1. **State the problem:** Find the indefinite integral $$\int (x+1) \, dx$$. 2. **Recall the integral rule:** The integral of a sum is the sum of the integrals, so $$\int (x+1) \, dx = \int x \, dx + \int 1 \, dx$$. 3. **Integrate each term:** - The integral of $$x$$ is $$\frac{x^2}{2}$$. - The integral of $$1$$ is $$x$$. 4. **Combine results and add the constant of integration:** $$\int (x+1) \, dx = \frac{x^2}{2} + x + C$$, where $$C$$ is an arbitrary constant. **Final answer:** $$\boxed{\frac{x^2}{2} + x + C}$$