`(1)/(7+6x-x^(2))`

Explanation

To solve the integral \( \int \frac{1}{7 + 6x - x^2} \, dx \), we will follow these steps:

### Step 1: Rewrite the Denominator
First, we rewrite the expression in the denominator to make it easier to integrate. We can rearrange \( 7 + 6x - x^2 \) as follows:
\[ -x^2 + 6x + 7 = -(x^2 - 6x - 7) \]
Next, we complete the square for the quadratic expression \( x^2 - 6x - 7 \).
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