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

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

Den Integranden vereinfachen:

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

Wenden Sie die Konstantenregel $$$\int c\, dx = c x$$$ mit $$$c=1$$$ an:

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

Daher,

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

Fügen Sie die Integrationskonstante hinzu:

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

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