The integral of \( x^2 \) with respect to \( x \) is calculated as follows:

\[
\int x^2 \, dx = \frac{x^3}{3} + C
\]

Where:
- \( \frac{x^3}{3} \) is the antiderivative of \( x^2 \),
- \( C \) is the constant of integration.

Would you like more details on the integration process, or do you have any specific questions?

Here are some related questions:
1. What is the integral of \( x^n \) for any value of \( n \)?
2. How do you compute the definite integral of \( x^2 \) between two limits?
3. What is the difference between definite and indefinite integrals?
4. How would you differentiate \( \frac{x^3}{3} \) to verify the result?
5. What happens when you integrate a polynomial function?

**Tip**: When integrating powers of \( x \), increase the exponent by 1 and divide by the new exponent.

Learn how to find the integral of x^2 using the power rule of integration. This guide provides a detailed explanation of how to compute ∫ x^2 dx and introduces key concepts in calculus, including polynomial integration and the constant of integration. Suitable for students in Grades 10-12.

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