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

Calculate the integral where

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