$$\int _ { - \pi } ^ { \pi } \cos n x d x$$
$\left\{\begin{matrix}\frac{2\sin(\pi n)}{n},&n\neq 0\\2\pi ,&n=0\end{matrix}\right.$
$\left\{\begin{matrix}\frac{2\left(\pi n\cos(\pi n)-\sin(\pi n)\right)}{n^{2}},&n\neq 0\\0,&n=0\end{matrix}\right.$
