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

问题

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

选项

[A].   $\int$ $f(\sqrt{x}) \frac{1}{\sqrt{x}}$ $\mathrm{d} x$ $=$ $2 \int$ $f(\sqrt{x})$ $\mathrm{d} x$

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

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

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



显示答案

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

常用的几种凑微分形式: