Primitive of Power of a x + b

Theorem

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

where $n \ne 1$.

Proof
Let $u = a x + b$.

Then:

Also see

 * Primitive of Reciprocal of $a x + b$ for the case when $n = -1$