How to solve $\int_0^\pi{\frac{\cos{nx}}{5 + 4\cos{x}}}dx$? How can I solve the following integral?
$$\int_0^\pi{\frac{\cos{nx}}{5 + 4\cos{x}}}dx, n \in \mathbb{N}$$

$2 I(n+1) + 5I(n) + 2I(n-1) = 0$
d’ou $I(n) = (-1/2)^n . I(0) = (-1/2)^n . \pi/3$
fjaclot
