) + 2)/(2(-1x^2 - 2x + 4) - 1)) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -3*x/2 + sqrt(2)*log(x + 1 + 3*sqrt(2)/2)/24 - sqrt(2)*log(x - 3*sqrt(2)/2 + 1)/24 | MATH |
[
{
"content": "Find the indefinite integral of f(x) = -4((3((-3x)/(-3x + 2)) + 1)/(2((-3x)/(-3x + 2)) - 3))^2 + 1((3((-3x)/(-3x + 2)) + 1)/(2((-3x)/(-3x + 2)) - 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... | -63*x - 242*log(x - 2) + 1936/(9*x - 18) | MATH |
[
{
"content": "Find the indefinite integral of f(x) = 2x - 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**2 - 2*x | MATH |
[
{
"content": "Determine ∫(-4(-1e^(-2(-5x + 5)) + 2) - 4) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -12*x + 2*exp(10*x - 10)/5 | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = (1x - 1)/(1x). Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | x - log(x) | MATH |
[
{
"content": "Determine ∫(5((3x + 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"
}
] | 4*x + 5*log(3*x - 1) | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = -1((1x + 3)/(3x - 2))^2 + 2((1x + 3)/(3x - 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"
}
] | -13*x/9 + 44*log(3*x - 2)/27 + 121/(81*x - 54) | MATH |
[
{
"content": "Determine ∫(-3x^2 - 5) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -x**3 - 5*x | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = -4(3e^(1x) - 1) - 3. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | x - 12*exp(x) | MATH |
[
{
"content": "Find the indefinite integral of f(x) = 3x^2 + 1x 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 + x**2/2 | MATH |
[
{
"content": "Determine ∫((3x - 3)/(-3x)) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -x + log(x) | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = (3x + 3)/(-1x - 1). 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 ∫(2(1(-3x^2 - 5x) - 1)^2) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 18*x**5/5 + 15*x**4 + 62*x**3/3 + 10*x**2 + 2*x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = 4x + 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"
}
] | 2*x**2 + 5*x | MATH |
[
{
"content": "Find the indefinite integral of f(x) = 2((1x + 3)/(1x + 3)) + 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"
}
] | 5*x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = -1(1(3x^2 + 1x - 3)^2 - 2(3x^2 + 1x - 3) - 3)^2 - 3(1(3x^2 + 1x - 3)^2 - 2(3x^2 + 1x - 3) - 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 ans... | -9*x**9 - 27*x**8/2 + 54*x**7 + 70*x**6 - 676*x**5/5 - 265*x**4/2 + 557*x**3/3 + 108*x**2 - 181*x | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = -4(1x + 3)^2 + 3(1x + 3). Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -4*x**3/3 - 21*x**2/2 - 27*x | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = (3(3x - 3))/(-2(3x - 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 + 3*log(2*x - 1)/4 | MATH |
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