$$$\tan^{3}{\left(x \right)} \cot^{3}{\left(x \right)}$$$ 的积分

求$$$\int \tan^{3}{\left(x \right)} \cot^{3}{\left(x \right)}\, dx$$$。

化简被积函数:

$${\color{red}{\int{\tan^{3}{\left(x \right)} \cot^{3}{\left(x \right)} d x}}} = {\color{red}{\int{1 d x}}}$$

应用常数法则 $$$\int c\, dx = c x$$$，使用 $$$c=1$$$：

$${\color{red}{\int{1 d x}}} = {\color{red}{x}}$$

因此，

$$\int{\tan^{3}{\left(x \right)} \cot^{3}{\left(x \right)} d x} = x$$

加上积分常数：

$$\int{\tan^{3}{\left(x \right)} \cot^{3}{\left(x \right)} d x} = x+C$$

$$$\int \tan^{3}{\left(x \right)} \cot^{3}{\left(x \right)}\, dx = x + C$$$A