If $x \in\left[2 n \pi-\frac{\pi}{4}, 2 n \pi+\frac{3 \pi}{4}\right]$ and $n \in Z$, then $\int \sqrt{1-\sin 2 x} d x=$

$\int e^x\left(\frac{x+2}{x+4}\right)^2 d x=$

If $\int \frac{1}{1-\cos x} d x=\tan \left(\frac{x}{\alpha}+\beta\right)+c$, then one of the values of $\frac{\pi \alpha}{4}-\beta$ is

If $n \geq 2$ is a natural number and $0<\theta<\frac{\pi}{2}$, then $\int \frac{\left(\cos ^n \theta-\cos \theta\right)^{1 / n}}{\cos ^{n+1} \theta} \sin \theta d \theta=$