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∫dxcos3x2sin(2x) =(tanx)A+C(tanx)B+k\large \int\dfrac{dx}{{\cos^3 x}\sqrt{2\sin(2x)}}\,= {(\tan x)^A} + C{(\tan x)^B}+k ∫cos3x2sin(2x)dx=(tanx)A+C(tanx)B+k
The equation above holds true for reals AAA, BBB and CCC such that A+B+C=pqA+B+C = \dfrac pqA+B+C=qp, where ppp and qqq are coprime positive integers and kkk is the arbitrary constant of integration. Find p+qp+qp+q.
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