1. **Problem:** Do an example of an integral. 2. **Formula used:** For a basic power integral, use $$\int x^n\,dx=\frac{x^{n+1}}{n+1}+C \quad \text{for } n\neq -1$$ 3. **Example integral:** Let’s evaluate $$\int x^2\,dx$$ 4. **Apply the rule:** Here $n=2$, so increase the power by $1$ and divide by the new power. $$\int x^2\,dx=\frac{x^{2+1}}{2+1}+C$$ $$\int x^2\,dx=\frac{x^3}{3}+C$$ 5. **Important rule:** The $+C$ is the constant of integration. It must be included because many different functions can have the same derivative. 6. **Final answer:** $$\frac{x^3}{3}+C$$