Integral of $$$x^{e}$$$

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

$${\color{red}{\int{x^{e} d x}}}={\color{red}{\frac{x^{1 + e}}{1 + e}}}={\color{red}{\frac{x^{1 + e}}{1 + e}}}$$

Therefore,

$$\int{x^{e} d x} = \frac{x^{1 + e}}{1 + e}$$

Add the constant of integration:

$$\int{x^{e} d x} = \frac{x^{1 + e}}{1 + e}+C$$

Answer: $$$\int{x^{e} d x}=\frac{x^{1 + e}}{1 + e}+C$$$