messages listlengths 1 1 | ground_truth stringlengths 1 3.09k | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "Determine ∫(-3(-3x^2 + 2x + 2)^2 + 1(-3x^2 + 2x + 2)) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -27*x**5/5 + 9*x**4 + 7*x**3 - 11*x**2 - 10*x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = 4(-5((1x + 2)/(-1x + 2))^2 - 4) - 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"
}
] | -41*x - 160*log(x - 2) + 320/(x - 2) | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = (2x)/(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"
}
] | 2*x/3 | 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 + 4*x | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = (-1(-1((-3x)/(-3x + 2)) - 2) + 1)/(1(-1((-3x)/(-3x + 2)) - 2)). Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -4*x/3 + 2*log(9*x - 4)/27 | MATH |
[
{
"content": "Determine ∫(1x^2 + 4x + 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 + 2*x**2 + 5*x | 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 |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = 2x^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"
}
] | 2*x**3/3 + 3*x**2/2 - 3*x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = (-2(-1(5x + 3) + 2) + 2)/(-2(-1(5x + 3) + 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"
}
] | x + log(10*x - 1)/2 | 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 - 7*log(x + 3) | MATH |
[
{
"content": "Find the indefinite integral of f(x) = -3(-5(-1x + 4)^2 - 3(-1x + 4) - 5) - 3 with respect to x. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5*x**3 - 129*x**2/2 + 288*x | 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": "Compute the indefinite integral for f(x) = 1x^2 + 4x - 4. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | x**3/3 + 2*x**2 - 4*x | MATH |
[
{
"content": "Find the indefinite integral of f(x) = 2(-1x - 5) + 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 - 7*x | MATH |
[
{
"content": "Find the indefinite integral of f(x) = -1(-5(5x - 3) - 4) - 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"
}
] | 25*x**2/2 - 16*x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = (2((-1(3x^2 - 2x + 1) - 1)/(-2(3x^2 - 2x + 1) + 1)) - 1)/(-2((-1(3x^2 - 2x + 1) - 1)/(-2(3x^2 - 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: \\bo... | -3*sqrt(5)*atan(3*sqrt(5)*x/5 - sqrt(5)/5)/10 | MATH |
[
{
"content": "Determine ∫(-4x^2 - 5x + 1) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -4*x**3/3 - 5*x**2/2 + x | MATH |
[
{
"content": "Find the indefinite integral of f(x) = 4(3x^2 + 2x + 4)^2 - 4(3x^2 + 2x + 4) + 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"
}
] | 36*x**5/5 + 12*x**4 + 100*x**3/3 + 28*x**2 + 53*x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = -3(-2x + 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"
}
] | 3*x**2 - 13*x | 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": "What is the symbolic antiderivative of the function f(x) = 4(-1x^2 - 1x - 2) - 3? Express your answer in terms of x and do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -4*x**3/3 - 2*x**2 - 11*x | MATH |
[
{
"content": "Determine ∫(-4(3e^(-2x) + 2)^2 - 1(3e^(-2x) + 2) + 4) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -14*x + 51*exp(-2*x)/2 + 9*exp(-4*x) | 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) = (1x - 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"
}
] | -x/2 + 5*log(2*x + 3)/4 | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = 4x^2 - 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"
}
] | 4*x**3/3 - x**2/2 - 5*x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = 2(1x^2 + 5x) - 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**3/3 + 5*x**2 - 5*x | MATH |
[
{
"content": "Determine ∫(4(-5x - 4)^2 - 1(-5x - 4) + 3) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 100*x**3/3 + 165*x**2/2 + 71*x | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = -1x + 3. 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": "Find the indefinite integral of f(x) = (-1x - 1)/(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)/2 | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = -1((-1x + 3)/(1x - 3))^2 + 5((-1x + 3)/(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"
