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