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Calculus Level 5

H=11(2xtan2(x)1+2x+3xtan4(x)1+3x) dx\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 HH can be represented as:

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

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

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