}
] | -2*x | MATH |
[
{
"content": "Determine ∫(3((-3x - 3)/(-2x - 3)) - 2) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5*x/2 - 9*log(2*x + 3)/4 | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = (-3x + 2)/(-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"
}
] | 3*x - 2*log(x) | MATH |
[
{
"content": "Determine ∫((3x - 3)/(3x - 1)) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | x - 2*log(3*x - 1)/3 | MATH |
[
{
"content": "Find the indefinite integral of f(x) = 1x^2 + 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**3/3 + x**2/2 - 2*x | MATH |
[
{
"content": "Determine ∫(-5x - 3) 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 - 3*x | MATH |
[
{
"content": "Find the indefinite integral of f(x) = -2e^(-1(-3x - 3)) + 3 with respect to x. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3*x - 2*exp(3*x + 3)/3 | MATH |
[
{
"content": "Find the indefinite integral of f(x) = (1(2x^2 + 5x + 1) + 2)/(1(2x^2 + 5x + 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"
}
] | x - 2*sqrt(7)*atan(4*sqrt(7)*x/7 + 5*sqrt(7)/7)/7 | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = -1cos(2π(2(-5x + 5) - 5) + 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 + sin(2*pi*(5 - 10*x) + 3)/(20*pi) | MATH |
[
{
"content": "Find the indefinite integral of f(x) = -5x - 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**2/2 - x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = 3x^2 + 5x + 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 + 5*x**2/2 + x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = (3((1x - 2)/(-2x + 1)) + 1)/(3((1x - 2)/(-2x + 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"
}
] | -x + 9*log(x + 4) | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = -5((-3x + 2)/(2x + 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"
}
] | 23*x/2 - 25*log(x + 1)/2 | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = -1(-3((-1x - 3)/(1x + 3))^2 - 2((-1x - 3)/(1x + 3)) - 4)^2 - 3(-3((-1x - 3)/(1x + 3))^2 - 2((-1x - 3)/(1x + 3)) - 4). Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -10*x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = 1e^(2(-1x + 2)) - 2? Express your answer in terms of x and do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2*x - exp(4 - 2*x)/2 | 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 - 4*log(x - 3) | MATH |
[
{
"content": "Determine ∫(1sin(3π(-2x) - 1) - 1) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -x + cos(6*pi*x + 1)/(6*pi) | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = (-1(1(-1x^2 - 4x - 2) - 3) - 3)/(-3(1(-1x^2 - 4x - 2) - 3) + 4). Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | x/3 - 13*sqrt(21)*atan(sqrt(21)*x/7 + 2*sqrt(21)/7)/63 | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = (1(-1(1x^2 - 3x + 3) + 2) - 1)/(-3(-1(1x^2 - 3x + 3) + 2) + 1). Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -x/3 - 2*sqrt(33)*log(x - 3/2 - sqrt(33)/6)/99 + 2*sqrt(33)*log(x - 3/2 + sqrt(33)/6)/99 | MATH |
[
{
"content": "Find the indefinite integral of f(x) = 3x^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 - x**2 + 5*x | MATH |
[
{
"content": "Determine ∫((-2(-1x^2 + 2x + 5) + 1)/(3(-1x^2 + 2x + 5) - 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 + sqrt(51)*log(x - 1 + sqrt(51)/3)/306 - sqrt(51)*log(x - sqrt(51)/3 - 1)/306 | 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": "Compute the indefinite integral for f(x) = 5x^2 + 5x + 1. 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 + x | MATH |
[
{
"content": "Determine ∫(-1((-3x + 1)/(2x - 1))^2 + 3((-3x + 1)/(2x - 1)) - 5) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -47*x/4 - 3*log(2*x - 1)/2 + 1/(16*x - 8) | MATH |
[
{
"content": "Determine ∫(3(-1((-1x + 2)/(-1x + 3))^2 + 4((-1x + 2)/(-1x + 3)) - 1)^2 - 5(-1((-1x + 2)/(-1x + 3))^2 + 4((-1x + 2)/(-1x + 3)) - 1) - 2) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | (-5*x**2 + 36*x - 64)/(x**3 - 9*x**2 + 27*x - 27) + 14*log(x - 3) | MATH |
