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Question:

$f^{\prime}(a x+b)[f(a x+b)]^{n}$

Solution:

$f^{\prime}(a x+b)[f(a x+b)]^{n}$

Let $f(a x+b)=t \Rightarrow a f^{\prime}(a x+b) d x=d t$

$\Rightarrow \int f^{\prime}(a x+b)[f(a x+b)]^{n} d x=\frac{1}{a} \int t^{n} d t$

$=\frac{1}{a}\left[\frac{t^{n+1}}{n+1}\right]$

$=\frac{1}{a(n+1)}(f(a x+b))^{n+1}+\mathrm{C}$

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