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Calculus Level 2

The value of the integral 0π/2dx2+cosx\int_0^{\pi/2}\dfrac{\text dx}{2+\cos x} can be expressed in the form πABC\dfrac{\pi^A\sqrt{B}}{C} where AA, BB, CC are positive integers and BB is not divisible by the square of any prime. Find the value of A+B+C.A+B+C.

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