[
{
"content": "Find the indefinite integral of f(x) = -3(5x^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 + 2*x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = -1(-1(-3x) + 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"
}
] | -3*x**2/2 - 5*x | MATH |
[
{
"content": "Find the indefinite integral of f(x) = 1((1x + 2)/(2x + 3)) - 3 with respect to x. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -5*x/2 + log(2*x + 3)/4 | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = (1(-1(5x^2 + 4x + 2)^2 + 2))/(-3(-1(5x^2 + 4x + 2)^2 + 2) + 2). Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -x/3 - 2*sqrt(1/192 - 5*sqrt(3)/1728)*atan(15*x/(5*sqrt(3)*sqrt(9 - 5*sqrt(3)) + 9*sqrt(9 - 5*sqrt(3))) + 6/(5*sqrt(3)*sqrt(9 - 5*sqrt(3)) + 9*sqrt(9 - 5*sqrt(3)))) - 2*sqrt(5*sqrt(3)/1728 + 1/192)*atan(15*x/(-9*sqrt(5*sqrt(3) + 9) + 5*sqrt(3)*sqrt(5*sqrt(3) + 9)) + 6/(-9*sqrt(5*sqrt(3) + 9) + 5*sqrt(3)*sqrt(5*sqrt(3) ... | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = -5x^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"
}
] | -5*x**3/3 + 3*x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = 1x^2 + 4x + 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 + 2*x**2 + 3*x | MATH |
[
{
"content": "Find the indefinite integral of f(x) = -1(-1(3x^2 - 1x + 4) - 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"
}
] | x**3 - x**2/2 + 2*x | MATH |
[
{
"content": "Determine ∫(-1((1(-5x + 5) - 1)/(-3(-5x + 5) - 1)) + 2) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7*x/3 + 4*log(15*x - 16)/45 | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = -4x^2 - 5x + 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 - 5*x**2/2 + 5*x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = 3cos(3π(2x + 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*(2*x + 5) - 1)/(2*pi) | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = 1(-1((-2x + 2)/(-2x + 1))^2 + 4((-2x + 2)/(-2x + 1)) + 5) + 4. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12*x - log(2*x - 1) + 1/(4*x - 2) | MATH |
[
{
"content": "Determine ∫(1x^2 - 5x + 4) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | x**3/3 - 5*x**2/2 + 4*x | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = (-3((-3x)/(1x + 1)) - 1)/(-3((-3x)/(1x + 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 + log(2*x - 1)/2 | MATH |
[
{
"content": "Find the indefinite integral of f(x) = (-3((2(5x - 1) - 3)/(-2(5x - 1) - 2)) + 3)/(-3((2(5x - 1) - 3)/(-2(5x - 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"
}
] | 6*x + 15*log(2*x - 3)/2 | MATH |
[
{
"content": "Determine ∫(-1sin(1π(-5x + 4) - 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 - cos(pi*(4 - 5*x) - 2)/(5*pi) | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = -1e^(1(1x - 5)) - 1? Express your answer in terms of x and do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -x - exp(x - 5) | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = -5x^2 + 3x + 1. 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) = -4((2(-5x^2 - 3x + 1) + 3)/(-2(-5x^2 - 3x + 1) + 1))^2 - 1((2(-5x^2 - 3x + 1) + 3)/(-2(-5x^2 - 3x + 1) + 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: \\... | x + (320*x + 96)/(190*x**2 + 114*x - 19) - 426*sqrt(19)*log(x + 3/10 + sqrt(19)/10)/361 + 426*sqrt(19)*log(x - sqrt(19)/10 + 3/10)/361 | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = (-2(-3(-2x + 3) + 2))/(-2(-3(-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 | 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": "What is the symbolic antiderivative of the function f(x) = 5(1(-5x^2 + 3x - 5))^2 + 3(1(-5x^2 + 3x - 5)) - 3? Express your answer in terms of x and do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 25*x**5 - 75*x**4/2 + 280*x**3/3 - 141*x**2/2 + 107*x | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = -2x^2 - 2x - 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 - x**2 - x | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = 1(-1(5x^2 - 3)^2 - 3(5x^2 - 3) - 1)^2 - 4(-1(5x^2 - 3)^2 - 3(5x^2 - 3) - 1) + 2. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 625*x**9/9 - 750*x**7/7 + 75*x**5 - 30*x**3 + 7*x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = (2x - 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"
