Hi! I'm new here, been a fan of this site for years, but only now I felt the need of registering. 1. The problem statement, all variables and given/known data Use the Residue Theorem to solve the integral: ∫[(cos(2t)) / (5-4*cos(t)) ] dt from t=0 to t=2pi 2. The attempt at a solution I did a variable change z=eit. With that: (1/(2i))*∫[ (z2 + z-2) / (-2z2 +5z -2)] Only taking the integral, I came up with: ∫[ (z4 +1) / (z2 * (z-1/2) * (z-2))] Which has 3 singularaties: 1/2 , 2 and 0 Only 2 is not in the path considered. The residue in 1/2 is -17/6 and in 0 is 5/2 as they are poles of order 1 and 2 respectively. And with that, I have: 1/(2i) * 2*pi*i * (-17/6 + 5/2) = - Pi/3 Which is wrong, as the answer is actually Pi/6 Where did I go wrong? Thanks in advance!