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A Tricky Integral!!

Calculus Level 2

\[\int _{ 0 }^{ { \pi } / { 2 } }{ \dfrac { \sqrt { \cot{x} } }{ \sqrt{\cot{x}}+ \sqrt{\tan{x}}}} \, dx = \, ? \]

0 \[\frac{\pi}{4}\] 1 \[\frac{\pi}{2}\] \[\pi\] The integral diverges

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by Rajdeep Dhingra

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