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

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

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

Therefore,

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

Add the constant of integration:

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

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