messages listlengths 1 1 | ground_truth stringlengths 1 3.09k | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Find the indefinite integral of f(x) = (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"
}
] | 2*x + 9*log(x - 3) | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = 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"
}
] | x**2/2 - 2*x | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = -4((3x)/(-3x - 1))^2 - 2((3x)/(-3x - 1)) - 2. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -4*x + 2*log(3*x + 1) + 4/(9*x + 3) | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = 4(-2e^(2x) + 1)^2 - 3(-2e^(2x) + 1) - 5. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -4*x + 4*exp(4*x) - 5*exp(2*x) | MATH |
[
{
"content": "Find the indefinite integral of f(x) = 4(-1e^(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"
}
] | 3*x - 4*exp(x) | 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": "Determine ∫(-5x^2 + 2x + 2) 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 + 2*x | MATH |
[
{
"content": "Find the indefinite integral of f(x) = -3(1e^(-2(-1x - 4)) - 2) - 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"
}
] | 5*x - 3*exp(2*x + 8)/2 | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = -3x - 1. 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": "Compute the indefinite integral for f(x) = 1e^(2(-1x^2 + 2x + 2)). Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | sqrt(2)*sqrt(pi)*exp(6)*erf(sqrt(2)*(4*x - 4)/4)/4 | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = 4(-2e^(-2x) + 2)^2 + 2. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 18*x + 16*exp(-2*x) - 4*exp(-4*x) | MATH |
[
{
"content": "Find the indefinite integral of f(x) = 4x^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"
}
] | 4*x**3/3 + 3*x**2/2 - 4*x | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = -1(-2((2x - 1)/(-3x - 2)) - 2). Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2*x/3 + 14*log(3*x + 2)/9 | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = -4x - 4. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2*x**2 - 4*x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = 1(5((-3x + 3)/(2x - 3)) - 1)^2 - 2(5((-3x + 3)/(2x - 3)) - 1) + 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"
}
] | 377*x/4 + 285*log(2*x - 3)/4 - 225/(16*x - 24) | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = -3x^2 + 2x + 1. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -x**3 + x**2 + x | MATH |
[
{
"content": "Find the indefinite integral of f(x) = -1x + 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**2/2 + 4*x | MATH |
[
{
"content": "Find the indefinite integral of f(x) = -4x^2 - 3x + 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"
}
] | -4*x**3/3 - 3*x**2/2 + 5*x | MATH |
[
{
"content": "Determine ∫((-2(-1e^(-2(-2x - 5))) + 3)/(-1(-1e^(-2(-2x - 5))) - 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(exp(4*x + 10) - 3)/4 | MATH |
[
{
"content": "Find the indefinite integral of f(x) = 1e^(-1(-5x^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"
}
] | -3*x + sqrt(5)*sqrt(pi)*erfi(sqrt(5)*x)/10 | MATH |
[
{
"content": "Determine ∫(-1cos(3π(4x) - 1) - 1) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -x - sin(12*pi*x - 1)/(12*pi) | MATH |
[
{
"content": "Determine ∫((-3(-1(-1x + 2)^2 + 4(-1x + 2) - 2) - 3)/(-2(-1(-1x + 2)^2 + 4(-1x + 2) - 2) + 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 - 15*sqrt(2)*log(x - sqrt(2)/2)/8 + 15*sqrt(2)*log(x + sqrt(2)/2)/8 | MATH |
[
{
"content": "Find the indefinite integral of f(x) = (-3(-3(2e^(-1x) - 3)^2 + 5(2e^(-1x) - 3) + 4) - 2)/(1(-3(2e^(-1x) - 3)^2 + 5(2e^(-1x) - 3) + 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"
}
] | -56*x/19 + RootSum(1387*_z**2 - 73*_z - 6, Lambda(_i, _i*log(1387*_i/138 - 301/138 + exp(-x)))) | 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": "What is the symbolic antiderivative of the function f(x) = 2x^2 + 1x + 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"
