Question

Evaluate: $\frac{\cos x}{(1+\sin x\left)\right(2+sinx)}$

Answer 1

$\int \frac{cosx}{(1+sinx)(2+sinx}dx.$

$=\int \frac{du}{u(u-1)}$ (2+sinx)=a

$\int \frac{-1}{u}+\frac{1}{u-1}du$ du=cox dx

$\int \frac{1}{u-1}-\frac{1}{u}du$ $\Rightarrow$ $1+sinx=u-1$

$ln(u-1)-inu+c.$ $\frac{1}{u-1}-\frac{1}{a}=\frac{u-u+1}{i}n\frac{a-1}{a}+c=$ln$\frac{1+sinx}{2+sinx}+c$ $(u-1)u$