# Let's get trigy

Calculus Level 3

$\int_{0}^{\pi/2} \frac{\sqrt{\cot(x)}}{\sqrt{\cot(x)} + \sqrt{\tan(x)}}dx$

The value of the integral above can be written as $\dfrac{a\pi^{c}}{b}$, where $a$ and $b$ are positive coprime integers. Enter $a+b+c$.

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