Solve ∫ x² dx

Step-by-step solution

1. Apply the power rule for integration: $\int x^n \, dx = \frac{x^{n+1}}{n+1} + C$ (valid for $n \neq -1$).

2. With $n = 2$: $\int x^2 \, dx = \frac{x^{2+1}}{2+1} + C = \frac{x^3}{3} + C$.

3. Always include the constant of integration $C$ — indefinite integrals represent a family of antiderivatives.