Reduction Formula for Primitive of Power of x by Power of a x + b/Increment of Power of x/Proof 2

Proof
From Reduction Formula for Primitive of Power of $a x + b$ by Power of $p x + q$: Increment of Power:
 * $\displaystyle \int \left({a x + b}\right)^m \left({p x + q}\right)^n \rd x = \frac 1 {\left({n + 1}\right) \left({b p - a q}\right)} \left({\left({a x + b}\right)^{m + 1} \left({p x + q}\right)^{n + 1} - a \left({m + n + 2}\right) \int \left({a x + b}\right)^m \left({p x + q}\right)^{n + 1} \rd x}\right)$

Setting $p := 1, q := 0, m := n, n := m$: