messages listlengths 1 1 | ground_truth stringlengths 1 71 | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "Evaluate the indefinite integral \\int \\frac{x + \\sqrt{x}}{1 + \\sqrt{x}} dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | \frac{2}{3}x^{3/2} | MATH |
[
{
"content": "Evaluate the indefinite integral \\int \\frac{e^{x+1}}{e^x + 1} dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | e \log(e^x + 1) | MATH |
[
{
"content": "Evaluate the indefinite integral \\int \\sqrt[3]{3 \\sin(x) - \\sin(3x)} dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -\frac{\sqrt{3}}{4} \cos(x) | MATH |
[
{
"content": "Evaluate the indefinite integral \\int \\frac{x \\log(x) \\cos(x) - \\sin(x)}{x \\log^2(x)} dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | \frac{\sin(x)}{\log(x)} | MATH |
[
{
"content": "Evaluate the indefinite integral \\int \\sqrt[3]{\\frac{x}{4/2}} \\sqrt{\\frac{x}{5/3}} \\sqrt[4]{x^{6/\\sqrt{4}}} \\cdots dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | \frac{x^2}{2} | MATH |
[
{
"content": "Evaluate the indefinite integral \\int \\frac{e^{2x}}{(x^2 + x)(xe^x)^4 + 1} dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | \frac{1}{2} \arctan(x^2 e^{2x}) | MATH |
[
{
"content": "Evaluate the indefinite integral \\int (\\sec^4(x) - \\tan^4(x)) dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 \tan(x) - x | MATH |
[
{
"content": "Evaluate the indefinite integral \\int \\frac{\\sin(4x) \\cos(x)}{\\cos(2x) \\sin(x)} dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2x + \sin(2x) | MATH |
[
{
"content": "Evaluate the indefinite integral \\int \\sin(x) \\sinh(x) dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | \frac{1}{2}(\sin(x) \cosh(x) - \cos(x) \sinh(x)) | MATH |
[
{
"content": "Evaluate the indefinite integral \\int \\frac{\\cos(x) + \\cos(x + \\frac{2\\pi}{3}) + \\cos(x - \\frac{2\\pi}{3})}{2} dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Evaluate the indefinite integral \\int \\frac{(x - 1)\\log(x+1)}{(x + 1)\\log(x-1)} dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | x | MATH |
[
{
"content": "Evaluate the indefinite integral \\int (x \\log x + 2x) dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | \frac{1}{2}x^2 \log x + \frac{3}{4}x^2 | MATH |
[
{
"content": "Evaluate the indefinite integral \\int \\frac{dx}{x \\log x + 2x}. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | \log(\log x + 2) | MATH |
[
{
"content": "Evaluate the indefinite integral \\int \\frac{\\cos x + \\cot x + \\csc x + 1}{\\sin x + \\tan x + \\sec x + 1} dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | \log(\sin x) | MATH |
[
{
"content": "Evaluate the indefinite integral \\int \\frac{x^{2024} - 1}{x^{506} - 1} dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | x + \frac{x^{507}}{507} + \frac{x^{1013}}{1013} + \frac{x^{1519}}{1519} | MATH |
[
{
"content": "Evaluate the indefinite integral \\int \\csc^2(x) \\tan^{2024}(x) dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | \frac{\tan^{2023}(x)}{2023} | MATH |
[
{
"content": "Evaluate the indefinite integral \\int \\cos^x(x)(\\log(\\cos x) - x \\tan x) dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | \cos^x(x) | MATH |
[
{
"content": "Evaluate the indefinite integral \\int (x + 1 - e^{-x})e^{xe^x} dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | e^{(e^x-1)x} | MATH |
[
{
"content": "Evaluate the indefinite integral \\int \\left(\\frac{\\arctan(x)}{1 - x^2} + \\frac{\\text{arctanh}(x)}{1 + x^2}\\right) dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | \arctan(x)\text{arctanh}(x) | MATH |
[
{
"content": "Evaluate the indefinite integral \\int \\sum_{k=0}^{\\infty} \\sin\\left(\\frac{k\\pi}{2}\\right) \\frac{x^k}{k!} dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | \frac{\log(x^2 + 1)}{2} | MATH |
[
{
"content": "Evaluate the indefinite integral \\int \\frac{x^4}{3 - 6x + 6x^2 - 4x^3 + 2x^4} dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | \frac{x^2}{2} + \frac{1}{4}\log(3 - 6x + 6x^2 - 4x^3 + 2x^4) | MATH |
[
{
"content": "Evaluate the indefinite integral \\int x^{\\frac{1}{\\log x}} dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | ex | MATH |
[
{
"content": "Evaluate the indefinite integral \\int \\text{sech}(x) dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 \arctan(e^x) | MATH |
[
{
"content": "Evaluate the indefinite integral \\int \\frac{e^x}{(1 + e^x) \\log(1 + e^x)} dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | \log(\log(1 + e^x)) | MATH |
[
{
"content": "Evaluate the indefinite integral \\int (1 + x + x^2 + x^3 + x^4)(1 - x + x^2 - x^3 + x^4) dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | x + \frac{x^3}{3} + \frac{x^5}{5} + \frac{x^7}{7} + \frac{x^9}{9} | MATH |
[
{
"content": "Evaluate the indefinite integral \\int (x + \\sin(x) + x \\cos(x) + \\sin(x) \\cos(x)) dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | \frac{(x + \sin(x))^2}{2} | MATH |
[
{
"content": "Evaluate the indefinite integral \\int (\\sin^2(x) + \\cos^2(x) + \\tan^2(x) + \\cot^2(x) + \\sec^2(x) + \\csc^2(x)) dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2 \tan(x) - 2 \cot(x) - x | MATH |
[
{
"content": "Evaluate the indefinite integral \\int (2 \\log x + 1)e^{(\\log x)^2} dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | xe^{(\log x)^2} | MATH |
[
{
"content": "Evaluate the indefinite integral \\int ((1 - x)^3 + (x - x^2)^3 + (x^2 - 1)^3 - 3(1 - x)(x - x^2)(x^2 - 1)) dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 0 | MATH |
[
{
"content": "Evaluate the indefinite integral \\int (\\sin^6 x + \\cos^6 x + 3 \\sin^2 x \\cos^2 x) dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | x | MATH |
[
{
"content": "Evaluate the indefinite integral \\int (x + e + 1)^x e^{ex} dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | x^{e+1}e^x | MATH |
[
{
"content": "Evaluate the indefinite integral \\int \\frac{1 + 2x^{2022}}{x + x^{2023}} dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | \frac{1}{2022} \log(x^{2022} + x^{4044}) | MATH |
[
{
"content": "Evaluate the indefinite integral \\int (3 \\sin(20x) \\cos(23x) + 20 \\sin(43x)) dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | \sin(20x) \sin(23x) | MATH |
[
{
"content": "Evaluate the indefinite integral \\int \\frac{\\sin x}{2e^x + \\cos x + \\sin x} dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | \frac{x - \log(2e^x + \cos x + \sin x)}{2} | MATH |
[
{
"content": "Evaluate the indefinite integral \\int \\frac{\\log(x/\\pi)}{(\\log x)^{\\log(\\pi e)}} dx. Do not include the constant +C.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | \frac{x}{(\log x)^{\log \pi}} | MATH |
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