`(x^(2))/(sqrt(x^(6)+a^(6)))`

Explanation

`int(x^(2))/(sqrt(x^(6)+a^(6)))dx=int(x^(2))/(sqrt((x^(3))^(2)+(a^(3))^(2))dx`
`=int(1)/(sqrt(t^(2)+(a^(3))^(2)))(dt)/(3)" माना "x^(3)=t`
`=(1)/(3)log|t+sqrt(t^(2)+(a^(3))^(2))|+c" "rArr 3x^(2)dx=dt`
`=(1)/(3)log|x^(3)+sqrt(x^(6)+a^(6))|+c" "rArr x^(2)dx=(dt)/(3)`