问题
设 $\int$ $f(u)$ $\mathrm{d}$ $u$ $=$ $F(u)$ $+$ $C$, 则：$\textcolor{Orange}{\int}$ $\textcolor{Orange}{f[\phi (x)] \phi ^{\prime} (x)}$ $\textcolor{Orange}{\mathrm{d} x}$ $\textcolor{White}{=}$ $?$
选项
[A]. $\int$ $f[\phi (x)] \phi ^{\prime} (x)$ $\mathrm{d} x$ $=$ $f[\phi(x)]$ $+$ $C$[B]. $\int$ $f[\phi (x)] \phi ^{\prime} (x)$ $\mathrm{d} x$ $=$ $F[\phi(x)]$
[C]. $\int$ $f[\phi (x)] \phi ^{\prime} (x)$ $\mathrm{d} x$ $=$ $F[\phi(x)]$ $+$ $C$
[D]. $\int$ $f[\phi (x)] \phi ^{\prime} (x)$ $\mathrm{d} x$ $=$ $F(x)$ $+$ $C$
$$\int \textcolor{Red}{f[\phi (x)] \phi ^{\prime} (x)} \mathrm{d} \textcolor{Yellow}{x} =$$ $$\int f[\phi(x)] \mathrm{d} [\phi(x)]$$ $$\textcolor{Orange}{\xrightarrow[]{u = \phi(x)}}$$ $$\int \textcolor{Red}{f(u)} \mathrm{d} \textcolor{Yellow}{u} =$$ $$\textcolor{Red}{F(u)} + \textcolor{Green}{C} =$$ $$\textcolor{Red}{F[\phi(x)]} + \textcolor{Green}{C}.$$