}
] | 2*x**3/3 + x**2/2 + 3*x | MATH |
[
{
"content": "Determine ∫((3x - 1)/(2x - 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 + log(2*x - 1)/4 | MATH |
[
{
"content": "Determine ∫(2(-3x^2 + 1x - 4)^2 - 4(-3x^2 + 1x - 4) - 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 - 3*x**4 + 62*x**3/3 - 10*x**2 + 46*x | MATH |
[
{
"content": "Determine ∫(4(-4((2x - 3)/(3x - 2))) + 4) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -20*x/3 + 80*log(3*x - 2)/9 | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = 2e^(2(-5(-4x^2 - 1x) - 5)) + 3. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3*x + sqrt(10)*sqrt(pi)*exp(-85/8)*erfi(sqrt(10)*(80*x + 10)/40)/20 | MATH |
[
{
"content": "Determine ∫(3x - 4) 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 - 4*x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = -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"
}
] | -3*x**2/2 + 5*x | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = (-1x - 2)/(-3x + 4). Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | x/3 + 10*log(3*x - 4)/9 | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = (-3((3(-2x^2 + 4) + 1)/(1(-2x^2 + 4))) - 1)/(1((3(-2x^2 + 4) + 1)/(1(-2x^2 + 4))) + 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}",
"... | -2*x + sqrt(210)*log(x - sqrt(210)/10)/420 - sqrt(210)*log(x + sqrt(210)/10)/420 | MATH |
[
{
"content": "Find the indefinite integral of f(x) = 1(-2x - 4) + 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 - 3*x | MATH |
[
{
"content": "Determine ∫(-5x^2 + 2x - 1) 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 - x | MATH |
[
{
"content": "Determine ∫((3(4(5x - 3) + 1) - 3)/(2(4(5x - 3) + 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/2 - 9*log(40*x - 21)/80 | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = (-2x - 1)/(-1x + 2). 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 - 2) | MATH |
[
{
"content": "Determine ∫(-1(4x - 5) - 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 + 2*x | MATH |
[
{
"content": "Determine ∫(1((-1((-2x + 2)/(-2x + 3)) - 1)/(2((-2x + 2)/(-2x + 3)) - 3)) + 1) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3*x + 5*log(2*x - 5)/2 | 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": "Compute the indefinite integral for f(x) = -3x - 1. 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": "What is the symbolic antiderivative of the function f(x) = -3(-4x - 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**2 + 2*x | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = 5(-1e^(-2x) - 1)^2 - 1(-1e^(-2x) - 1) + 2. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8*x - 11*exp(-2*x)/2 - 5*exp(-4*x)/4 | MATH |
[
{
"content": "Find the indefinite integral of f(x) = (3(-2((-1x + 2)/(-3x)) + 5) + 1)/(1(-2((-1x + 2)/(-3x)) + 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"
}
] | 42*x/13 - 12*log(13*x + 4)/169 | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = -2(2(-3x^2 + 2x - 2) - 1) + 3. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4*x**3 - 4*x**2 + 13*x | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = -2x^2 + 1x - 4. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2*x**3/3 + x**2/2 - 4*x | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = (-2x + 3)/(2x + 3). Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -x + 3*log(2*x + 3) | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = 2(4x^2 + 5x - 4)^2 - 2(4x^2 + 5x - 4). Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 32*x**5/5 + 20*x**4 - 22*x**3/3 - 45*x**2 + 40*x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = (1(2x^2 - 1x - 4))/(2(2x^2 - 1x - 4) - 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 - sqrt(37)*log(x - 1/4 + sqrt(37)/4)/148 + sqrt(37)*log(x - sqrt(37)/4 - 1/4)/148 | MATH |
[
{
"content": "Determine ∫(1x^2 - 1x - 5) 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 - 5*x | MATH |
[
{
