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

Theorem

 * $\displaystyle \int x^m \left({a x + b}\right)^n \rd x = \frac {-x^{m+1} \left({a x + b}\right)^{n + 1} } {\left({n + 1}\right) b} + \frac {m + n + 2} {\left({n + 1}\right) b} \int x^m \left({a x + b}\right)^{n + 1} \rd x$