1. Let's restate the question: why do we add 1 to the exponent in the integral rule $\int x^n \, dx = \frac{x^{n+1}}{n+1} + C$? 2. The $2 + 1$ in your example comes from the power rule for integration, which says when integrating $x^n$, you increase the exponent by 1. 3. This happens because integration is the reverse process of differentiation. When you differentiate $x^{n+1}$, you multiply by the exponent and subtract 1, so integration reverses this. 4. Specifically, if $f(x) = x^{n+1}$, then $f'(x) = (n+1)x^n$. To find the integral of $x^n$, you need to find a function whose derivative is $x^n$, which is $\frac{x^{n+1}}{n+1}$. 5. In your example, $n=2$, so $n+1=3$. That's why you have $3 \cdot \frac{x^{3}}{3}$, which simplifies to $x^3$. 6. So, the $2 + 1$ is the exponent increased by 1 as part of the integral power rule formula.