Integral von $$$\frac{\sin{\left(x \right)} \sec{\left(x \right)}}{\tan{\left(x \right)}}$$$

Bestimme $$$\int \frac{\sin{\left(x \right)} \sec{\left(x \right)}}{\tan{\left(x \right)}}\, dx$$$.

Den Integranden vereinfachen:

$${\color{red}{\int{\frac{\sin{\left(x \right)} \sec{\left(x \right)}}{\tan{\left(x \right)}} d x}}} = {\color{red}{\int{1 d x}}}$$

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

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

Daher,

$$\int{\frac{\sin{\left(x \right)} \sec{\left(x \right)}}{\tan{\left(x \right)}} d x} = x$$

Fügen Sie die Integrationskonstante hinzu:

$$\int{\frac{\sin{\left(x \right)} \sec{\left(x \right)}}{\tan{\left(x \right)}} d x} = x+C$$

$$$\int \frac{\sin{\left(x \right)} \sec{\left(x \right)}}{\tan{\left(x \right)}}\, dx = x + C$$$A