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

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

Setting $a := 1, b := 0, p x + q := a x + b$: