1. **Problem Statement:** Solve the integral $\int x \, dx$. 2. **Formula Used:** The integral of $x$ with respect to $x$ is given by the power rule for integration: $$\int x^n \, dx = \frac{x^{n+1}}{n+1} + C, \quad \text{for } n \neq -1$$ 3. **Apply the formula:** Here, $n=1$, so $$\int x \, dx = \frac{x^{1+1}}{1+1} + C = \frac{x^2}{2} + C$$ 4. **Explanation:** The power rule states that to integrate a power of $x$, increase the exponent by 1 and divide by the new exponent. The constant $C$ represents the constant of integration, which accounts for any constant term lost during differentiation. 5. **Final answer:** $$\int x \, dx = \frac{x^2}{2} + C$$