$\int \log x \cdot(\log x+2) dx =$

$\int {{e^x}\left[ {f(x) + f'(x)} \right]\,dx} $ is equal to

$\int e^{-2x} \left( \frac{1 - \sin 2x}{1 + \cos 2x} \right) dx = $

Integrate the function: $\frac{2+\sin 2x}{1+\cos 2x} e^x$

$\int e^x \left( \log x + \frac{1}{x} - \frac{1}{x} + \frac{1}{x^2} \right) dx$ is not the original,the question is $\int e^x \left( \log x + \frac{1}{x} \right) dx$ or similar. Given the options,the integral is $\int e^x \left( \log x + \frac{1}{x} \right) dx$. Let us evaluate $\int e^x \left( \log x + \frac{1}{x} \right) dx$.

The value of $\int e^{x}(x^{5}+5x^{4}+1)dx$ is