# Interesting Integrals 7

Calculus Level 5

$\large \int\dfrac{dx}{{\cos^3 x}\sqrt{2\sin(2x)}}\,= {(\tan x)^A} + C{(\tan x)^B}+k$

The equation above holds true for reals $$A$$, $$B$$ and $$C$$ such that $$A+B+C = \dfrac pq$$, where $$p$$ and $$q$$ are coprime positive integers and $$k$$ is the arbitrary constant of integration. Find $$p+q$$.

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