[User]
Evaluate the indefinite integral \int \frac{x + \sqrt{x}}{1 + \sqrt{x}} dx. Do not include the constant +C.

Present the answer in LaTex format: \boxed{Your answer}

dataset: MATH


[User]
Evaluate the indefinite integral \int \frac{e^{x+1}}{e^x + 1} dx. Do not include the constant +C.

Present the answer in LaTex format: \boxed{Your answer}

ground_truth: e \log(e^x + 1)


[User]
Evaluate the indefinite integral \int \sqrt[3]{3 \sin(x) - \sin(3x)} dx. Do not include the constant +C.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Evaluate the indefinite integral \int \frac{x \log(x) \cos(x) - \sin(x)}{x \log^2(x)} dx. Do not include the constant +C.

Present the answer in LaTex format: \boxed{Your answer}

ground_truth: \frac{\sin(x)}{\log(x)}


[User]
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.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Evaluate the indefinite integral \int \frac{e^{2x}}{(x^2 + x)(xe^x)^4 + 1} dx. Do not include the constant +C.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Evaluate the indefinite integral \int (\sec^4(x) - \tan^4(x)) dx. Do not include the constant +C.

Present the answer in LaTex format: \boxed{Your answer}

ground_truth: 2 \tan(x) - x


[User]
Evaluate the indefinite integral \int \frac{\sin(4x) \cos(x)}{\cos(2x) \sin(x)} dx. Do not include the constant +C.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Evaluate the indefinite integral \int \sin(x) \sinh(x) dx. Do not include the constant +C.

Present the answer in LaTex format: \boxed{Your answer}

ground_truth: \frac{1}{2}(\sin(x) \cosh(x) - \cos(x) \sinh(x))


[User]
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.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Evaluate the indefinite integral \int \frac{(x - 1)\log(x+1)}{(x + 1)\log(x-1)} dx. Do not include the constant +C.

Present the answer in LaTex format: \boxed{Your answer}

ground_truth: x


[User]
Evaluate the indefinite integral \int (x \log x + 2x) dx. Do not include the constant +C.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Evaluate the indefinite integral \int \frac{dx}{x \log x + 2x}. Do not include the constant +C.

Present the answer in LaTex format: \boxed{Your answer}

ground_truth: \log(\log x + 2)


[User]
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.

Present the answer in LaTex format: \boxed{Your answer}

ground_truth: \log(\sin x)


[User]
Evaluate the indefinite integral \int \frac{x^{2024} - 1}{x^{506} - 1} dx. Do not include the constant +C.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Evaluate the indefinite integral \int \csc^2(x) \tan^{2024}(x) dx. Do not include the constant +C.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Evaluate the indefinite integral \int \cos^x(x)(\log(\cos x) - x \tan x) dx. Do not include the constant +C.

Present the answer in LaTex format: \boxed{Your answer}

ground_truth: \cos^x(x)


[User]
Evaluate the indefinite integral \int (x + 1 - e^{-x})e^{xe^x} dx. Do not include the constant +C.

Present the answer in LaTex format: \boxed{Your answer}


[User]
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.

Present the answer in LaTex format: \boxed{Your answer}

ground_truth: \arctan(x)\text{arctanh}(x)


[User]
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.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Evaluate the indefinite integral \int \frac{x^4}{3 - 6x + 6x^2 - 4x^3 + 2x^4} dx. Do not include the constant +C.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Evaluate the indefinite integral \int x^{\frac{1}{\log x}} dx. Do not include the constant +C.

Present the answer in LaTex format: \boxed{Your answer}

ground_truth: ex


[User]
Evaluate the indefinite integral \int \text{sech}(x) dx. Do not include the constant +C.

Present the answer in LaTex format: \boxed{Your answer}

ground_truth: 2 \arctan(e^x)


[User]
Evaluate the indefinite integral \int \frac{e^x}{(1 + e^x) \log(1 + e^x)} dx. Do not include the constant +C.

Present the answer in LaTex format: \boxed{Your answer}


[User]
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.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Evaluate the indefinite integral \int (x + \sin(x) + x \cos(x) + \sin(x) \cos(x)) dx. Do not include the constant +C.

Present the answer in LaTex format: \boxed{Your answer}


[User]
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.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Evaluate the indefinite integral \int (2 \log x + 1)e^{(\log x)^2} dx. Do not include the constant +C.

Present the answer in LaTex format: \boxed{Your answer}


[User]
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.

Present the answer in LaTex format: \boxed{Your answer}


[User]
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.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Evaluate the indefinite integral \int (x + e + 1)^x e^{ex} dx. Do not include the constant +C.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Evaluate the indefinite integral \int \frac{1 + 2x^{2022}}{x + x^{2023}} dx. Do not include the constant +C.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Evaluate the indefinite integral \int (3 \sin(20x) \cos(23x) + 20 \sin(43x)) dx. Do not include the constant +C.

Present the answer in LaTex format: \boxed{Your answer}


[User]
Evaluate the indefinite integral \int \frac{\sin x}{2e^x + \cos x + \sin x} dx. Do not include the constant +C.

Present the answer in LaTex format: \boxed{Your answer}

ground_truth: \frac{x - \log(2e^x + \cos x + \sin x)}{2}


[User]
Evaluate the indefinite integral \int \frac{\log(x/\pi)}{(\log x)^{\log(\pi e)}} dx. Do not include the constant +C.

Present the answer in LaTex format: \boxed{Your answer}

ground_truth: \frac{x}{(\log x)^{\log \pi}}