Task 7.9: Prove that \int_0^(2\pi ) (cosx)/(a+cosx)dx=2\pi (1-(a)/(\sqrt(a^(2)-1))), for a>1.
All statements must be verified by means of complex analysis. The question is from "Com-
plex Analysis" by Christian Berg 2012 version, so I can only use the theory from the first 7
chapters.