Evaluate: `int1/(sqrt(x)+sqrt(x+1))\ dx`

Explanation

To evaluate the integral \( I = \int \frac{1}{\sqrt{x} + \sqrt{x+1}} \, dx \), we will follow these steps:

### Step 1: Rationalize the denominator
We start by multiplying and dividing by the conjugate of the denominator:

\[ I = \int \frac{1}{\sqrt{x} + \sqrt{x+1}} \cdot \frac{\sqrt{x+1} - \sqrt{x}}{\sqrt{x+1} - \sqrt{x}} \, dx \]
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