https://file.aiquickdraw.com/mathbot/file/1725933243494xpgzuz3p.jpg

The integral shown in the image is:

\[
\int (6x^2 + 3x) \, dx
\]

Let's compute this integral step by step:

1. For the first term, \(6x^2\):
\[
\int 6x^2 \, dx = 6 \cdot \frac{x^3}{3} = 2x^3
\]

2. For the second term, \(3x\):
\[
\int 3x \, dx = 3 \cdot \frac{x^2}{2} = \frac{3x^2}{2}
\]

Now, combining these results:
\[
2x^3 + \frac{3x^2}{2} + C
\]

Looking at the options provided in the image, the correct answer is:

**Option b: \( 2x^3 + \frac{3x^2}{2} + C \)**

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Do you need further details or have any questions?

Here are 5 related questions for deeper understanding:
1. How do you find the antiderivative of a general polynomial expression?
2. What is the constant of integration, and why is it important?
3. How does the power rule for integration work for negative exponents?
4. What happens when you integrate a sum of multiple terms?
5. How would you integrate a more complex polynomial with higher degree terms?

**Tip:** When integrating a sum of terms, handle each term individually and then combine the results.

Calculate the indefinite integral of the polynomial expression 6x^2 + 3x. This problem uses the power rule for integration and is suitable for students in Grades 10-12.

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