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