Let's get trigy

Calculus Level 2

0π/2cot(x)cot(x)+tan(x)dx\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 aπcb\dfrac{a\pi^{c}}{b}, where aa and bb are positive coprime integers. Enter a+b+ca+b+c.

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