Yeah I can't immediately spot something that would make it easy. It's much easier to prove that the difference between the integral of log(a^2 - 2 a cos(x) + 1

Yeah I can't immediately spot something that would make it easy. It's much easier to prove that the difference between the integral of log(a^2 - 2 a cos(x) + 1) and 2 pi log(a) goes to 0 when a goes to infinity.