How to use complex analysis to evaluate the trigonometric integral $\int_{0}^{2 \pi}{\frac {\cos \left( x \right) }{2+\cos \left( x \right) }}$
Using residues to evaluate the integral $\int_{-\pi}^{\pi} \frac{\cos(n\theta)}{1-2a\cos(\theta)+a^2}d\theta$, $|a|<1$