Integral von $$$\frac{2^{a}}{b}$$$ nach $$$a$$$

Bestimme $$$\int \frac{2^{a}}{b}\, da$$$.

Wende die Konstantenfaktorregel $$$\int c f{\left(a \right)}\, da = c \int f{\left(a \right)}\, da$$$ mit $$$c=\frac{1}{b}$$$ und $$$f{\left(a \right)} = 2^{a}$$$ an:

$${\color{red}{\int{\frac{2^{a}}{b} d a}}} = {\color{red}{\frac{\int{2^{a} d a}}{b}}}$$

Apply the exponential rule $$$\int{a^{a} d a} = \frac{a^{a}}{\ln{\left(a \right)}}$$$ with $$$a=2$$$:

$$\frac{{\color{red}{\int{2^{a} d a}}}}{b} = \frac{{\color{red}{\frac{2^{a}}{\ln{\left(2 \right)}}}}}{b}$$

Daher,

$$\int{\frac{2^{a}}{b} d a} = \frac{2^{a}}{b \ln{\left(2 \right)}}$$

Fügen Sie die Integrationskonstante hinzu:

$$\int{\frac{2^{a}}{b} d a} = \frac{2^{a}}{b \ln{\left(2 \right)}}+C$$

$$$\int \frac{2^{a}}{b}\, da = \frac{2^{a}}{b \ln\left(2\right)} + C$$$A