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

问题

通过凑微分,如何计算 [$\textcolor{Orange}{\int f(\ln x) \frac{1}{x} \mathrm{d} x}$] ?

选项

[A].   $\int$ $f(\ln x) \frac{1}{x}$ $\mathrm{d} x$ $=$ $\int$ $f(\ln x)$ $\mathrm{d} (\ln x)$

[B].   $\int$ $f(\ln x) \frac{1}{x}$ $\mathrm{d} x$ $=$ $- \int$ $f(\ln x)$ $\mathrm{d} (\ln x)$

[C].   $\int$ $f(\ln x) \frac{1}{x}$ $\mathrm{d} x$ $=$ $\int$ $f(\ln x)$ $\mathrm{d} x$

[D].   $\int$ $f(\ln x) \frac{1}{x}$ $\mathrm{d} x$ $=$ $\int$ $f(\ln x)$ $\mathrm{d} (\ln x)$ $+$ $C$


上一题 - 荒原之梦   答 案   下一题 - 荒原之梦

$$\int \textcolor{Red}{f(\ln x)} \textcolor{Green}{\times} \textcolor{Red}{\frac{1}{x}} \mathrm{d} \textcolor{Yellow}{x} =$$ $$\int \textcolor{Red}{f(\ln x)} \mathrm{d} (\textcolor{Yellow}{\ln x})$$

常用的几种凑微分形式: