Answer
See below.
Work Step by Step
$\displaystyle \int(ax+b)^{n}dx=\quad \left[\begin{array}{ll}
u=ax+b, & du=adx, \\
& dx=\frac{1}{a}du
\end{array}\right]$
$=\displaystyle \frac{1}{a}\int u^{n}du$
apply power rule for $n\neq-1$
$=\displaystyle \frac{1}{a}\cdot\frac{u^{n+1}}{n+1}+C\qquad (n\neq-1)$
bring back the variable $x$
= $ \displaystyle \frac{(ax+b)^{n+1}}{a(n+1)}+C,\qquad (n\neq-1)$
