Integral dari $$$\tan^{3}{\left(x \right)} \cot^{3}{\left(x \right)}$$$

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

Sederhanakan integran:

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

Terapkan aturan konstanta $$$\int c\, dx = c x$$$ dengan $$$c=1$$$:

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

Oleh karena itu,

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

Tambahkan konstanta integrasi:

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

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