`(x^(3))/(sqrt(1-x^(8)))`

Explanation

माना `I=int(x^(3))/(sqrt(1-x^(8)))dx`
माना `x&(4)=t" "rArr" "4x^(3)dx=dt" "rArr x^(3)dx=(dt)/(4)`
`I=(1)/(4)int(1)/(sqrt(1-t^(2)))dt=(1)/(4)sin^(-1)t+C`
`=(1)/(4)sin^(-1)(x^(4))+C`