To evaluate the integral \(\int x \, dx\), we can use the basic power rule for integration. The power rule states that for any real number \(n \neq -1\),

\[ \int x^n \, dx = \frac{x^{n+1}}{n+1} + C \]

where \(C\) is the constant of integration.

For \(n = 1\), the integral becomes:

\[ \int x \, dx = \frac{x^{1+1}}{1+1} + C \]

Simplify the exponent and the denominator:

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

So, the integral of \(x\) with respect to \(x\) is:

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

Would you like more details or have any questions about this integral?

Here are five questions you can ask:
1. Can you show the steps for integrating a polynomial function?
2. How do you determine the constant of integration in definite and indefinite integrals?
3. What is the power rule for integration, and how is it applied?
4. Can you explain the difference between definite and indefinite integrals?
5. How do you integrate functions that involve products or quotients of variables?

**Tip:** Always remember to add the constant of integration \(C\) when performing indefinite integrals. This represents the family of antiderivatives and is important for capturing the general solution.

Learn how to evaluate the integral \( \int x \, dx \) using the power rule for integration. This problem covers basic integration concepts and the application of the power rule theorem. Suitable for high school students and anyone interested in calculus basics.

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