1. The problem is to find the indefinite integral of $x^2$ with respect to $x$. 2. Recall that the integral of $x^n$ with respect to $x$ is given by the formula: $$\int x^n \, dx = \frac{x^{n+1}}{n+1} + C$$ where $C$ is the constant of integration. 3. For $x^2$, here $n=2$. Applying the formula: $$\int x^2 \, dx = \frac{x^{2+1}}{2+1} + C = \frac{x^3}{3} + C$$ 4. Therefore, the integral of $x^2$ with respect to $x$ is: $$\frac{x^3}{3} + C$$