Integral von $$$2 e^{y}$$$

Bestimme $$$\int 2 e^{y}\, dy$$$.

Wende die Konstantenfaktorregel $$$\int c f{\left(y \right)}\, dy = c \int f{\left(y \right)}\, dy$$$ mit $$$c=2$$$ und $$$f{\left(y \right)} = e^{y}$$$ an:

$${\color{red}{\int{2 e^{y} d y}}} = {\color{red}{\left(2 \int{e^{y} d y}\right)}}$$

Das Integral der Exponentialfunktion lautet $$$\int{e^{y} d y} = e^{y}$$$:

$$2 {\color{red}{\int{e^{y} d y}}} = 2 {\color{red}{e^{y}}}$$

Daher,

$$\int{2 e^{y} d y} = 2 e^{y}$$

Fügen Sie die Integrationskonstante hinzu:

$$\int{2 e^{y} d y} = 2 e^{y}+C$$

$$$\int 2 e^{y}\, dy = 2 e^{y} + C$$$A