I want to compute $\int\_{|z|=R} \frac{|dz|}{|z-a|^4}$ when $R>0, |a|\neq R$.
I did so by parametrizing the circle, but this way required many pages of tedious calculations. 

Do you have a more straightforward way to do it?

Let me mention that my issue here is that we integrate by $|dz|$ not by $dz$, so all the known theorems I know fail to be applied -at least in this form of the integral. 

Thanks