对 $\int$ $f(\frac{1}{x}) \frac{1}{x^{2}}$ $\mathrm{d} x$ 凑微分的计算方法(B006)

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].   $\int$ $f(\frac{1}{x}) \frac{1}{x^{2}}$ $\mathrm{d} x$ $=$ $- \int$ $f(\frac{1}{x})$ $\mathrm{d} x$

[C].   $\int$ $f(\frac{1}{x}) \frac{1}{x^{2}}$ $\mathrm{d} x$ $=$ $- \int$ $f(\frac{1}{x})$ $\mathrm{d} (\frac{1}{x})$ $+$ $C$

[D].   $\int$ $f(\frac{1}{x}) \frac{1}{x^{2}}$ $\mathrm{d} x$ $=$ $- \int$ $f(\frac{1}{x})$ $\mathrm{d} (\frac{1}{x})$



显示答案

$$\int \textcolor{Red}{f(\frac{1}{x})} \textcolor{Green}{\times} \textcolor{Red}{\frac{1}{x^{2}}} \mathrm{d} \textcolor{Yellow}{x} =$$ $$\textcolor{Orange}{-} \int \textcolor{Red}{f(\frac{1}{x})} \mathrm{d} (\textcolor{Yellow}{\frac{1}{x}}).$$

常用的几种凑微分形式: