$$\int_{-\infty }^{+\infty }\frac{1}{(e^x-x)^2+\pi ^2}dx=\frac{1}{e^{-e^{-e^{-e..}}}+1}$$ I saw this integral in a mathematical book but I don't know how to find this result.
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Numerically, this does not seem to be correct. I found $0.638104$ – Claude Leibovici Jan 01 '15 at 16:46
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What book did you find this in? – Pedro Jan 01 '15 at 16:48
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The integral is Adamchik's Integral. You may see detailed solution here and my blog entry here – r9m Jan 01 '15 at 16:49
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You changed the rhs, so I don't say anything (except that I don't know how to compute the rhs with sufficient accuracy). It would be good to know the book. Happy New Year !! – Claude Leibovici Jan 01 '15 at 16:51
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I am not completely sure, but I would bet this is a duplicate. I remember a robjohn's solution, with the residue theorem, of a similar integral, giving a value of the Lambert W function as answer - found. Voting for closing as a duplicate. – Jack D'Aurizio Jan 01 '15 at 16:58
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See my answer under username mathematics. – Mhenni Benghorbal Jan 01 '15 at 23:21