$$$\tan^{3}{\left(x \right)} \cot^{3}{\left(x \right)}$$$ 的積分
相關計算器: 定積分與廣義積分計算器
您的輸入
求$$$\int \tan^{3}{\left(x \right)} \cot^{3}{\left(x \right)}\, dx$$$。
解答
簡化被積函數:
$${\color{red}{\int{\tan^{3}{\left(x \right)} \cot^{3}{\left(x \right)} d x}}} = {\color{red}{\int{1 d x}}}$$
配合 $$$c=1$$$，應用常數法則 $$$\int c\, dx = c x$$$：
$${\color{red}{\int{1 d x}}} = {\color{red}{x}}$$
因此，
$$\int{\tan^{3}{\left(x \right)} \cot^{3}{\left(x \right)} d x} = x$$
加上積分常數：
$$\int{\tan^{3}{\left(x \right)} \cot^{3}{\left(x \right)} d x} = x+C$$
答案
$$$\int \tan^{3}{\left(x \right)} \cot^{3}{\left(x \right)}\, dx = x + C$$$A