Integraal van $$$2^{3 x}$$$

Bepaal $$$\int 2^{3 x}\, dx$$$.

De invoer is herschreven: $$$\int{2^{3 x} d x}=\int{8^{x} d x}$$$.

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

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

Dus,

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

Vereenvoudig:

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

Voeg de integratieconstante toe:

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

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