messages listlengths 1 1 | ground_truth stringlengths 1 3.09k | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "What is the symbolic antiderivative of the function f(x) = -1cos(1π(2x - 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"
}
] | 3*x - sin(pi*(2*x - 4))/(2*pi) | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = -1(-2x^2 + 1x - 1) - 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"
}
] | 2*x**3/3 - x**2/2 - 3*x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = -1(1e^(1x) + 3)^2 + 2(1e^(1x) + 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"
}
] | -2*x - exp(2*x)/2 - 4*exp(x) | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = 5x^2 + 2x + 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"
}
] | 5*x**3/3 + x**2 + x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = (-2(-1((1x + 1)/(-2x - 1))^2 + 4((1x + 1)/(-2x - 1)) + 2) + 2)/(3(-1((1x + 1)/(-2x - 1))^2 + 4((1x + 1)/(-2x - 1)) + 2) + 1)? Express your answer in terms of x and do not include the constant of integration C.\n\nPresent the answer in LaTe... | 10*x + (80 - 604*sqrt(57)/57)*log(x - 7 + sqrt(57)) + (80 + 604*sqrt(57)/57)*log(x - sqrt(57) - 7) | MATH |
[
{
"content": "Find the indefinite integral of f(x) = (-2(-3(-5x + 3) - 3) + 1)/(-1(-3(-5x + 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": "user"
}
] | 2*x + log(15*x - 14)/5 | MATH |
[
{
"content": "Find the indefinite integral of f(x) = -2e^(1(1x^2 + 3x - 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"
}
] | 3*x - sqrt(pi)*exp(-13/4)*erfi(x + 3/2) | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = -1cos(1π((-2(-5x^2 + 2x - 1) - 2)/(-2(-5x^2 + 2x - 1) - 2)) + 3) - 3. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | x*(-3 + cos(3)) | MATH |
[
{
"content": "Determine ∫(-3cos(2π(-1(-1x + 5) + 3) + 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 - 3*sin(2*pi*(x - 2) + 2)/(2*pi) | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = (1((2(-5x^2 - 2x - 2) + 1)/(-3(-5x^2 - 2x - 2) + 1)) + 1)/(3((2(-5x^2 - 2x - 2) + 1)/(-3(-5x^2 - 2x - 2) + 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:... | -x/9 - 20*sqrt(71)*atan(15*sqrt(71)*x/71 + 3*sqrt(71)/71)/1917 | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = -3cos(1π(-4x + 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 - 3*sin(pi*(4*x - 3))/(4*pi) | 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": "Find the indefinite integral of f(x) = 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**2/2 + 2*x | MATH |
[
{
"content": "Determine ∫((-3x - 3)/(-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 + 9*log(2*x - 1)/4 | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = 2x^2 - 5x? 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 - 5*x**2/2 | MATH |
[
{
"content": "Find the indefinite integral of f(x) = -1x^2 + 2x + 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"
}
] | -x**3/3 + x**2 + 5*x | MATH |
[
{
"content": "Find the indefinite integral of f(x) = (3(-3cos(1π(-2x + 1) + 3) - 1) + 2)/(1(-3cos(1π(-2x + 1) + 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"
}
] | 3*x - sqrt(2)*log(tan(pi*x - 3/2) - sqrt(2)/2)/(4*pi) + sqrt(2)*log(tan(pi*x - 3/2) + sqrt(2)/2)/(4*pi) | MATH |
[
{
"content": "Determine ∫((-2x)/(-1x + 2)) 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 - 2) | MATH |
[
{
"content": "Determine ∫((-1(4x - 1) + 1)/(2(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/2 + 3*log(8*x - 1)/16 | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = (3(5(-2x^2 - 4x - 4) + 2) - 1)/(-2(5(-2x^2 - 4x - 4) + 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/2 + 7*sqrt(95)*atan(2*sqrt(95)*x/19 + 2*sqrt(95)/19)/380 | MATH |
[
{
"content": "Find the indefinite integral of f(x) = (-2(-2(3x^2 - 5x)^2 + 3(3x^2 - 5x) + 4) + 1)/(2(-2(3x^2 - 5x)^2 + 3(3x^2 - 5x) + 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 - RootSum(21167152*_t**4 - 11152*_t**2 + 1, Lambda(_t, _t*log(4388312*_t**3/9 - 1525*_t/9 + x - 5/6))) | MATH |
[
{
"content": "Determine ∫(-1(3x^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"
}
] | -x**3 + x**2 - 3*x | MATH |
[
{
"content": "Determine ∫((3x)/(3x)) 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^2 + 5x? 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**3/3 + 5*x**2/2 | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = (-1(3((2x)/(3x - 2))^2 + 1((2x)/(3x - 2)) + 2) - 2)/(-1(3((2x)/(3x - 2))^2 + 1((2x)/(3x - 2)) + 2) + 2). 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) + 16*log(x - 2/9)/9 | MATH |
[
{
"content": "Find the indefinite integral of f(x) = 1x^2 + 4x - 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 + 2*x**2 - 4*x | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = -4x^2 - 1x + 1. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -4*x**3/3 - x**2/2 + x | MATH |
[
{
"content": "Find the indefinite integral of f(x) = (3(-1e^(2x)) + 3)/(2(-1e^(2x))) 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 + 3*exp(-2*x)/4 | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = (1(-5(4x^2 - 4)^2 - 3(4x^2 - 4) + 5) + 3)/(-1(-5(4x^2 - 4)^2 - 3(4x^2 - 4) + 5) + 2). Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -x - RootSum(15844608*_t**4 - 204240*_t**2 + 625, Lambda(_t, _t*log(-1062048*_t**3/125 + 1438*_t/25 + x))) | MATH |
[
{
"content": "Determine ∫(2((-2(-4x^2 + 2x + 5) + 1)/(3(-4x^2 + 2x + 5) - 2))^2 + 3) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 35*x/9 + (1 - 4*x)/(5940*x**2 - 2970*x - 6435) + 74*sqrt(165)*log(x - 1/4 + sqrt(165)/12)/27225 - 74*sqrt(165)*log(x - sqrt(165)/12 - 1/4)/27225 | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = (-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 + 5*log(x - 2) | MATH |
[
{
"content": "Find the indefinite integral of f(x) = -1(-2(-1x - 3)^2 - 5(-1x - 3) + 3)^2 + 1(-2(-1x - 3)^2 - 5(-1x - 3) + 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"
}
] | -4*x**5/5 - 7*x**4 - 17*x**3 - 7*x**2/2 - 5*x | MATH |
[
{
"content": "Find the indefinite integral of f(x) = -1x^2 + 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**3/3 + x**2 - 2*x | MATH |
[
{
"content": "Determine ∫((2(2(5x^2 - 1x - 1)^2 + 5(5x^2 - 1x - 1) + 2) + 2)/(-1(2(5x^2 - 1x - 1)^2 + 5(5x^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"
}
] | -2*x + 2*sqrt(11)*log(x - 1/10 + sqrt(11)/10)/33 - 2*sqrt(11)*log(x - sqrt(11)/10 - 1/10)/33 + 4*sqrt(19)*atan(10*sqrt(19)*x/19 - sqrt(19)/19)/57 | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = (-3x - 3)/(-1x). Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3*x + 3*log(x) | MATH |
[
{
"content": "Find the indefinite integral of f(x) = -1(-2e^(1x) + 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"
}
] | -5*x + 2*exp(x) | MATH |
[
{
"content": "Find the indefinite integral of f(x) = 5(2x^2 + 1x - 4) + 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"
}
] | 10*x**3/3 + 5*x**2/2 - 16*x | MATH |
[
{
"content": "Determine ∫((1x - 1)/(-3x - 1)) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -x/3 + 4*log(3*x + 1)/9 | MATH |
[
{
"content": "Determine ∫((3((1x - 1)/(1x - 3)) - 1)/(-2((1x - 1)/(1x - 3)) - 3)) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2*x/5 - 22*log(5*x - 11)/25 | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = 3(-4(1x + 5)^2 + 2(1x + 5) - 2)^2 + 1(-4(1x + 5)^2 + 2(1x + 5) - 2) + 1. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 48*x**5/5 + 228*x**4 + 6536*x**3/3 + 10469*x**2 + 25301*x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = 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"
}
] | x**3/3 - 5*x | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = 3((2(3x^2 - 2x + 1))/(1(3x^2 - 2x + 1) + 3))^2 - 5((2(3x^2 - 2x + 1))/(1(3x^2 - 2x + 1) + 3)) - 3. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -x - (54 - 162*x)/(33*x**2 - 22*x + 44) - 300*sqrt(11)*atan(3*sqrt(11)*x/11 - sqrt(11)/11)/121 | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = -2e^(-2(2(4x^2 + 4x - 4) + 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 - sqrt(pi)*exp(10)*erf(4*x + 2)/4 | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = (-3x - 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"
}
] | 3*x + 11*log(x - 3) | MATH |
[
{
"content": "Find the indefinite integral of f(x) = (-1x - 3)/(-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*log(2*x + 3)/4 | 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": "Compute the indefinite integral for f(x) = 3((-2x - 1)/(2x - 3))^2 - 2((-2x - 1)/(2x - 3)) + 2. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7*x + 16*log(2*x - 3) - 24/(2*x - 3) | MATH |
[
{
"content": "Find the indefinite integral of f(x) = 3x^2 + 1x + 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"
}
] | x**3 + x**2/2 + 5*x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = 1((-3x + 2)/(2x + 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"
}
] | 3*x/2 + 13*log(2*x + 3)/4 | 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": "Compute the indefinite integral for f(x) = -4(4((-1x)/(2x - 1))^2 + 2((-1x)/(2x - 1)) - 5) - 5. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 15*x - 2*log(2*x - 1) + 2/(2*x - 1) | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = -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**2/2 - x | MATH |
[
{
"content": "Determine ∫((3x - 3)/(-1x + 2)) 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(x - 2) | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = 2(-1(-5x + 1)^2 - 1(-5x + 1) - 3)^2 + 3(-1(-5x + 1)^2 - 1(-5x + 1) - 3) - 1. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 250*x**5 - 375*x**4 + 875*x**3/3 - 255*x**2/2 + 34*x | MATH |
[
{
"content": "Determine ∫(-5((1x - 3)/(1x - 3))^2 - 2((1x - 3)/(1x - 3)) + 3) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -4*x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = -2(2x - 4)^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"
}
] | -8*x**3/3 + 16*x**2 - 33*x | MATH |
[
{
"content": "Find the indefinite integral of f(x) = 3cos(3π(-5x - 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 - sin(3*pi*(-5*x - 2) + 1)/(5*pi) | MATH |
[
{
"content": "Determine ∫((2x - 1)/(-1x - 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*log(x + 1) | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = -5(-4((3x + 1)/(-1x + 2))^2 + 2((3x + 1)/(-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"
}
] | 205*x + 910*log(x - 2) - 980/(x - 2) | 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) = -2(2x^2 + 5x - 4) - 1. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -4*x**3/3 - 5*x**2 + 7*x | MATH |
[
{
"content": "Determine ∫(-4x + 4) dx. 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": "Determine ∫((1(4x - 2) + 1)/(1(4x - 2) + 2)) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | x - log(x)/4 | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = 3x + 5. 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) = 4((-2(4x - 1) + 2)/(2(4x - 1)))^2 - 3((-2(4x - 1) + 2)/(2(4x - 1))) - 3. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4*x - 11*log(4*x - 1)/4 - 1/(4*x - 1) | 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": "Find the indefinite integral of f(x) = 4(-4x - 3)^2 + 3(-4x - 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"
}
] | 64*x**3/3 + 42*x**2 + 28*x | MATH |
[
{
"content": "Find the indefinite integral of f(x) = 2cos(1π(-5x + 5) - 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*sin(pi*(5 - 5*x) - 3)/(5*pi) | MATH |
[
{
"content": "Determine ∫(-3x^2 - 5x + 2) 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**2/2 + 2*x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = (-1x - 3)/(-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"
}
] | x/3 + 10*log(3*x - 1)/9 | MATH |
[
{
"content": "Determine ∫(-5x^2 + 4x - 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 + 2*x**2 - 4*x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = 2(-1x + 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**2 + 8*x | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = (2(-4(-2e^(1x) + 2) + 2) - 3)/(2(-4(-2e^(1x) + 2) + 2) + 1). Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 15*x/11 - 4*log(exp(x) - 11/16)/11 | MATH |
[
{
"content": "Find the indefinite integral of f(x) = 5x^2 - 3x 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 - 3*x**2/2 | MATH |
