Integral von $$$b d m o \cos{\left(x \right)}$$$ nach $$$x$$$

Bestimme $$$\int b d m o \cos{\left(x \right)}\, dx$$$.

Wende die Konstantenfaktorregel $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ mit $$$c=b d m o$$$ und $$$f{\left(x \right)} = \cos{\left(x \right)}$$$ an:

$${\color{red}{\int{b d m o \cos{\left(x \right)} d x}}} = {\color{red}{b d m o \int{\cos{\left(x \right)} d x}}}$$

Das Integral des Kosinus ist $$$\int{\cos{\left(x \right)} d x} = \sin{\left(x \right)}$$$:

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

Daher,

$$\int{b d m o \cos{\left(x \right)} d x} = b d m o \sin{\left(x \right)}$$

Fügen Sie die Integrationskonstante hinzu:

$$\int{b d m o \cos{\left(x \right)} d x} = b d m o \sin{\left(x \right)}+C$$

$$$\int b d m o \cos{\left(x \right)}\, dx = b d m o \sin{\left(x \right)} + C$$$A