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) = -1(-3((-2x)/(3x - 2)) + 3)^2 - 3(-3((-2x)/(3x - 2)) + 3) + 5? Express your answer in terms of x and do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -35*x - 52*log(3*x - 2)/3 + 16/(9*x - 6) | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = 2x^2 - 2x + 5. 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": "Find the indefinite integral of f(x) = 4(-5(3x + 1) + 3)^2 + 4(-5(3x + 1) + 3) + 2 with respect to x. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 300*x**3 + 90*x**2 + 10*x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = 3(4(1e^(2x)) + 5)^2 - 3(4(1e^(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"
}
] | 58*x + 12*exp(4*x) + 54*exp(2*x) | MATH |
[
{
"content": "Determine ∫(-1(1e^(1x) - 3) + 5) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8*x - exp(x) | MATH |
[
{
"content": "Determine ∫(-5((3(4x^2 - 5x + 2) + 1)/(-1(4x^2 - 5x + 2) + 2)) + 4) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 19*x - 7*log(x) + 7*log(x - 5/4) | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = 5(-1e^(1x) + 1)^2 - 3(-1e^(1x) + 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"
}
] | -3*x + 5*exp(2*x)/2 - 7*exp(x) | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = 5x - 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 - 5*x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = -1e^(-2(5x^2 + 1x - 1)) - 3? Express your answer in terms of x and do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -3*x - sqrt(10)*sqrt(pi)*exp(21/10)*erf(sqrt(10)*(20*x + 2)/20)/20 | MATH |
[
{
"content": "Determine ∫((-3(3x^2 + 4x - 4))/(-3(3x^2 + 4x - 4) + 4)) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | x - sqrt(5)*log(x + 2/3 + 2*sqrt(5)/3)/15 + sqrt(5)*log(x - 2*sqrt(5)/3 + 2/3)/15 | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = 1(4(3e^(-1x) + 2)^2 + 5(3e^(-1x) + 2))^2 - 2(4(3e^(-1x) + 2)^2 + 5(3e^(-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"... | 624*x - 3150*exp(-x) - 5769*exp(-2*x)/2 - 1512*exp(-3*x) - 324*exp(-4*x) | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = (-2((-3((-1x + 2)/(-2x + 3)) + 1)/(-1((-1x + 2)/(-2x + 3)) - 2)) - 1)/(-1((-3((-1x + 2)/(-2x + 3)) + 1)/(-1((-1x + 2)/(-2x + 3)) - 2)))? Express your answer in terms of x and do not include the constant of integration C.\n\nPresent the ans... | 7*x + 7*log(x - 3) | MATH |
[
{
"content": "Find the indefinite integral of f(x) = (-1((3x)/(1x)) + 2)/(3((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"
}
] | -x/12 | MATH |
[
{
"content": "Find the indefinite integral of f(x) = -3cos(3π(4((-2x)/(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"
}
] | x*(3 - 3*cos(2)) | MATH |
[
{
"content": "Find the indefinite integral of f(x) = (-1(-5((2x + 2)/(1x + 3)) + 3) - 3)/(-1(-5((2x + 2)/(1x + 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"
}
] | 4*x/9 - 100*log(9*x + 7)/81 | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = -1(1x + 2)^2 + 5(1x + 2). 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 + 6*x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = 4(-1x^2 - 3x - 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"
}
] | -4*x**3/3 - 6*x**2 - 17*x | MATH |
[
{
"content": "Determine ∫(-3e^(-2(5x^2 - 3x - 2)) - 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(10)*sqrt(pi)*exp(49/10)*erf(sqrt(10)*(20*x - 6)/20)/20 | MATH |
[
{
"content": "Find the indefinite integral of f(x) = -1x^2 + 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"
}
] | -x**3/3 + 5*x**2/2 + 5*x | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = (-2x + 2)/(1x + 1). 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 + 1) | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = 2(-5((-1x + 1)/(-1x + 2))^2 + 2((-1x + 1)/(-1x + 2)) + 2) - 2. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -4*x - 16*log(x - 2) + 10/(x - 2) | 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) = 2((3(3x^2 + 2x - 1))/(-1(3x^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"
}
] | -6*x | MATH |
[
{
"content": "Determine ∫((-3x + 2)/(-1x)) 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(x) | MATH |
[
{
"content": "Determine ∫((-1(-3((-1x - 2)/(3x + 1)) - 3) + 1)/(3(-3((-1x - 2)/(3x + 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 - 10*log(3*x - 4)/9 | MATH |
[
{
"content": "Determine ∫((1x - 2)/(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 - 7*log(2*x + 3)/4 | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = 3x^2 + 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 + x**2 + 3*x | MATH |
[
{
"content": "Find the indefinite integral of f(x) = 3((-1x + 3)/(-2x - 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/2 - 6*log(x + 1) | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = (-1(2(5x^2 + 4) + 5) - 3)/(1(2(5x^2 + 4) + 5) - 3). Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -x - 3*atan(x)/5 | MATH |
[
{
"content": "Find the indefinite integral of f(x) = (-1x - 1)/(-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 + 5*log(2*x - 3)/4 | MATH |
[
{
"content": "Determine ∫((3((3x + 2)/(-2x + 3)) + 3)/(-3((3x + 2)/(-2x + 3)) + 4)) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -3*x/17 - 273*log(17*x - 6)/289 | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = 5((-1x + 1)/(-1x + 2))^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"
