So, H (x)=
メーメー12
h(X)=]
-dx
* - x-12
= (x+3)(x-4)đu
3
4
7
7
=
*+3+
x-4
du
= 흑7x+3+흑미×-4

It seems like your input has some formatting issues and potentially some characters that are not typically part of standard mathematical notation. I'll do my best to interpret and correct what you've written, but it would help if you could clarify any unclear parts.

Let's break down the expression step by step:

1. **Original Function \( H(x) \):** 
   - It seems to start with \( H(x) = \) but the expression following it is unclear. There may be some missing or incorrectly formatted terms.
   
2. **Integral \( h(x) \):**
   - You mention \( h(X) = \), followed by an integral involving \( dx \), \( x - 12 \), and a product of polynomials.
   - It seems like you're trying to express the integral of a function, potentially something like:

   \[
   h(x) = \int (x + 3)(x - 4) \, du
   \]

   But the exact function and limits are unclear.

3. **Possible Integration Steps:**
   - If the function inside the integral is \( (x + 3)(x - 4) \), we might want to expand this to:

   \[
   (x + 3)(x - 4) = x^2 - 4x + 3x - 12 = x^2 - x - 12
   \]

   - Then, if you're integrating this with respect to \( u \), it would be:

   \[
   h(x) = \int (x^2 - x - 12) \, du
   \]

4. **Further Simplifications:**
   - If the integral involves \( x^2 - x - 12 \) with respect to \( du \), the solution will depend on whether \( x \) or \( u \) is a function of the other. If it's a simple indefinite integral with respect to \( u \):

   \[
   h(x) = \frac{x^2}{2} - \frac{x}{2} - 12u + C
   \]

   Here, \( C \) is the constant of integration.

If you could clarify the original function and any specific details or terms that might have been incorrectly formatted, I can provide a more accurate solution.

Would you like to clarify any parts, or would you like more details on how to solve similar integrals?

---

**5 Relative Questions:**

1. What is the exact expression for \( H(x) \) that you want to evaluate or integrate?
2. Are there any specific integration limits or additional conditions for \( h(x) \)?
3. Is \( u \) a function of \( x \), or is it an independent variable?
4. Do you need a step-by-step breakdown of how to integrate similar polynomial functions?
5. Are there any particular integration techniques you'd like to focus on, such as substitution or integration by parts?

**Tip:** Always ensure that mathematical expressions are clearly formatted to avoid confusion during interpretation and calculation.

So, H(x)= メーメー12 h(X)=] -dx * - x-12 = (x+3)(x-4)đu 3 4 7 7 = *+3+ x-4 du = 흑7x+3+흑미×-4

Explore how to expand and integrate the polynomial expression (x+3)(x-4) using basic algebra and calculus. This solution walks through the steps of polynomial multiplication and integration, focusing on key concepts like polynomial expansion and the application of the Fundamental Theorem of Calculus. Suitable for Grades 11-12.

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