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

Find $$$\int \left(- e^{u}\right)\, du$$$.

Apply the constant multiple rule $$$\int c f{\left(u \right)}\, du = c \int f{\left(u \right)}\, du$$$ with $$$c=-1$$$ and $$$f{\left(u \right)} = e^{u}$$$:

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

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

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

Therefore,

$$\int{\left(- e^{u}\right)d u} = - e^{u}$$

Add the constant of integration:

$$\int{\left(- e^{u}\right)d u} = - e^{u}+C$$

$$$\int \left(- e^{u}\right)\, du = - e^{u} + C$$$A