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Calculus Level 5

0π/2sinxdx=Aπ(Γ(CD))B\int _{ 0 }^{ \pi /2 }{ \sqrt { \sin { x } } \, dx } =\dfrac { \sqrt { A } }{ \sqrt { \pi } } \left(\Gamma \left( \frac { C }{ D } \right)\right)^B

The equation above holds for positive integers A,B,CA,B,C and DD with C,DC,D coprime. Find A+B+C+D A+B+C+D.

Notation: Γ() \Gamma(\cdot) denotes the Gamma function.

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