Find the integral.

Question

x^4/the square root of (x^5-1)

Answer 1

did you notice that the derivative of x^5=1 is 4x^4 which is a multiple of x^4, so it is straightforward

integral [ x4/(√(x^5 - 1)^(1/2)
= int [ x^4 (x^5 - 1)^(-1/2)
= (2/5) (x^5 - 1)^(1/2) + c

check by taking the derivative, it works

Answer 2

correctin: the derivative of x^5=1 is 5x^4