1. Let's solve an example integral: $$\int (3x^2 + 2x + 1) \, dx$$. 2. The formula for integrating a power function is $$\int x^n \, dx = \frac{x^{n+1}}{n+1} + C$$ where $n \neq -1$ and $C$ is the constant of integration. 3. We apply the integral to each term separately: $$\int 3x^2 \, dx = 3 \int x^2 \, dx = 3 \cdot \frac{x^{3}}{3} = x^3$$ $$\int 2x \, dx = 2 \int x \, dx = 2 \cdot \frac{x^{2}}{2} = x^2$$ $$\int 1 \, dx = x$$ 4. Combine all results and add the constant of integration: $$x^3 + x^2 + x + C$$ 5. So, the integral of $$3x^2 + 2x + 1$$ with respect to $x$ is $$x^3 + x^2 + x + C$$. This process shows how to integrate polynomial terms by increasing the power by one and dividing by the new power.