"content": "Determine ∫(4x^2 + 3x - 3) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4*x**3/3 + 3*x**2/2 - 3*x | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = -1((-1(-1x^2 + 2x - 1) - 3)/(-2(-1x^2 + 2x - 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(x)/2 + log(x - 2)/2 | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = (3(3sin(1π(-2x - 1) + 1) - 2) - 1)/(-3(3sin(1π(-2x - 1) + 1) - 2) + 1). Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = -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**2/2 - 4*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": "Find the indefinite integral of f(x) = 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"
}
] | 3*x**2/2 + 3*x | MATH |
[
{
"content": "Determine ∫((2((-3x - 2)/(3x)) + 2)/(3((-3x - 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*log(3*x + 3)/3 | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = -2(-1x^2 - 5x + 3) - 1. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2*x**3/3 + 5*x**2 - 7*x | MATH |
[
{
"content": "Determine ∫((3(1e^(1x) - 2) + 2)/(-1(1e^(1x) - 2) - 1)) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -4*x + log(exp(x) - 1) | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = (-3(1x^2 - 5x + 5) + 1)/(-3(1x^2 - 5x + 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"
}
] | x - 2*sqrt(33)*log(x - 5/2 - sqrt(33)/6)/33 + 2*sqrt(33)*log(x - 5/2 + sqrt(33)/6)/33 | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = -3e^(-2(-4x - 1)) + 3. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3*x - 3*exp(8*x + 2)/8 | MATH |
[
{
"content": "Find the indefinite integral of f(x) = -1((-1x - 3)/(-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 - log(x + 1) | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = (1((-2x - 3)/(-1x - 3)) - 3)/(2((-2x - 3)/(-1x - 3)) + 3). Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -x/7 - 27*log(7*x + 15)/49 | MATH |
[
{
"content": "Find the indefinite integral of f(x) = -2((-1((-1x - 1)/(3x)) + 2)/(1((-1x - 1)/(3x)) + 2)) - 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"
}
] | -19*x/5 - 24*log(5*x - 1)/25 | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = 1x - 1. 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": "Find the indefinite integral of f(x) = -4x - 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"
}
] | -2*x**2 - 5*x | 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": "Compute the indefinite integral for f(x) = -4x^2 - 3x + 5. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -4*x**3/3 - 3*x**2/2 + 5*x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = 4(-5((-2x - 3)/(1x + 3))^2 + 5((-2x - 3)/(1x + 3)) + 4)^2 - 5(-5((-2x - 3)/(1x + 3))^2 + 5((-2x - 3)/(1x + 3)) + 4) + 2? Express your answer in terms of x and do not include the constant of integration C.\n\nPresent the answer in LaTex for... | 2836*x + (-32085*x**2 - 179010*x - 250965)/(x**3 + 9*x**2 + 27*x + 27) - 15975*log(x + 3) | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = (3((1x + 1)/(1x + 2)))/(1((1x + 1)/(1x + 2))). Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3*x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = (2(-2x - 3))/(2(-2x - 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"
}
] | x + log(x + 1)/2 | MATH |
[
{
"content": "Find the indefinite integral of f(x) = -5(-1x^2 + 1x + 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"
}
] | 5*x**3/3 - 5*x**2/2 - 12*x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = (1((-2x + 1)/(1x - 2)) - 2)/(2((-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"
}
] | x - 3*log(2*x - 1)/4 | MATH |
[
{
"content": "Determine ∫(3(-2e^(1x) + 3) + 2) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11*x - 6*exp(x) | MATH |
[
{
"content": "Find the indefinite integral of f(x) = (-2x - 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"
}
] | -2*x + 3*log(x + 2) | MATH |
[
{
"content": "Determine ∫(-3(1x^2 - 3x + 1) + 3) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -x**3 + 9*x**2/2 | MATH |
