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Calculus Level 2

The value of the integral \[\int_0^{\pi/2}\dfrac{\text dx}{2+\cos x}\] can be expressed in the form \(\dfrac{\pi^A\sqrt{B}}{C}\) where \(A\), \(B\), \(C\) are positive integers and \(B\) is not divisible by the square of any prime. Find the value of \(A+B+C.\)

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