Integrate the following w.r.t.x.
`(x sin^(-1)x)/(sqrt(1-x^(2)))`

Explanation

`"Let I"=int (x sin^(-1)x)/(sqrt(1-x^(2)))dx=int x sin^(-1)x.(1)/(sqrt(1-x^(2)))dx`
`"Put" sin^(-1)x=t " "therefore (1)/(sqrt(1-x^(2)))dx=dt and x=sin t`
`therefore I=int (sin t).t dt=int t sint dt`
`=t int sin tdt-int [(d)/(dt)(t) int sin t dt]dt`
`=t(-cos t)-int 1.(-cos t)dt `
`=-t cos t+int cos t dt " "=-t cos t+sin t+c`
`=-t sqrt(1-sin^(2)t)+sint+c`
`=-sin^(-1)x.sqrt(1-x^(2))+x+c`
`=-sqrt(1-x^(2)).sin^(-1)x+x+c`