Question

Integrate the function $\frac{\cos x}{\sqrt{4-{\sin }^{2}x}}$

Answer 1

Let $\sin x=t\Rightarrow \cos xdx=dt$
$\Rightarrow \int \frac{\cos x}{\sqrt{4-{\sin }^{2}x}}dx=\int \frac{dt}{\sqrt{(2{)}^2-(t{)}^2}}$
$={\sin }^{-1}\left(\frac{t}{2}\right)+C$
$={\sin }^{-1}\left(\frac{\sin x}{2}\right)+C$