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

问题

通过凑微分,如何计算 [$\textcolor{Orange}{\int f(\cot x) \csc ^{2} x \mathrm{d} x}$] ?

选项

[A].   $\int$ $f(\cot x) \csc ^{2} x$ $\mathrm{d} x$ $=$ $- \int$ $f(\cot x)$ $\mathrm{d}$ $(\cos x)$

[B].   $\int$ $f(\cot x) \csc ^{2} x$ $\mathrm{d} x$ $=$ $- \int$ $f(\cot x)$ $\mathrm{d}$ $(\sin x)$

[C].   $\int$ $f(\cot x) \csc ^{2} x$ $\mathrm{d} x$ $=$ $\int$ $f(\cot x)$ $\mathrm{d}$ $(\cot x)$

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



显示答案

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

常用的几种凑微分形式: