Having difficulties proving this equality: Let $a \in \mathbb{R}_+^*$.
$\int_{-\infty}^{\infty}\frac{cos(x)}{x^2+a^2}dx = \frac{\pi e^{-a}}{a}$
So far I have identified that $\frac{cos(x)}{x^2+a^2} = \frac{Re(e^{ix})}{x^2+a^2}$ but I still don't know if this is the right way.
