1. Let's solve the integral example: $$\int x^2 \, dx$$. 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. Here, $n=2$, so applying the formula: $$\int x^2 \, dx = \frac{x^{2+1}}{2+1} + C = \frac{x^3}{3} + C$$. 4. This means the antiderivative of $x^2$ is $\frac{x^3}{3} + C$. 5. Remember, the constant $C$ is important because integration is the reverse of differentiation and constants vanish when differentiating. Final answer: $$\int x^2 \, dx = \frac{x^3}{3} + C$$