Evaluate `int (dx)/(xsqrt(x^6-1))`

Explanation

Put `x^(3)=t` so that `3x^(2)dx=dt" or "x^(2)dx=(1)/(3)dt`.
`:.int(dx)/(x*sqrt(x^(6)-1))dx`
[multiplying numerator and denominator by `x^(2)]`
`=(1)/(3)int(1)/(tsqrt(t^(2)-1))dt=(1)/(3)sec^(-1)t+C=(1)/(3)sec^(-1)t+C=(1)/(3)sec^(-1)x+C`.