Integrate this one!

Calculus Level 5

\[\large{\displaystyle \int^{\infty}_{0} \frac{(12-x^2)}{(x^2+4)^3} \cos (2x) dx=\frac{A \pi^{B}}{C e^{D}}}\]

where \(A,B,C,D\) are integers and \(A,C\) being coprime.

Find \(A+B+C+D\)

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