The given expression is:

\[
x^3 x^2 + 9 \, dx
\]

First, let's simplify the expression inside the integral:

\[
x^3 x^2 = x^{3+2} = x^5
\]

So the expression becomes:

\[
\int \left( x^5 + 9 \right) dx
\]

Now, we can integrate each term separately:

1. The integral of \( x^5 \) is:

\[
\frac{x^{6}}{6}
\]

2. The integral of \( 9 \) is:

\[
9x
\]

Thus, the indefinite integral is:

\[
\frac{x^6}{6} + 9x + C
\]

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

Would you like more details or have any questions?

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Here are 5 related questions:
1. How do you integrate a general power of \( x \)?
2. What is the significance of the constant of integration?
3. How do you solve definite integrals with limits?
4. How does the power rule for integration work?
5. How can we check if an indefinite integral is correct?

**Tip**: Always check your integral by differentiating the result to see if it matches the original expression!

Learn how to solve the indefinite integral of x^3 x^2 + 9 with step-by-step instructions. This problem covers key calculus concepts, including the power rule for integration and exponent addition, making it suitable for Grades 11-12 and early college students.

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