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: - For $3x^2$, integrate as $3 \times \frac{x^{2+1}}{2+1} = 3 \times \frac{x^3}{3} = x^3$. - For $2x$, integrate as $2 \times \frac{x^{1+1}}{1+1} = 2 \times \frac{x^2}{2} = x^2$. - For $1$, integrate as $1 \times x = x$. 4. Combine all integrated terms and add the constant of integration $C$: $$x^3 + x^2 + x + C$$ 5. Therefore, the integral of $3x^2 + 2x + 1$ with respect to $x$ is: $$\int (3x^2 + 2x + 1) \, dx = x^3 + x^2 + x + C$$.