Primitive of x over a x + b cubed/Proof 2

Theorem

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

Proof
From Primitive of $x$ by Power of $a x + b$:
 * $\displaystyle \int x \left({a x + b}\right)^n \ \mathrm d x = \frac {\left({a x + b}\right)^{n + 2} } {\left({n + 2}\right) a^2} - \frac {b \left({a x + b}\right)^{n + 1} } {\left({n + 1}\right) a^2} + C$

where $n \ne - 1$ and $n \ne - 2$.

The result follows by setting $n = -3$.