`int sqrt((1-sqrt(x))/(1+sqrt(x)))dx=`

Explanation

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

### Step 1: Substitution
Let \( \sqrt{x} = t \). Then, \( x = t^2 \) and differentiating gives \( dx = 2t \, dt \).

### Step 2: Rewrite the Integral
Substituting \( \sqrt{x} = t \) into the integral, we get:
\[
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