# The Little Monster Integral

Calculus Level 5

The following integral involving inverse trigonometric and trigonometric functions has a gee-whiz closed-form

$$${\large\int_0^{\Large\frac{\pi}{2}}} {\rm{arccot}}\sqrt{\frac{1+\sin\theta}{\sin\theta}}\,\,d\theta={\large\frac{\pi^{\alpha}}{\beta}}$$$

Find the value of $$\large\alpha+\beta$$.

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