Question

Integrate:

${\int }_0^{\pi }\frac{dx}{5+3cosx}$

Answer 1

$\int 1/5+3cosx.dx$

use$t=tanx/2$ thus, $cosx=1-t^2/1+t^2$ and $co{s}^{(}2)x/2=1/(1+t{)}^2$

$dt/dx=1/2.se{c}^{(}2).x/2$
$dt/dx=\left(\right[1+t^2\left]/2\right)$

By substitution, we eliminate cosx etc and get ...
int $1/5+3cosx.dx=int2/(8-2t^2).dt$
=int$1/(4-t^2).dt$
=$1/4.ln\left(\right[2+t\left]/\right[2-t\left]\right)+C$