$\int \frac{\sin x + \cos x}{\sqrt{1 + \sin 2x}} \, dx = $

If $\int(1-\cos x) \operatorname{cosec}^2 x \, dx = f(x) + c$,then $f(x)$ is equal to

$\int {(\sin^4 x - \cos^4 x) \, dx} = $

$\int \left(1 + \frac{x}{1!} + \frac{x^2}{2!} + \dots \infty \right) dx = $

The solution of the equation $\frac{d^2y}{dx^2} = e^{-2x}$ is

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