1. The problem is to find the integral of the function $x + 4$ with respect to $x$. 2. Recall that the integral of a sum is the sum of the integrals: $$\int (x + 4) \, dx = \int x \, dx + \int 4 \, dx$$ 3. Use the power rule for integration: $$\int x \, dx = \frac{x^2}{2} + C$$ and the integral of a constant: $$\int 4 \, dx = 4x + C$$ 4. Combine the results: $$\int (x + 4) \, dx = \frac{x^2}{2} + 4x + C$$ where $C$ is the constant of integration. Final answer: $$\frac{x^2}{2} + 4x + C$$