Hi I'm having some problems with the below question

Use the residue theorem to compute

$\displaystyle \int\limits_{-\infty}^{\infty} \frac{\cos(x)}{1+x^2} dx$

So i rewrote the intergral as

$\displaystyle \int\limits_{-\infty}^{\infty} \frac{\cos(x)}{1+x^2} dx = \Re(\int\limits_{-\infty}^{\infty} \frac{e^{jx}}{1+x^2} dx)$

Where do i go from here?

Thanks