$\int\sin(\log x)\,dx = $

The value of $\int\dfrac{n\sqrt{\text{cosec}^2 x^n - 1}}{x^{(1-n)}}\,dx$ is ...

$\int\dfrac{(x+1)\,dx}{x(1+xe^x)} = \ldots\ldots$

The value of the definite integral $\int_0^{\log_e 5}\dfrac{e^x\sqrt{e^x-1}}{e^x+3}\,dx$ is equal to...