Integrate the function f(x) = 6x4 - 9x2 - √𝑥 (

To integrate the function \( f(x) = 6x^4 - 9x^2 - \sqrt{x} \), we will integrate term by term.

### Step 1: Rewrite the function in terms of powers of \(x\)

Recall that \( \sqrt{x} = x^{1/2} \), so we rewrite the function as:
\[
f(x) = 6x^4 - 9x^2 - x^{1/2}
\]

### Step 2: Apply the power rule of integration

The power rule for integration is:
\[
\int x^n \, dx = \frac{x^{n+1}}{n+1} + C \quad \text{(for } n \neq -1\text{)}
\]

Now, apply this rule to each term in the function.

#### 1. **Integrating \( 6x^4 \):**
\[
\int 6x^4 \, dx = 6 \cdot \frac{x^{4+1}}{4+1} = 6 \cdot \frac{x^5}{5} = \

Integrate the function f(x) = 6x^4 - 9x^2 - √x

Learn how to integrate the polynomial function f(x) = 6x^4 - 9x^2 - √x with a detailed step-by-step solution. This tutorial covers key integration concepts, including the power rule. Suitable for students in Grades 11-12.

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