Homework Statement
Consider the inner product
$$\frac{1}{2\pi}\int_0^{2\pi} \left(\frac{3}{5 - 4\cos(x)}\right) e^{-ikx} dx, \quad k \in \mathbb{Z}, \quad x \in \mathbb{R}.$$
Homework Equations
Is there a method to solve this without using the residue theorem, e.g. integration by parts...