The integral of \( \frac{x}{dx} \) with respect to \( x \) is:

\[
\int x \, dx
\]

To solve this, we use the power rule of integration, which states:

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

For \( x^1 \), we have:

\[
\int x \, dx = \frac{x^{1+1}}{1+1} + C = \frac{x^2}{2} + C
\]

So, the integral is:

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

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

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

Here are some related questions:

1. How do you integrate a function like \( x^n \) for any integer \( n \)?
2. What happens when you integrate a polynomial function?
3. How can you apply the power rule to integrals of negative exponents?
4. How do you determine the constant of integration in definite integrals?
5. What is the difference between indefinite and definite integrals?

**Tip:** When integrating, always remember to add the constant of integration \( C \) unless you are evaluating a definite integral.

Understand how to integrate x with respect to x using the power rule of integration. This detailed explanation covers the steps to solve the integral \( \int x \, dx = \frac{x^2}{2} + C \), where C is the constant of integration. Suitable for college-level calculus students.

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