Integrate the functions`1/(sqrt(x^2+2x+2))`

Explanation

To solve the integral \( \int \frac{1}{\sqrt{x^2 + 2x + 2}} \, dx \), we can follow these steps:

### Step 1: Simplify the expression under the square root
First, we rewrite the expression \( x^2 + 2x + 2 \). We can complete the square for the quadratic expression:

\[ x^2 + 2x + 2 = (x^2 + 2x + 1) + 1 = (x + 1)^2 + 1 \]
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