Question

Integrate the following functions w.r.t. x.

$\int \frac{cosx}{\sqrt{4-si{n}^{2}x}}dx.$

Answer 1

$LetI=\int \frac{cosx}{\sqrt{4-si{n}^{2}x}}dxPutsinx=t\Rightarrow cosxdx=dt\therefore I=\int \frac{cosx}{\sqrt{4-t^2}}\frac{dt}{cosx}=\int \frac{1}{\sqrt{4-t^2}}dt=si{n}^{-1}\left(\frac{t}{2}\right)+C[\int \frac{dx}{\sqrt{a^2-x^2}}=si{n}^{-1}\left(\frac{x}{a}\right)]=si{n}^{-1}\left(\frac{sinx}{2}\right)+C$