Question

Solve:
$\frac{x{\cos }^{-1}x}{\sqrt{1-x^2}}dx$

Answer 1

$\frac{x{\cos }^{-1}x}{\sqrt{1-x^2}}dx$

Put $t={\cos }^{-1}x$

$x=\cos t$

$dt=\frac{-1}{\sqrt{1-x^2}}dx$

$=-\int \cos tdt$

$=-\sin t+c$

Put value of $t={\cos }^{-1}x$

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

$\frac{x{\cos }^{-1}x}{\sqrt{1-x^2}}dx=-\sin \left({\cos }^{-1}x\right)+c$.