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Question: some ugly double integral

Question:some ugly double integral

Axel Vogt 5821 Maple
June 01 2014
0 
g := (-12*y^2+1)/(4*y^2+1)^3 * ln(abs(-1+2^(1-x-I*y)));

Compute Int(g, [x=1/2 .. infinity, y=0 .. infinity]).

PS: this stems from How to calculate hard integral?, 
but it is not related to the RH.
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