1. The problem statement, all variables and given/known data integral 1/(a+cos(t))^2 from 0 to pi. 2. Relevant equations cos(t)=1/2(e^it+e^-it) z=e^it dz/(ie^it)=dt 3. The attempt at a solution int dt/(a+cos(t))^2 = int dz/iz(a2+az+az-1+z2/4 +1/2 +z-2/4) so with these types of problems I normally can factor this guy some how and get a nice looking quadratic to find the roots and calculate the residue and I'm done. I don't know what to do with this thing in the denominator how can I find the poles of this guy?