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Polylogarithm Integration - Bis

Some more example for the integral:

  Integrate[PolyLog[2, Exp[I*(x - y)]], {y, 0, 2*Pi}]

with x=5/2, I get 0 as expected. But with x=2.5 I get

19.634954084936204 + I*1.7763568394002505`*^-15

which is not close to zero! With x=-2.5 I get

  44.964016795241896 + I*1.7763568394002505`*^-15


I have only one conclusion: there is a
bug with Integrate or PolyLog or both.

Any suggestion?

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