Integral of $$$b^{x}$$$ with respect to $$$x$$$

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

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

Therefore,

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

Add the constant of integration:

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

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