Integral of $$$x^{2}$$$

Apply the power rule $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ with $$$n=2$$$:

$${\color{red}{\int{x^{2} d x}}}={\color{red}{\frac{x^{1 + 2}}{1 + 2}}}={\color{red}{\left(\frac{x^{3}}{3}\right)}}$$

Therefore,

$$\int{x^{2} d x} = \frac{x^{3}}{3}$$

Add the constant of integration:

$$\int{x^{2} d x} = \frac{x^{3}}{3}+C$$

$$$\int x^{2}\, dx = \frac{x^{3}}{3} + C$$$A