1. The problem is to find the integral of a function, but since the function is not specified, let's consider a general example: find $\int x^2 \, dx$. 2. The formula for integrating a power function $x^n$ is: $$\int x^n \, dx = \frac{x^{n+1}}{n+1} + C$$ where $n \neq -1$ and $C$ is the constant of integration. 3. Applying this formula to $x^2$, we have $n=2$: $$\int x^2 \, dx = \frac{x^{2+1}}{2+1} + C = \frac{x^3}{3} + C$$ 4. This means the antiderivative of $x^2$ is $\frac{x^3}{3} + C$. 5. In plain language, to integrate $x^2$, increase the exponent by 1 to get 3, then divide by this new exponent, resulting in $\frac{x^3}{3}$, and don't forget to add the constant $C$ because integration is indefinite. Final answer: $$\int x^2 \, dx = \frac{x^3}{3} + C$$