Reduction Formula for Primitive of Power of x by Power of a x + b/Increment of Power of a x + b/Proof 1

Proof
From Reduction Formula for Primitive of Power of $x$ by Power of $a x + b$: Decrement of Power of $x$:


 * $\displaystyle \int x^m \left({a x + b}\right)^n \rd x = \frac {x^{m + 1} \left({a x + b}\right)^n} {m + n + 1} + \frac {n b} {m + n + 1} \int x^m \left({a x + b}\right)^{n - 1} \rd x$

Substituting $n + 1$ for $n$: