messages listlengths 1 1 | ground_truth stringlengths 1 3.09k | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Compute the indefinite integral for f(x) = -4(4(-2x^2 - 5x + 3) - 5)^2 + 1(4(-2x^2 - 5x + 3) - 5) - 4. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -256*x**5/5 - 320*x**4 - 1160*x**3/3 + 550*x**2 - 193*x | MATH |
[
{
"content": "Determine ∫((1(-3(-1x + 4)^2 + 2(-1x + 4) + 1))/(-1(-3(-1x + 4)^2 + 2(-1x + 4) + 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*sqrt(13)*log(x - 11/3 - sqrt(13)/3)/26 + 3*sqrt(13)*log(x - 11/3 + sqrt(13)/3)/26 | MATH |
[
{
"content": "Determine ∫(3x - 2) 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 - 2*x | MATH |
[
{
"content": "Find the indefinite integral of f(x) = 4(-5(-2e^(-1x) + 2)^2 + 4(-2e^(-1x) + 2) - 5) + 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"
}
] | -64*x - 128*exp(-x) + 40*exp(-2*x) | MATH |
[
{
"content": "Determine ∫(3(1e^(2x))^2 + 2(1e^(2x)) - 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*exp(4*x)/4 + exp(2*x) | MATH |
[
{
"content": "Find the indefinite integral of f(x) = (-1x + 3)/(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*log(x) | MATH |
[
{
"content": "Determine ∫(-1x^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**3/3 + x**2 - x | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = (1(1e^(-1x) - 1) - 3)/(-3(1e^(-1x) - 1) - 2). Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -4*x - 11*log(-1/3 + exp(-x))/3 | MATH |
[
{
"content": "Determine ∫(-5x + 5) 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 + 5*x | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = (-1(5(2x^2 + 3x + 1)^2 + 1(2x^2 + 3x + 1) + 5) - 1)/(3(5(2x^2 + 3x + 1)^2 + 1(2x^2 + 3x + 1) + 5) - 1). Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -x/3 - RootSum(16538245389*_t**4 + 239328*_t**2 + 1280, Lambda(_t, _t*log(-19901619*_t**3/5120 + 13287*_t/320 + x + 3/4))) | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = -4((-3x + 1)/(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"
}
] | 6*x - 11*log(2*x + 3) | MATH |
[
{
"content": "Find the indefinite integral of f(x) = -3(3sin(1π(2x - 5) + 1) - 2)^2 + 1(3sin(1π(2x - 5) + 1) - 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"
}
] | -27*x*sin(2*pi*x + 1)**2/2 - 27*x*cos(2*pi*x + 1)**2/2 - 12*x + 27*sin(2*pi*x + 1)*cos(2*pi*x + 1)/(4*pi) + 18*cos(2*pi*x + 1)/pi - 3*cos(pi*(2*x - 5) + 1)/(2*pi) | MATH |
[
{
"content": "Find the indefinite integral of f(x) = (1(-1((2x - 1)/(1x + 1)) + 3) + 3)/(1(-1((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"
}
] | 4*x - 9*log(x + 4) | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = -5((-1x - 3)/(1x + 2))^2 + 1((-1x - 3)/(1x + 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"
}
] | -5*x - 11*log(x + 2) + 5/(x + 2) | MATH |
[
{
"content": "Find the indefinite integral of f(x) = 4(1(4x + 4)^2 - 1)^2 + 1(1(4x + 4)^2 - 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"
}
] | 1024*x**5/5 + 1024*x**4 + 6032*x**3/3 + 1936*x**2 + 917*x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = (-2(-4(1x + 2) + 3) - 1)/(-1(-4(1x + 2) + 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"
}
] | 2*x + 5*log(2*x + 1)/4 | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = 1x^2 - 4x + 2. 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": "Find the indefinite integral of f(x) = -1(3e^(-1(3x)) + 2)^2 + 5(3e^(-1(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"
}
] | 3*x - exp(-3*x) + 3*exp(-6*x)/2 | MATH |
[
{
"content": "Find the indefinite integral of f(x) = (-1x)/(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"
}
] | -x/3 - 2*log(3*x - 2)/9 | MATH |
[
{
"content": "Find the indefinite integral of f(x) = (3x)/(-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 + 9*log(x + 3) | MATH |
[
{
"content": "Find the indefinite integral of f(x) = 4(-3(-3x + 3) + 3)^2 + 1(-3(-3x + 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"
}
] | 108*x**3 - 423*x**2/2 + 136*x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = 5(1x)^2 - 3(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"
}
] | 5*x**3/3 - 3*x**2/2 + x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = (-1x + 1)/(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"
}
] | -x/2 + log(2*x - 1)/4 | MATH |
[
{
"content": "Determine ∫((-2x)/(1x)) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2*x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = 3cos(3π(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 + sin(3*pi*(x - 5) + 1)/pi | MATH |
[
{
"content": "Find the indefinite integral of f(x) = (-3(-2((-1x)/(-2x - 3))))/(1(-2((-1x)/(-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"
}
] | -3*x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = (1((1(5x - 2) + 1)/(-1(5x - 2) - 2)) + 2)/(1((1(5x - 2) + 1)/(-1(5x - 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": ... | -x - 2*log(5*x - 1)/5 | MATH |
[
{
"content": "Find the indefinite integral of f(x) = -1((-3x - 1)/(-2x - 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"
}
] | -5*x/2 + 7*log(2*x + 3)/4 | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = 2x + 1. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | x**2 + x | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = (2((-3x + 2)/(2x + 3)) + 3)/(-1((-3x + 2)/(2x + 3)) + 2). Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 13*log(7*x + 4)/7 | MATH |
[
{
"content": "Determine ∫(3x^2 + 5x + 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**2/2 + 5*x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = -5((-1(3e^(-1x)))/(-1(3e^(-1x)) - 3))^2 - 3((-1(3e^(-1x)))/(-1(3e^(-1x)) - 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... | -4*x + 8*log(1 + exp(-x)) + 5/(1 + exp(-x)) | MATH |
[
{
"content": "Determine ∫(4((-2((-3x - 2)/(-1x - 3)) + 1)/(2((-3x - 2)/(-1x - 3)) - 3))^2 - 2((-2((-3x - 2)/(-1x - 3)) + 1)/(2((-3x - 2)/(-1x - 3)) - 3)) - 2) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 112*x/9 + 1288*log(3*x - 5)/27 - 3136/(81*x - 135) | MATH |
[
{
"content": "Find the indefinite integral of f(x) = (-2(1sin(2πx) + 2) - 2)/(1(1sin(2πx) + 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"
}
] | -2*x - 3*log(tan(i*p*x))/(i*p) | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = (1x + 2)/(2x + 3). 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)/4 | MATH |
[
{
"content": "Determine ∫(1(-3e^(-1(-5x)) + 1)^2 - 4(-3e^(-1(-5x)) + 1) + 3) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9*exp(10*x)/10 + 6*exp(5*x)/5 | MATH |
[
{
"content": "Find the indefinite integral of f(x) = -5x^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"
}
] | -5*x**3/3 - 2*x**2 - 4*x | MATH |
[
{
"content": "Find the indefinite integral of f(x) = (3(-1e^(-1x) + 3))/(-2(-1e^(-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"
}
] | -x + log(-9/2 + exp(-x))/2 | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = 1(5(1x + 4)^2 - 3)^2 + 3(5(1x + 4)^2 - 3) - 3. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5*x**5 + 100*x**4 + 795*x**3 + 3140*x**2 + 6157*x | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = (1((3(3x + 5) + 1)/(2(3x + 5) + 1)) - 1)/(-1((3(3x + 5) + 1)/(2(3x + 5) + 1)) + 3). Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | x/3 - 2*log(9*x + 17)/27 | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = 3((3(2x^2 - 2x - 2) - 1)/(1(2x^2 - 2x - 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"
}
] | 6*x + 5*log(x - 2)/2 - 5*log(x + 1)/2 | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = -3(-5(2e^(2x) + 2)^2 + 4(2e^(2x) + 2) - 5)^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"
}
] | -863*x - 150*exp(8*x) - 640*exp(6*x) - 1278*exp(4*x) - 1632*exp(2*x) | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = 1((-1x + 3)/(2x - 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"
}
] | x/2 + 5*log(2*x - 1)/4 | MATH |
[
{
"content": "Find the indefinite integral of f(x) = 3e^(1(-1x^2 + 4x + 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"
}
] | x + 3*sqrt(pi)*exp(6)*erf(x - 2)/2 | 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) = 4(-5((3x - 2)/(2x + 2)) + 1) - 5. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -31*x + 50*log(x + 1) | MATH |
[
{
"content": "Determine ∫(3(1(-4x^2 - 5x - 5) - 3)^2 + 2(1(-4x^2 - 5x - 5) - 3) + 2) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 48*x**5/5 + 30*x**4 + 259*x**3/3 + 115*x**2 + 178*x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = 5(3(-3x^2 + 5x - 1)^2 + 4(-3x^2 + 5x - 1) + 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"
}
] | 27*x**5 - 225*x**4/2 + 135*x**3 - 25*x**2 + 8*x | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = 4((1(3x))/(-3(3x) + 1)) + 1. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -x/3 - 4*log(9*x - 1)/27 | 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 ∫(3(-2e^(-1(-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"
}
] | -4*x - 3*sqrt(5)*sqrt(pi)*exp(-5/4)*erfi(sqrt(5)*(10*x + 5)/10)/5 | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = -1x^2 + 5x - 4. 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 - 4*x | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = (1x - 2)/(2x + 2). Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | x/2 - 3*log(x + 1)/2 | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = (-2(4x + 2))/(-1(4x + 2) - 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(4*x + 5)/2 | MATH |
[
{
"content": "Determine ∫(5x - 5) 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 - 5*x | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = -1(-1e^(-1x) - 2)^2 + 4(-1e^(-1x) - 2) + 5. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -7*x + 8*exp(-x) + exp(-2*x)/2 | 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"
}
] | 3*x/2 - log(2*x - 1)/4 | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = 3(-2(1e^(-1x) - 1)^2 - 3(1e^(-1x) - 1) + 3) - 5. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7*x - 3*exp(-x) + 3*exp(-2*x) | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = -1sin(2π((-3((-2x + 3)/(-2x - 1)) - 3)/(-2((-2x + 3)/(-2x - 1)) - 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 | MATH |
[
{
"content": "Determine ∫(5(-1sin(3π(5x - 1) - 2) + 1)) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5*x + cos(3*pi*(5*x - 1) - 2)/(3*pi) | MATH |
[
{
"content": "Find the indefinite integral of f(x) = (1x)/(-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": "Compute the indefinite integral for f(x) = (3x - 3)/(3x - 2). 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 |
[
{
"content": "Determine ∫(-2x^2 + 2x + 5) 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 + x**2 + 5*x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = (2x)/(-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 + 3*log(2*x + 3)/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": "Find the indefinite integral of f(x) = 2(3e^(1(-2x + 2)) + 3)^2 + 5(3e^(1(-2x + 2)) + 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"
}
] | 35*x - 51*exp(2 - 2*x)/2 - 9*exp(4 - 4*x)/2 | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = 5x^2 + 3x + 4. 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": "Determine ∫(-2e^(1(-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 + 2*exp(-3*x - 5)/3 | MATH |
[
{
"content": "Find the indefinite integral of f(x) = (2((-2x + 3)/(-2x - 2)) - 3)/(1((-2x + 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 - 15*log(2*x - 3)/2 | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = (3((3(-3x^2 + 1x - 2) + 1)/(-3(-3x^2 + 1x - 2))) - 3)/(3((3(-3x^2 + 1x - 2) + 1)/(-3(-3x^2 + 1x - 2))) - 2). Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 6*x/5 + 2*sqrt(515)*atan(6*sqrt(515)*x/103 - sqrt(515)/103)/2575 | MATH |
[
{
