Integrate the following functions w. r. t. x : ∫ 1/(4 - 5 cos x) . dx

Question

Integrate the following functions w. r. t. x :

\(\int \frac{1}{4 - 5\,cos\,x}.dx\)

∫ 1/(4 - 5 cos x) . dx

Answer 1

∫ 1/(4 - 5 cos x) . dx

\(-\frac{2}{9}\times \frac{1}{2\times \frac{1}{3}}\) log\(\left|\cfrac{t - \frac{1}{3}}{t + \frac{1}{3}}\right| + c\)