}
] | 6*x + 10*log(x - 2) - 5/(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 - 2*log(3*x - 4) | MATH |
[
{
"content": "Find the indefinite integral of f(x) = (-1x - 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 - 5*log(2*x + 1)/4 | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = 1x^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"
}
] | x**3/3 - 3*x**2/2 - 3*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": "Determine ∫(-5(-2x - 1) + 1) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5*x**2 + 6*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": "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": "What is the symbolic antiderivative of the function f(x) = 1(-4((-2x - 1)/(-2x)) + 2)^2 + 5(-4((-2x - 1)/(-2x)) + 2)? Express your answer in terms of x and do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -6*x - 2*log(x) - 4/x | MATH |
[
{
"content": "Find the indefinite integral of f(x) = 4x 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 | MATH |
[
{
"content": "Determine ∫((-3(1cos(1π(-1x + 1) - 1) + 3) - 1)/(-2(1cos(1π(-1x + 1) - 1) + 3) + 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 + 11*sqrt(5)*(atan(sqrt(5)*tan(pi*x/2 + 1/2)) + pi*floor((pi*x/2 - pi/2 + 1/2)/pi))/(5*pi) | MATH |
[
{
"content": "Find the indefinite integral of f(x) = 1((1x - 2)/(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 - 4*log(3*x - 2)/9 | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = 3(-3x + 4) - 2. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -9*x**2/2 + 10*x | MATH |
[
{
"content": "Find the indefinite integral of f(x) = 1cos(1π(1x - 3) - 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(pi*(x - 3) - 1)/pi | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = (1x - 1)/(3x - 2). Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | x/3 - log(3*x - 2)/9 | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = 2(-1((1x - 2)/(-2x + 3)) - 2)^2 - 3(-1((1x - 2)/(-2x + 3)) - 2) - 1. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8*x + 9*log(2*x - 3)/4 - 1/(8*x - 12) | MATH |
[
{
"content": "Find the indefinite integral of f(x) = (1(-1e^(1x) + 3) - 1)/(-1(-1e^(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"
}
] | -2*x + log(exp(x) - 1) | MATH |
[
{
"content": "Find the indefinite integral of f(x) = 2(-2e^(1(-2x^2 + 5x + 2)) + 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 - sqrt(2)*sqrt(pi)*exp(41/8)*erf(sqrt(2)*(4*x - 5)/4) | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = 4((2x - 2)/(-1x + 3))^2 - 3((2x - 2)/(-1x + 3)) + 3. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 25*x + 76*log(x - 3) - 64/(x - 3) | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = 5x + 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**2/2 + 3*x | MATH |
[
{
"content": "Determine ∫(3(2x^2 + 1x + 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**2/2 + 15*x | MATH |
[
{
"content": "Find the indefinite integral of f(x) = (2x - 3)/(-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"
}
] | -2*x/3 + 13*log(3*x + 2)/9 | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = -2x - 5. 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) = 5(1(-3x^2 - 1x + 2) + 5) - 4? Express your answer in terms of x and do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -5*x**3 - 5*x**2/2 + 31*x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = -5((-2x + 1)/(-2x + 3))^2 + 4((-2x + 1)/(-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"
}
] | -4*x - 6*log(2*x - 3) + 10/(2*x - 3) | MATH |
[
{
"content": "Find the indefinite integral of f(x) = (-1x)/(-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 | MATH |
[
{
"content": "Find the indefinite integral of f(x) = 3cos(3π((2x - 1)/(2x - 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"
}
] | x*(3 - 3*cos(2)) | MATH |
[
{
"content": "Determine ∫((2x)/(2x + 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(2*x + 3)/2 | 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**3/3 + x**2 + 3*x | MATH |
[
{
"content": "Find the indefinite integral of f(x) = 4x - 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"
}
] | 2*x**2 - x | MATH |
[
{
"content": "Find the indefinite integral of f(x) = 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"
}
] | x**2/2 - 3*x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = 4((3((2x - 2)/(2x + 2)) + 1)/(-1((2x - 2)/(2x + 2)) + 2))^2 - 3((3((2x - 2)/(2x + 2)) + 1)/(-1((2x - 2)/(2x + 2)) + 2)) + 4? Express your answer in terms of x and do not include the constant of integration C.\n\nPresent the answer in LaTex... | 56*x - 406*log(x + 3) - 784/(x + 3) | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = 2e^(-1(2x^2 - 3x - 5)) - 1. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -x + sqrt(2)*sqrt(pi)*exp(49/8)*erf(sqrt(2)*(4*x - 3)/4)/2 | 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": "Compute the indefinite integral for f(x) = -5(2sin(1π(2x + 4) - 2) + 1)^2 + 1(2sin(1π(2x + 4) - 2) + 1) - 1. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -10*x*sin(2*pi*x - 2)**2 - 10*x*cos(2*pi*x - 2)**2 - 5*x + 5*sin(2*pi*x - 2)*cos(2*pi*x - 2)/pi + 10*cos(2*pi*x - 2)/pi - cos(pi*(2*x + 4) - 2)/pi | MATH |
