Integrate the functions`sqrt((1-sqrt(x))/(1+sqrt(x)))`

Explanation

To solve the integral \( I = \int \sqrt{\frac{1 - \sqrt{x}}{1 + \sqrt{x}}} \, dx \), we will follow a systematic approach.

### Step 1: Substitution
Let \( \sqrt{x} = \cos t \). Then, squaring both sides gives us:
\[ x = \cos^2 t \]
Differentiating both sides with respect to \( t \) gives:
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