Question

Integrate the function $\frac{\cos x}{\sqrt{1+\sin x}}$

Answer 1

Put $1+\sin x=t$
$\therefore \cos xdx=dt$
$\Rightarrow \int \frac{\cos x}{\sqrt{1+\sin x}}dx=\int \frac{dt}{\sqrt{t}}$
$=\frac{t^{\frac{1}{2}}}{\frac{1}{2}}+C$
$=2\sqrt{t}+C=2\sqrt{1+\sin x}+C$