Integral of $$$5^{x}$$$

Apply the exponential rule $$$\int{a^{x} d x} = \frac{a^{x}}{\ln{\left(a \right)}}$$$ with $$$a=5$$$:

$${\color{red}{\int{5^{x} d x}}} = {\color{red}{\frac{5^{x}}{\ln{\left(5 \right)}}}}$$

Therefore,

$$\int{5^{x} d x} = \frac{5^{x}}{\ln{\left(5 \right)}}$$

Add the constant of integration:

$$\int{5^{x} d x} = \frac{5^{x}}{\ln{\left(5 \right)}}+C$$

$$$\int 5^{x}\, dx = \frac{5^{x}}{\ln\left(5\right)} + C$$$A