$$ \int_{\frac{5}{6}}^\pi \cos ^{-4} x d x= $$

$$ \int\limits_0^{\frac{3 \pi}{2}} \frac{\cos ^3 x}{\cos ^3 x+\sin ^3 x} d x= $$

If $k \in N$, then $\lim\limits_{n \rightarrow \infty}\left[\frac{1}{n+1}+\frac{1}{n+2}+\frac{1}{n+3}+\ldots .+\frac{1}{k n}\right]=$

$$ \int_{-1}^4 \sqrt{\frac{4-x}{x+1}} d x= $$