The positive integer $n \leq 5$ for which $\int_0^1 e^x(x-1)^n d x=16-6 e$ is

If $f(x)=\sin ^6 x+\cos ^6 x+2 \sin ^3 x \cos ^3 x$, then $\int_0^{\pi / 4} \frac{\sin ^2 2 x}{f(x)} d x=$

$$ \int_3^5(x-3)^3(5-x)^5 d x= $$

$$\mathop {\lim }\limits_{x \to \infty } \frac{\pi}{2 n}\left[\sin \frac{\pi}{2 n}+\sin \frac{2 \pi}{2 n}+\ldots+\sin \frac{\pi}{2}\right]= $$