Question

Slove
$\int \frac{3+2cosx}{(2+3cosx{)}^2}dx$

Answer 1

$I=\int \frac{3+2cosx}{(2+3cosx{)}^2}dx$

multiplying Nr & Dr by $Cose{c}^{2}x$

$=\int \frac{3cose{c}^{2}x+2cotx.cotex}{(2cosecx+3cotx{)}^2}dx$

Let $2cosecx+3cotx=t$

$(-2cosecx-cotx-3cose{c}^{2}x)dx=dt$

$I=-\int \frac{1}{t^2}dt=\frac{1}{t}=\frac{1}{2cosecx+cotx}+c$

$=\frac{sinx}{2+3cosx}+c$