}
] | 2*x/3 - 5*log(x + 1)/3 | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = 3((2x - 2)/(-1x + 2))^2 - 1((2x - 2)/(-1x + 2)) - 5. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9*x + 26*log(x - 2) - 12/(x - 2) | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = 1sin(3π(-5x - 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"
}
] | x + cos(3*pi*(-5*x - 2) + 2)/(15*pi) | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = -1sin(2π(-1x - 4) - 2) + 2? Express your answer in terms of x and do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2*x - cos(2*pi*(-x - 4) - 2)/(2*pi) | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = (-2x - 3)/(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"
}
] | -2*x/3 - log(x) | MATH |
[
{
"content": "Find the indefinite integral of f(x) = 5x - 3 with respect to x. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5*x**2/2 - 3*x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = (-3(-5x + 4) - 1)/(-1(-5x + 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}",
"role": "user"
}
] | 3*x - 7*log(5*x - 2)/5 | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = 5x - 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**2/2 - 5*x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = (2(3cos(3π(1x - 1) + 2) + 2) - 3)/(-2(3cos(3π(1x - 1) + 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"
}
... | -x + 4*sqrt(13)*(atan(sqrt(13)*tan(3*pi*x/2 + 1)) + pi*floor((3*pi*x/2 - pi/2 + 1)/pi))/(13*pi) | MATH |
[
{
"content": "Determine ∫(-5(-1(3x - 5) - 1) + 5) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 15*x**2/2 - 15*x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = -5(1((-3x - 1)/(-3x))^2 + 4((-3x - 1)/(-3x)) + 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"
}
] | -48*x - 10*log(x) + 5/(9*x) | MATH |
[
{
"content": "Determine ∫(-1sin(3π(2x - 2) + 1) + 1) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | x + cos(3*pi*(2*x - 2) + 1)/(6*pi) | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = 3sin(3π((-1((1x + 2)/(-3x - 3)) + 1)/(-3((1x + 2)/(-3x - 3)) - 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": "use... | -x - 3*cos(3 - 3*pi*(1 - (x + 2)/(-3*x - 3))/(-1 - 3*(x + 2)/(-3*x - 3)))/(4*pi) | MATH |
[
{
"content": "Find the indefinite integral of f(x) = (3(5x + 4))/(2(5x + 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"
}
] | 3*x/2 + 3*log(10*x + 7)/20 | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = (2(-3(-1e^(-1x) + 3) + 1))/(2(-3(-1e^(-1x) + 3) + 1) - 1). Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 16*x/17 - log(-17/6 + exp(-x))/17 | 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": "Determine ∫(5(-2(-1e^(-2x) - 2)^2 + 1(-1e^(-2x) - 2) + 3) - 4) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -39*x + 45*exp(-2*x)/2 + 5*exp(-4*x)/2 | 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": "Compute the indefinite integral for f(x) = -4(3x^2 - 1x + 2)^2 - 4(3x^2 - 1x + 2). Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -36*x**5/5 + 6*x**4 - 64*x**3/3 + 10*x**2 - 24*x | MATH |
[
{
"content": "What is the symbolic antiderivative of the function f(x) = 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**2 - 3*x | MATH |
[
{
"content": "Determine ∫(4(2((-3x + 3)/(2x + 3))^2 + 2((-3x + 3)/(2x + 3)) - 1)^2 + 1) dx. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2*x + (-16200*x**2 - 21600*x - 12825)/(16*x**3 + 72*x**2 + 108*x + 54) - 60*log(2*x + 3) | MATH |
[
{
"content": "Compute the indefinite integral for f(x) = 5((-2(1x - 1))/(-2(1x - 1) - 1)) + 2. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7*x - 5*log(2*x - 1)/2 | MATH |
[
{
"content": "Find the indefinite integral of f(x) = (-2x)/(1x + 3) with respect to x. Do not include the constant of integration C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2*x + 6*log(x + 3) | MATH |
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