I am trying to evaluate ∫∞0arctan(x)log(x2+1)x(x2+1) I have tried differentiating under the integral sign, with different parameters, as well as contour integration, but I have not succeeded with neither of them. Wolfram Alpha gives a numerical value ≈0.754694, but I suspect that there is a more exact answer.
I would be very glad to get some hints on how to solve it.
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