问题
通过凑微分，如何计算 [$\textcolor{Orange}{\int f(\frac{1}{x}) \frac{1}{x^{2}} \mathrm{d} x}$] ?选项
[A]. $\int$ $f(\frac{1}{x}) \frac{1}{x^{2}}$ $\mathrm{d} x$ $=$ $- \int$ $f(\frac{1}{x})$ $\mathrm{d} (\frac{1}{x})$[B]. $\int$ $f(\frac{1}{x}) \frac{1}{x^{2}}$ $\mathrm{d} x$ $=$ $\int$ $f(\frac{1}{x})$ $\mathrm{d} (\frac{1}{x})$
[C]. $\int$ $f(\frac{1}{x}) \frac{1}{x^{2}}$ $\mathrm{d} x$ $=$ $- \int$ $f(\frac{1}{x})$ $\mathrm{d} x$
[D]. $\int$ $f(\frac{1}{x}) \frac{1}{x^{2}}$ $\mathrm{d} x$ $=$ $- \int$ $f(\frac{1}{x})$ $\mathrm{d} (\frac{1}{x})$ $+$ $C$
$$\int \textcolor{Red}{f(\frac{1}{x})} \textcolor{Green}{\times} \textcolor{Red}{\frac{1}{x^{2}}} \mathrm{d} \textcolor{Yellow}{x} =$$ $$\textcolor{Orange}{-} \int \textcolor{Red}{f(\frac{1}{x})} \mathrm{d} (\textcolor{Yellow}{\frac{1}{x}}).$$