$f'\left( {ax + b} \right){\left[ {f\left( {ax + b} \right)} \right]^n}$

Let $I = \int {f'\left( {ax + b} \right){{\left[ {f\left( {ax + b} \right)} \right]}^n}} dx$

Let $f\left( {ax + b} \right) = t$ $\Rightarrow$ $af'\left( {ax + b} \right)dx = dt$

$\therefore$ $I = \cfrac{1}{a}\int {{t^n}dt} = \cfrac{1}{a} \cdot \cfrac{{{t^{n + 1}}}}{{n + 1}} + C$

$= \cfrac{1}{{\left( {n + 1} \right)a}}{\left[ {f\left( {ax + b} \right)} \right]^{n + 1}} + C$ $\Rightarrow$