Question

Solve

$\int \frac{dx}{5+4cosx}$

Answer 1

$\int \frac{dx}{5+4\cos x}$

Let $t=tan\frac{x}{2}$ $dt=\frac{1}{2}{\sec }^2\frac{x}{2}dx$

$=\frac{1}{2}(1+t^2)dx$

$\Rightarrow dx=\frac{2dt}{1+t^2}$