1. The problem is to evaluate the integral $\int x \, dx$. 2. Recall the power rule for integration: $\int x^n \, dx = \frac{x^{n+1}}{n+1} + C$ for $n \neq -1$. 3. Here, $x$ is $x^1$, so applying the rule: $$\int x \, dx = \frac{x^{1+1}}{1+1} + C = \frac{x^2}{2} + C$$ 4. Therefore, the integral of $x$ with respect to $x$ is $\frac{x^2}{2} + C$ where $C$ is the constant of integration.