A closed form for the double integral $J=\int_0^1\int_0^1 {\log(1+xy)\over 1+x^2+y^2}\,dx \,dy$

Ideas
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1

With the help of Mathematica (version 14.3 ) I have obtained a closed form for
the double integral :

J = Integrate[Log[1 + x y]/(1 + x^2 + y^2), {x, 0, 1}, {y, 0, 1}]
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INTEGRALDOBLE.pdf (75.2 KB)