[
{
"content": "Determine ∫(5(-4(2x - 4) - 2)^2 - 4) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 320*x**3/3 - 560*x**2 + 976*x | MATH |
[
{
"content": "Find the indefinite integral of f(x) = -1cos(1π(1(-3x + 4) + 1) + 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 + sin(pi*(5 - 3*x) + 2)/(3*pi) | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = 3cos(3π(-4x - 1) - 2) + 3. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3*x - sin(3*pi*(-4*x - 1) - 2)/(4*pi) | MATH |
[
{
"content": "Find the indefinite integral of f(x) = (-3(2x^2 - 4x + 5) - 2)/(-3(2x^2 - 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"
}
] | x + sqrt(6)*atan(sqrt(6)*x/3 - sqrt(6)/3)/9 | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = 3(-2e^(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": "user"
}
] | -13*x - 6*exp(x) | MATH |
[
{
"content": "Determine ∫(-1(-4((-1x - 1)/(1x + 2))^2 + 4((-1x - 1)/(1x + 2)) - 5)^2 - 3(-4((-1x - 1)/(1x + 2))^2 + 4((-1x - 1)/(1x + 2)) - 5) - 4) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -134*x - (-708*x**2 - 2688*x - 2560)/(3*x**3 + 18*x**2 + 36*x + 24) + 276*log(x + 2) | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = -1e^(1(-2x)) + 2. 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 | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = 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"
}
] | 3*x**2/2 | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = -2(-2e^(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"
}
] | 5*x + 4*exp(x) | MATH |
[
{
"content": "Determine ∫(3(-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"
}
] | -x**3 + 7*x | MATH |
[
{
"content": "Determine ∫((2x + 2)/(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 | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = -3(-3e^(-1(1x - 3)) + 3) + 4? Express your answer in terms of x and do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -5*x - 9*exp(3 - x) | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = (2x - 1)/(-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 + 7*log(x + 3) | MATH |
[
{
"content": "Find the indefinite integral of f(x) = -2x^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"
}
] | -2*x**3/3 + 3*x**2/2 + 4*x | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = (1(-3x - 2) + 2)/(-1(-3x - 2) - 2). Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -x | MATH |
[
{
"content": "Determine ∫(-3((2((-1x - 1)/(1x - 3)) - 2)/(3((-1x - 1)/(1x - 3)) + 3))^2 - 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**2/3 - 10*x/3 | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = (2x)/(-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)/2 | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = -1e^(2(2(3x - 2) - 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 - exp(12*x - 18)/12 | MATH |
[
{
"content": "Determine ∫((-1(4x^2 + 4x - 3) + 1)/(-2(4x^2 + 4x - 3) + 3)) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | x/2 - sqrt(22)*log(x + 1/2 + sqrt(22)/4)/176 + sqrt(22)*log(x - sqrt(22)/4 + 1/2)/176 | MATH |
[
{
"content": "Determine ∫(2(-1cos(3π(4x - 5) - 1) + 1)^2 + 4(-1cos(3π(4x - 5) - 1) + 1) - 2) 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)**2 + x*cos(12*pi*x - 1)**2 + 4*x + sin(12*pi*x - 1)*cos(12*pi*x - 1)/(12*pi) + sin(12*pi*x - 1)/(3*pi) - sin(3*pi*(4*x - 5) - 1)/(3*pi) | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = 4(2x + 2)^2 - 4(2x + 2) + 2. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16*x**3/3 + 12*x**2 + 10*x | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = 1x^2 - 2x - 4. 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 - 4*x | MATH |
[
{
"content": "Determine ∫(2cos(3π(1x + 4) + 3) - 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*sin(3*pi*(x + 4) + 3)/(3*pi) | MATH |
[
{
"content": "Determine ∫(1(-2x - 4) - 2) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -x**2 - 6*x | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = (1x - 3)/(1x + 3). 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": "Compute the indefinite integral for f(x) = -3(4((2x - 1)/(-2x)) + 3)^2 + 1(4((2x - 1)/(-2x)) + 3) - 3. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -7*x + 14*log(x) + 12/x | 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 ∫(5(-1x^2 - 1x + 3)^2 - 4(-1x^2 - 1x + 3) + 4) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | x**5 + 5*x**4/2 - 7*x**3 - 13*x**2 + 37*x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = 3(-2e^(2x) + 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"
}
] | 11*x - 3*exp(2*x) | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = 5x + 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"
}
] | 5*x**2/2 + 4*x | MATH |
[
{
"content": "Determine ∫(4x^2 + 3x + 5) 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 + 5*x | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = -4x^2 - 4x + 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 - 2*x**2 + x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = -4(-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"
}
] | 8*x**2 + 4*x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = (3x + 2)/(-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 - 2*log(x)/3 | MATH |
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