[
{
"content": "Determine ∫(-2(-1x^2 + 5x + 4) + 2) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2*x**3/3 - 5*x**2 - 6*x | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = -4x - 1. 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(-3x^2 - 1x + 4) - 1)/(2(-3x^2 - 1x + 4))) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | x + log(x - 1)/14 - log(x + 4/3)/14 | MATH |
[
{
"content": "Determine ∫(3cos(1π(-1x + 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 + 3*sin(pi*(x - 2))/pi | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = 3(-4((2x + 3)/(-2x + 3))^2 - 5((2x + 3)/(-2x + 3)) - 3)^2 + 1(-4((2x + 3)/(-2x + 3))^2 - 5((2x + 3)/(-2x + 3)) - 3) - 5? Express your answer in terms of x and do not include the constant of integration C.\n\nPresent the answer in LaTex for... | 5*x + (-5112*x**2 + 7560*x - 10206)/(8*x**3 - 36*x**2 + 54*x - 27) + 99*log(2*x - 3) | MATH |
[
{
"content": "Determine ∫(-1x^2 + 4x + 4) 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 + 4*x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = (1x + 1)/(3x)? 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)/3 | MATH |
[
{
"content": "Determine ∫(3(-2(5x + 1)^2 - 4(5x + 1) - 3)^2 + 5(-2(5x + 1)^2 - 4(5x + 1) - 3) + 2) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1500*x**5 + 3000*x**4 + 7250*x**3/3 + 980*x**2 + 200*x | MATH |
[
{
"content": "Determine ∫((1x)/(1x)) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = 1x + 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**2/2 + 3*x | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = 3(1e^(2x) + 1) + 2. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5*x + 3*exp(2*x)/2 | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = 1e^(1(-5x^2 - 1x)) + 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 + sqrt(5)*sqrt(pi)*exp(1/20)*erf(sqrt(5)*(10*x + 1)/10)/10 | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = (1x - 3)/(-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"
}
] | -x/3 + 4*log(x + 1)/3 | 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": "What is the symbolic antiderivative of the function f(x) = 2e^(1(-3x^2 - 3x + 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 + sqrt(3)*sqrt(pi)*exp(11/4)*erf(sqrt(3)*(6*x + 3)/6)/3 | MATH |
[
{
"content": "Determine ∫((1(1cos(3π(3x + 5) - 2) - 3))/(-2(1cos(3π(3x + 5) - 2) - 3) - 2)) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -x/2 - sqrt(3)*(atan(sqrt(3)*tan(9*pi*x/2 - 1)/3) + pi*floor((9*pi*x/2 - pi/2 - 1)/pi))/(27*pi) | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = -5(-4(4x - 5) + 1) + 3. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 40*x**2 - 102*x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = 1(5(-3e^(-2x) - 1)^2 + 2(-3e^(-2x) - 1) + 3)^2 - 4(5(-3e^(-2x) - 1)^2 + 2(-3e^(-2x) - 1) + 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 answ... | 7*x - 96*exp(-2*x) - 234*exp(-4*x) - 360*exp(-6*x) - 2025*exp(-8*x)/8 | MATH |
[
{
"content": "Find the indefinite integral of f(x) = (-2(1x^2 + 3x - 1))/(-1(1x^2 + 3x - 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 - 4*sqrt(21)*log(x + 3/2 + sqrt(21)/2)/21 + 4*sqrt(21)*log(x - sqrt(21)/2 + 3/2)/21 | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = 1e^(1(3(-5x^2 - 4x - 1))) + 2. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2*x + sqrt(15)*sqrt(pi)*exp(-3/5)*erf(sqrt(15)*(30*x + 12)/30)/30 | MATH |
[
{
"content": "Determine ∫(-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**2/2 + 4*x | MATH |
[
{
"content": "Determine ∫(1(-3x^2 + 2x + 1)) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -x**3 + x**2 + x | MATH |
[
{
"content": "Determine ∫((-3x + 3)/(-2x)) dx. 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(x)/2 | MATH |
[
{
"content": "Find the indefinite integral of f(x) = (-3(-2x - 1) + 3)/(3(-2x - 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 - log(3*x + 2)/3 | MATH |
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