Evaluate : `intx^(2)sin^(-1)xdx`.

Explanation

Integrating by parts, taking `sin^(-1)` x a the first function we get
`intx^(2)sin^(-1)xdx=(sin^(-1)x)*(x^(3))/(3)-int(1)/(sqrt1-x^(2))*(x^(3))/(3)dx`
`=(x^(2)sin^(-1)x)/(3)-(1)/(3)int(x^(3))/(sqrt(1-x^(2)))dx`
`=(x^(2)sin^(-1)x)/(3)+(1)/(3)int(t(1-t^(2)))/(t)dt," where"(1-x^(2))=t^(2)`
`=(x^(2)sin^(-1)x)/(3)+(1)/(3)intdt-(1)/(3)int^(2)dt`
`=(x^(2)sin^(-1)x)/(3)+(1)/(3)t-(1)/(9)t^(3)+C`
`=(x^(2)sin^(-1)x)/(3)+(1)/(3)sqrt(1-x^(2))-(1)/(9)(1-x^(2))^(3//2)+C`.