To evaluate the given integral, we have:

\[
\int 9x \, dx
\]

We will use the power rule for integration, which states:

\[
\int x^n \, dx = \frac{x^{n+1}}{n+1} + C \quad \text{(where \(n \neq -1\))}
\]

So for the integral \( \int 9x \, dx \), treat \( 9x \) as:

\[
9 \cdot \int x \, dx
\]

Using the power rule on \( x^1 \):

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

Thus, we multiply this result by 9:

\[
9 \cdot \frac{x^2}{2} = \frac{9x^2}{2}
\]

Finally, include the constant of integration \( C \):

\[
\frac{9x^2}{2} + C
\]

So the evaluated integral is:

\[
\boxed{\frac{9x^2}{2} + C}
\]

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Would you like further details on this step? Here are some related questions:

1. What is the power rule for integration, and how is it derived?
2. How does the constant of integration affect indefinite integrals?
3. Can you explain the difference between definite and indefinite integrals?
4. How do you apply the power rule for functions with negative exponents?
5. How do you solve integrals involving polynomials of higher degree?

**Tip:** Always check if a constant factor (like 9 here) can be factored out of the integral to simplify the process.

Learn how to evaluate the integral 9∫4x dx step-by-step using the power rule of integration. This problem introduces calculus concepts such as basic integration and constant factors. Suitable for students in Grades 10-12 studying introductory calculus.

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