Integral of $$$11 e^{u}$$$

Find $$$\int 11 e^{u}\, du$$$.

Apply the constant multiple rule $$$\int c f{\left(u \right)}\, du = c \int f{\left(u \right)}\, du$$$ with $$$c=11$$$ and $$$f{\left(u \right)} = e^{u}$$$:

$${\color{red}{\int{11 e^{u} d u}}} = {\color{red}{\left(11 \int{e^{u} d u}\right)}}$$

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

$$11 {\color{red}{\int{e^{u} d u}}} = 11 {\color{red}{e^{u}}}$$

Therefore,

$$\int{11 e^{u} d u} = 11 e^{u}$$

Add the constant of integration:

$$\int{11 e^{u} d u} = 11 e^{u}+C$$

$$$\int 11 e^{u}\, du = 11 e^{u} + C$$$A