Integral von $$$\frac{e^{a}}{b}$$$ nach $$$a$$$

Bestimme $$$\int \frac{e^{a}}{b}\, da$$$.

Wende die Konstantenfaktorregel $$$\int c f{\left(a \right)}\, da = c \int f{\left(a \right)}\, da$$$ mit $$$c=\frac{1}{b}$$$ und $$$f{\left(a \right)} = e^{a}$$$ an:

$${\color{red}{\int{\frac{e^{a}}{b} d a}}} = {\color{red}{\frac{\int{e^{a} d a}}{b}}}$$

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

$$\frac{{\color{red}{\int{e^{a} d a}}}}{b} = \frac{{\color{red}{e^{a}}}}{b}$$

Daher,

$$\int{\frac{e^{a}}{b} d a} = \frac{e^{a}}{b}$$

Fügen Sie die Integrationskonstante hinzu:

$$\int{\frac{e^{a}}{b} d a} = \frac{e^{a}}{b}+C$$

$$$\int \frac{e^{a}}{b}\, da = \frac{e^{a}}{b} + C$$$A