Evaluate the integral. (Use C for the constant of integration.)
 

 (x2 − 9x) dx

The given integral is:

\[
\int (x^2 - 9x) \, dx
\]

To solve this, we can split the integral into two parts:

\[
\int x^2 \, dx - \int 9x \, dx
\]

### Step 1: Evaluate each integral separately.

1. For \(\int x^2 \, dx\):

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

2. For \(\int 9x \, dx\):

\[
\int 9x \, dx = \frac{9x^2}{2}
\]

### Step 2: Combine the results.

Now, subtract the two integrals:

\[
\frac{x^3}{3} - \frac{9x^2}{2} + C
\]

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

### Final answer:
\[
\frac{x^3}{3} - \frac{9x^2}{2} + C
\]

Do you want more details or have any questions?

Here are 5 related questions to expand on this topic:

1. How do you handle integrals of polynomials in general?
2. What happens if there is a constant multiplier in the integrand?
3. How do you solve integrals involving higher powers of \(x\)?
4. What are the general rules for finding antiderivatives?
5. How would you compute the definite integral of this function from 0 to 2?

**Tip:** Always remember to include the constant of integration \(C\) when solving indefinite integrals.

Evaluate the integral. (Use C for the constant of integration.) (x^2 − 9x) dx

Learn how to evaluate the indefinite integral ∫(x^2 - 9x) dx using the power rule of integration. This detailed step-by-step solution explains how to split the integral, compute each part, and combine the results, including the constant of integration. Ideal for students in Grades 11-12 or early college calculus.

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