Originally Posted by

**roshx** Hi, I'm really stuck on this question, I don't really know where to start.

Calculate the integral $\displaystyle \int_0^\pi \displaystyle\frac{1}{(\alpha+cos\theta)^2}d\theta$ where $\displaystyle \alpha>1$

In my notes I have similar-ish examples which used the substitution $\displaystyle z=e^{i\theta}$ but in those, the integral went from 0 to $\displaystyle 2\pi$, so gave a closed contour & then we could use residues. I thought maybe I could substitute $\displaystyle z=e^{2i\theta}$ instead but that didn't seem to get me anywhere. So now I'm clueless, any hints would be much appreciated.