Integrate the following functions `x^2/sqrt(x^6+a^6)`

Explanation

Puttinng `x^3 = t`, we have
`dt = 3x^2 dx gt x^2 dx = 1/3 dt`
therefore` int x^2/sqrt(x^6+a^6) dx = int1/sqrt(t^2+(a^3)^2) 1/3 dt`
`=1/3 log|t+sqrt(t^2+(a^3)^2)|+c`
`=1/3 log|x^3+sqrt(x^6+a^6)|+c`