Integral von $$$8^{x}$$$

Bestimme $$$\int 8^{x}\, dx$$$.

Apply the exponential rule $$$\int{a^{x} d x} = \frac{a^{x}}{\ln{\left(a \right)}}$$$ with $$$a=8$$$:

$${\color{red}{\int{8^{x} d x}}} = {\color{red}{\frac{8^{x}}{\ln{\left(8 \right)}}}}$$

Daher,

$$\int{8^{x} d x} = \frac{8^{x}}{\ln{\left(8 \right)}}$$

Vereinfachen:

$$\int{8^{x} d x} = \frac{8^{x}}{3 \ln{\left(2 \right)}}$$

Fügen Sie die Integrationskonstante hinzu:

$$\int{8^{x} d x} = \frac{8^{x}}{3 \ln{\left(2 \right)}}+C$$

$$$\int 8^{x}\, dx = \frac{8^{x}}{3 \ln\left(2\right)} + C$$$A