Integral of $$$x$$$

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

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

Therefore,

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

Add the constant of integration:

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

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