Evaluate the following integral: `int_0^(pi//2)(sqrt(cotx))/(sqrt(cotx\ )+sqrt(tanx))dx`

Explanation

To evaluate the integral

\[ I = \int_0^{\frac{\pi}{2}} \frac{\sqrt{\cot x}}{\sqrt{\cot x} + \sqrt{\tan x}} \, dx, \]

we can use a symmetry property of definite integrals. We will start by rewriting the integral using the substitution \( x = \frac{\pi}{2} - t \).

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