# Elementary contour integral

I have an integral

$$\int_{-\infty}^{\infty}\frac{1}{(\omega^{2}-4)(\omega-2-i)(\omega+2-i)}d\omega$$

And I wish to evaluate this using Cauchy's Integral Theorem. I understand that with a simple pole on the real axis like

$$\frac{sin(x)}{x}$$

We can break the contour around $$x=0$$ and use Jordan's Lemma as the real axis goes to infinity. However I'm still unconfident in dealing with two poles on the real axis ($$\omega=\pm2)$$. How should I go about this?

Hint: All the poles are simple, so you could break the integrand into a sum of four simple fractions of the form $$\frac{c_k}{w-p_k}$$, right?