Integral von $$$\cos{\left(x \right)} \tan{\left(x \right)}$$$

Bestimme $$$\int \cos{\left(x \right)} \tan{\left(x \right)}\, dx$$$.

Den Integranden vereinfachen:

$${\color{red}{\int{\cos{\left(x \right)} \tan{\left(x \right)} d x}}} = {\color{red}{\int{\sin{\left(x \right)} d x}}}$$

Das Integral des Sinus lautet $$$\int{\sin{\left(x \right)} d x} = - \cos{\left(x \right)}$$$:

$${\color{red}{\int{\sin{\left(x \right)} d x}}} = {\color{red}{\left(- \cos{\left(x \right)}\right)}}$$

Daher,

$$\int{\cos{\left(x \right)} \tan{\left(x \right)} d x} = - \cos{\left(x \right)}$$

Fügen Sie die Integrationskonstante hinzu:

$$\int{\cos{\left(x \right)} \tan{\left(x \right)} d x} = - \cos{\left(x \right)}+C$$

$$$\int \cos{\left(x \right)} \tan{\left(x \right)}\, dx = - \cos{\left(x \right)} + C$$$A