Integrate the functions`1/(sqrt(7-6x-x^2)`

Explanation

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

### Step 1: Rewrite the expression under the square root
We start by rewriting the expression \( 7 - 6x - x^2 \) in a more manageable form. We can rearrange it as:
\[ 7 - 6x - x^2 = - (x^2 + 6x - 7) \]
Next, we complete the square for the quadratic \( x^2 + 6x - 7 \).
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