Primitive of Power of a x + b

Theorem

 * $\displaystyle \int \paren {a x + b}^n \rd x = \frac {\paren {a x + b}^{n + 1} } {\paren {n + 1} a} + C$

where $n \ne 1$.

Proof
Let $u = a x + b$.

Then:

Also see

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