"content": "Find the indefinite integral of f(x) = -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**2/2 - x | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = -2x + 4. 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": "What is the symbolic antiderivative of the function f(x) = 3((-1(1x^2 + 4x))/(2(1x^2 + 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/2 + 9*sqrt(10)*log(x - sqrt(10)/2 + 2)/40 - 9*sqrt(10)*log(x + sqrt(10)/2 + 2)/40 | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = (-1x)/(2x + 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 + 1)/2 | MATH |
[
{
"content": "Determine ∫((-1(-3x - 2) + 2)/(-2(-3x - 2) + 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(6*x + 7)/12 | MATH |
[
{
"content": "Determine ∫(4(3x^2 - 5x - 5)^2 - 5(3x^2 - 5x - 5) + 2) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 36*x**5/5 - 30*x**4 - 35*x**3/3 + 225*x**2/2 + 127*x | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = 2((-1((1x - 2)/(1x + 3)) - 2)/(2((1x - 2)/(1x + 3)) - 3)) - 1. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5*x - 70*log(x + 13) | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = 2x^2 - 2x + 2. 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*x | MATH |
[
{
"content": "Find the indefinite integral of f(x) = 1((-1x - 1)/(-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"
}
] | 3*x/2 + log(x)/2 | MATH |
[
{
"content": "Find the indefinite integral of f(x) = 3x^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 + x**2 + 2*x | MATH |
[
{
"content": "Determine ∫((-3(-3(-5x + 4)^2 - 1(-5x + 4) - 5) + 1)/(3(-3(-5x + 4)^2 - 1(-5x + 4) - 5) + 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(51)*atan(10*sqrt(51)*x/17 - 25*sqrt(51)/51)/255 | MATH |
[
{
"content": "Find the indefinite integral of f(x) = (2x - 2)/(-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 + log(2*x - 1)/2 | MATH |
[
{
"content": "Determine ∫(-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 + 3*x | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = -2e^(1(-1x^2 + 2x + 1)) + 3. 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(2)*erf(x - 1) | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = 1(1x^2 + 1x + 5)^2 - 2(1x^2 + 1x + 5) + 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**5/5 + x**4/2 + 3*x**3 + 4*x**2 + 20*x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = 2x? 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 | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = -3x^2 + 3x - 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 + 3*x**2/2 - 4*x | MATH |
[
{
"content": "Find the indefinite integral of f(x) = -1(3(-1x^2 - 2x)^2 - 4(-1x^2 - 2x) - 5) - 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"
}
] | -3*x**5/5 - 3*x**4 - 16*x**3/3 - 4*x**2 + x | 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": "Find the indefinite integral of f(x) = 1(5x^2 + 3x - 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"
}
] | 5*x**3/3 + 3*x**2/2 - 5*x | 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": "Compute the indefinite integral for f(x) = -3(-1e^(-2x) + 3)^2 - 1(-1e^(-2x) + 3). Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -30*x - 19*exp(-2*x)/2 + 3*exp(-4*x)/4 | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = -4x^2 - 5x + 4. 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**2/2 + 4*x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = (-1(-1(2x - 1) - 3) + 3)/(2(-1(2x - 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: \\boxed{Your answer}",
"role": "user"
}
] | -x/2 - 5*log(4*x + 5)/8 | 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 ∫((-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 + 5*log(2*x + 1)/4 | MATH |
[
{
"content": "Determine ∫((-1x - 3)/(-2x)) 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(x)/2 | MATH |
[
{
"content": "Determine ∫(-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": "What is the symbolic antiderivative of the function f(x) = (1x - 3)/(3x + 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 - 11*log(3*x + 2)/9 | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = -4x^2 - 4x + 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"
}
] | -4*x**3/3 - 2*x**2 + 4*x | MATH |
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