问题
通过凑微分，如何计算 [$\textcolor{Orange}{\int f(ax^{n}+b)x^{n-1} \mathrm{d} x}$] ?选项
[A]. $\int$ $f(ax^{n}+b)x^{n-1}$ $\mathrm{d} x$ $=$ $\frac{1}{na}$ $\int$ $f(ax^{n}+b)$ $\mathrm{d}$ $(ax^{n}+b)$ $+$ $C$[B]. $\int$ $f(ax^{n}+b)x^{n-1}$ $\mathrm{d} x$ $=$ $\frac{1}{na}$ $\int$ $f(ax^{n}+b)$ $\mathrm{d}$ $(ax^{n}+b)$
[C]. $\int$ $f(ax^{n}+b)x^{n-1}$ $\mathrm{d} x$ $=$ $\frac{1}{a}$ $\int$ $f(ax^{n}+b)$ $\mathrm{d}$ $(ax^{n}+b)$
[D]. $\int$ $f(ax^{n}+b)x^{n-1}$ $\mathrm{d} x$ $=$ $\frac{1}{na}$ $\int$ $f(ax^{n}+b)$ $\mathrm{d}$ $(ax^{n+1}+b)$
$$\int \textcolor{Red}{f(ax^{n}+b)x^{n-1}} \mathrm{d} \textcolor{Yellow}{x} =$$ $$\textcolor{Orange}{\frac{1}{na}} \textcolor{Green}{\times} \int \textcolor{Red}{f(ax^{n}+b)} \mathrm{d} \textcolor{Yellow}{(ax^{n}+b)}.$$其中，$a$ 和 $n$ 都是常数且 $a$ $\neq$ $0$, $n$ $\neq$ $0$.