Integral of $$$\frac{e^{a}}{b}$$$ with respect to $$$a$$$

Find $$$\int \frac{e^{a}}{b}\, da$$$.

Apply the constant multiple rule $$$\int c f{\left(a \right)}\, da = c \int f{\left(a \right)}\, da$$$ with $$$c=\frac{1}{b}$$$ and $$$f{\left(a \right)} = e^{a}$$$:

$${\color{red}{\int{\frac{e^{a}}{b} d a}}} = {\color{red}{\frac{\int{e^{a} d a}}{b}}}$$

The integral of the exponential function is $$$\int{e^{a} d a} = e^{a}$$$:

$$\frac{{\color{red}{\int{e^{a} d a}}}}{b} = \frac{{\color{red}{e^{a}}}}{b}$$

Therefore,

$$\int{\frac{e^{a}}{b} d a} = \frac{e^{a}}{b}$$

Add the constant of integration:

$$\int{\frac{e^{a}}{b} d a} = \frac{e^{a}}{b}+C$$

$$$\int \frac{e^{a}}{b}\, da = \frac{e^{a}}{b} + C$$$A