`int(sin^(-1)x)^(2)dx`

Explanation

`int(sin^(-1)x)^(2)dx`
`=inttheta^(2).cos theta d theta" माना "x=sin theta`
`=theta^(2) int cos theta d theta" "rArr dx = cos theta d theta`
`" "-int{(d)/(d theta).theta^(2). Int cos theta d theta}d theta`
`=theta^(2)sin theta - int 2 theta sin theta d theta`
`=theta^(2)sin theta -2 [theta int sin theta d theta - int{(d)/(d theta )theta. int sin theta d theta } d theta ]`
`=theta^(2)sin theta - 2 [- theta cos theta+ int cos theta d theta]`
`=theta^(2) sin theta+ 2 theta cos theta - 2 sin theta +c`
`=x.(sin^(-1)x)^(2)+2sqrt(1-x^(2)).sin^(-1)x-2x+C`