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Calculus Level 5

\[\large{H = \int_{-1}^1 \left( \dfrac{2^x \tan^2(x)}{1+2^x} + \dfrac{3^x\tan^4(x)}{1+3^x} \right) \ dx} \]

If \(H\) can be represented as:

\[\large{\dfrac{\left(\tan\left(\frac{\pi^A}{B}\right)\right)^C}{D}}\]

where \(A,B,C,D\) are non-negative integers, find the value of \(A+B+C+D\)?

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