$\int {e^{\log (\sin x)}} \, dx = $

$\int \frac{\cos 2x - \cos 2\alpha}{\cos x - \cos \alpha} dx$ is equal to

$\int {\frac{{a{x^{ - 2}} + b{x^{ - 1}} + c}}{{{x^{ - 3}}}}} \,dx = $

$\int \frac{\sin ^{2} x-\cos ^{2} x}{\sin ^{2} x \cos ^{2} x} d x$ is equal to

If $x \neq (2n+1) \frac{\pi}{2}, n \in Z$ and $\cos x \neq \frac{-1}{2}$,then evaluate the integral:
$\int \left( \frac{\sin x + \sin 2x}{1 + \cos x + \cos 2x} \right)^2 dx$

$\int \frac{\sin x + \csc x}{\tan x} \, dx = $