Integral of $$$4 e^{u}$$$

Find $$$\int 4 e^{u}\, du$$$.

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

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

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

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

Therefore,

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

Add the constant of integration:

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

$$$\int 4 e^{u}\, du = 4 e^{u} + C$$$A