Primitive of x over a x + b cubed

Theorem

 * $\displaystyle \int \frac {x \ \mathrm d x} {\left({a x + b}\right)^3} = \frac {-1} {a^2 \left({a x + b}\right)} + \frac b {2 a \left({a x + b}\right)^2} + C$

Proof
Put $u = a x + b$.

Then:

Then: