im stuck halfway through this problem.
The question is: if a>0, integral from 0 to 2pi of
I= [a dX]/[a^2+ sin^2(X)]=pi/(1+a^2)^.5
i let z=e^iX. then did some working and have
I=2/i integral az dz/(z-g)(z-f)(z-k)(z-L) where g=a-(a^2+1)^.5
f=a+(a^2+1)^.5 k==-a+(a^2+1)^.5 L=-a-(a^2+1)^.5
i dont know how to work out the residue. could someone show me how using laurent series.