Integral of $$$e$$$

Apply the power rule $$$\int e^{n}\, de = \frac{e^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ with $$$n=1$$$:

$${\color{red}{\int{e d e}}}={\color{red}{\frac{e^{1 + 1}}{1 + 1}}}={\color{red}{\left(\frac{e^{2}}{2}\right)}}$$

Therefore,

$$\int{e d e} = \frac{e^{2}}{2}$$

Add the constant of integration:

$$\int{e d e} = \frac{e^{2}}{2}+C$$

Answer: $$$\int{e d e}=\frac{e^{2}}{2}+C$$$