Question:
$f^{\prime}(a x+b)[f(a x+b)]^{n}$
Solution:
$f^{\prime}(a x+b)[f(a x+b)]^{n}$
Let $f(a x+b)=t \Rightarrow a f^{\prime}(a x+b) d x=d t$
$\Rightarrow \int f^{\prime}(a x+b)[f(a x+b)]^{n} d x=\frac{1}{a} \int t^{n} d t$
$=\frac{1}{a}\left[\frac{t^{n+1}}{n+1}\right]$
$=\frac{1}{a(n+1)}(f(a x+b))^{n+1}+\mathrm{C}$