How to find indefinite integral using substitution?

Question

How to find indefinite integral using substitution?

4y-2/(y^2-y)^4 dy

Thanks for help on showing steps.

Answer 1

If u = y^2 - y, then du = 2u - 1. Use this to substitute into your original equation (S means the integration symbol):

S (4y - 2)/(y^2 - y)^4 dy = S 2/u^4 du
= S 2u^(-4) du
= 2u^(-3)/(-3) + C
= -2/3u^3 + C
= -2/3(y^2 - y)^3 + C