Integral von $$$\frac{e^{t}}{100}$$$

Bestimme $$$\int \frac{e^{t}}{100}\, dt$$$.

Wende die Konstantenfaktorregel $$$\int c f{\left(t \right)}\, dt = c \int f{\left(t \right)}\, dt$$$ mit $$$c=\frac{1}{100}$$$ und $$$f{\left(t \right)} = e^{t}$$$ an:

$${\color{red}{\int{\frac{e^{t}}{100} d t}}} = {\color{red}{\left(\frac{\int{e^{t} d t}}{100}\right)}}$$

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

$$\frac{{\color{red}{\int{e^{t} d t}}}}{100} = \frac{{\color{red}{e^{t}}}}{100}$$

Daher,

$$\int{\frac{e^{t}}{100} d t} = \frac{e^{t}}{100}$$

Fügen Sie die Integrationskonstante hinzu:

$$\int{\frac{e^{t}}{100} d t} = \frac{e^{t}}{100}+C$$

$$$\int \frac{e^{t}}{100}\, dt = \frac{e^{t}}{100} + C$$$A