How to evaluate $\int (5u-3)^{-6}\, du$?

Question

How do I integrate $$\int(5u-3)^{-6} du$$

This is my answer but I am not sure:

$$\frac{(5u-3)^{-5}}{-5}$$

I wish you would help me.

Answer 1

You just missed a $5$ factor in the denominator. How?

First substitute $t = 5u -3$ giving us: $$I = \int \frac{1}{(5u-3)^6}\, du = \frac{1}{5}\int \frac{1}{t^6}\, dt= \frac{-1}{25t^5} + c= -\frac{1}{25(5u-3)^5}+c$$

Answer 2

Substitute $$t=5u-3$$ then you will get $$dt=5du$$ can you finish?