[
{
"content": "Find the indefinite integral of f(x) = 5((2(2x) - 3)/(1(2x) - 2))^2 + 2((2(2x) - 3)/(1(2x) - 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"
}
] | 27*x + 11*log(x - 1) - 5/(4*x - 4) | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = (-1x - 3)/(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 - 6*log(x - 3) | MATH |
[
{
"content": "Find the indefinite integral of f(x) = (1x + 2)/(-2x) 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) | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = -1(3x^2 - 2x - 2)^2 + 3(3x^2 - 2x - 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"
}
] | -9*x**5/5 + 3*x**4 + 17*x**3/3 - 7*x**2 - 9*x | MATH |
[
{
"content": "Determine ∫(-1((3(-1x - 2) + 1)/(2(-1x - 2) + 2))^2 + 4((3(-1x - 2) + 1)/(2(-1x - 2) + 2)) - 1) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 11*x/4 + log(x + 1) + 1/(x + 1) | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = -2(1x^2 + 2x) + 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"
}
] | -2*x**3/3 - 2*x**2 + 4*x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = 3(-3((-2x - 2)/(-3x + 1)) - 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"
}
] | -6*x - 8*log(3*x - 1) | MATH |
[
{
"content": "Determine ∫((3x + 2)/(-1x + 3)) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -3*x - 11*log(x - 3) | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = (2x - 2)/(-2x). 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": "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": "What is the symbolic antiderivative of the function f(x) = -4x^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"
}
] | -4*x**3/3 - 3*x | MATH |
[
{
"content": "Determine ∫((-1x + 2)/(3x - 2)) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -x/3 + 4*log(3*x - 2)/9 | MATH |
[
{
"content": "Find the indefinite integral of f(x) = -5x 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 | MATH |
[
{
"content": "Determine ∫((3(-1x) - 3)/(-2(-1x) - 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*log(2*x - 3)/4 | MATH |
[
{
"content": "Find the indefinite integral of f(x) = (-1((2((2x - 1)/(1x)) + 3)/(-2((2x - 1)/(1x)) + 1)) + 2)/(3((2((2x - 1)/(1x)) + 3)/(-2((2x - 1)/(1x)) + 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"
... | -13*x/12 + log(x)/2 | MATH |
[
{
"content": "Determine ∫(3x^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 + x**2/2 + x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = (1(-4((3x + 3)/(-1x - 1)) + 1) - 1)/(-3(-4((3x + 3)/(-1x - 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"
}
... | -4*x/13 | MATH |
[
{
"content": "Find the indefinite integral of f(x) = (2(-2x) + 2)/(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"
}
] | 2*x/3 - 5*log(3*x + 1)/9 | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = 3(-2x^2 + 3x + 1)^2 + 1(-2x^2 + 3x + 1) - 1. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12*x**5/5 - 9*x**4 + 13*x**3/3 + 21*x**2/2 + 3*x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = -5(-5(-2x^2 + 1x - 3) - 3)^2 - 5(-5(-2x^2 + 1x - 3) - 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"
}
] | -100*x**5 + 125*x**4 - 1375*x**3/3 + 625*x**2/2 - 783*x | MATH |
[
{
"content": "Find the indefinite integral of f(x) = 1(3sin(2π((-1x - 2)/(1x + 2)) + 1) + 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*sin(1) + 5*x | MATH |
[
{
"content": "Determine ∫(2((2x + 1)/(-2x + 3))^2 - 5((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"
}
] | 7*x + 18*log(2*x - 3) - 16/(2*x - 3) | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = 1(-2x^2 - 2x). 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 | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = 3(-1x^2 + 5x + 2)^2 - 5(-1x^2 + 5x + 2) + 1. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3*x**5/5 - 15*x**4/2 + 68*x**3/3 + 35*x**2/2 + 3*x | MATH |
[
{
"content": "Determine ∫(3((-2x + 1)/(1x - 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 - 9*log(x - 2) | 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 |
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