Integral of $4 e^{x}$

Find $\int 4 e^{x}\, dx$.

Apply the constant multiple rule $\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$ with $c=4$ and $f{\left(x \right)} = e^{x}$:

$${\color{red}{\int{4 e^{x} d x}}} = {\color{red}{\left(4 \int{e^{x} d x}\right)}}$$

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

$$4 {\color{red}{\int{e^{x} d x}}} = 4 {\color{red}{e^{x}}}$$

Therefore,

$$\int{4 e^{x} d x} = 4 e^{x}$$

Add the constant of integration:

$$\int{4 e^{x} d x} = 4 e^{x}+C$$

$\int 4 e^{x}\, dx = 4 e^{x} + C$A