Question

Evaluate
$\int \frac{cosx}{\sqrt{1+\sin x}}dx$

Answer 1

$I=\int \frac{\cos x}{\sqrt{1+\sin x}}dx$

Let $1+\sin x=t$

$\cos xdx=dt$

$I=\int \frac{dt}{\sqrt{t}}$

$I=2\sqrt{t}+C$

$=2\sqrt{1+\sin x}+C$