Question

Solve:-
$\int \frac{x}{\sqrt{4-x^2}}dx$

Answer 1

Let

$x=2sina$

$dx=2cosada$

$\int \frac{x}{\sqrt{4-x^2}}dx$

$=\int \frac{2sina}{2\sqrt{1-{\sin }^{2}a}}2cosada$

$=\int 2sinada$

$=-2cosa+C$

$=-2cos{\sin }^{-1}\left(\frac{x}{2}\right)+C$