Evaluate : `int x " sin"^(2) " x dx "`

Explanation

`int (x " sin"^(-1) x)/(sqrt(1-x^(2))) dx " " underset(rArr dx =cos 0 d0)("Let" x = sin 0)`
`int ("sin 0.0)/(sqrt(1-sin^(2)0)). cos 0do= int 0sin 0d0`
`=0int sin 0 d0 - int { (d)/(dp)0. int sin 0 do } d0`
` "(Taking 0 as 1st function)"`
`=0(-cos 0) - int 1.(-cos 0)do`
`=- 0 cos 0 + int cos + int cos 0 do0`
`=- 0 sqrt(1-sin^(2))0 + sin 0 +c`
`=x -sqrt(1-x^(2)) . sin ^(-1) x+c.`