Integral of $$$x^{n}$$$ with respect to $$$x$$$

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

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

Therefore,

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

Add the constant of integration:

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

$$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1} + C$$$A