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MathGroup Archive 2010

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Integrate 'learns'?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg106269] Integrate 'learns'?
  • From: "Tony Harker" <a.harker at ucl.ac.uk>
  • Date: Thu, 7 Jan 2010 02:28:14 -0500 (EST)

  If I open a clean notebook in Version 7.0 for Microsoft Windows (32-bit)
and enter 
  Integrate[x/(3 Sin[x]),{x,\[Pi]/4,\[Pi]/2}]
  the result (after a warning message) is
  (8*Catalan - I*Pi^2 + Pi*(-Log[1 - (-1)^(1/4)] + Log[1 + (-1)^(1/4)]) -
(4*I)*(PolyLog[2, -(-1)^(1/4)] - PolyLog[2, (-1)^(1/4)]))/12
  and if I then repeat the command I get no error and
  (5*Catalan)/6 - ((23*I)/288)*Pi^2 + (Pi*ArcTanh[(-1)^(1/4)])/6 +
((2*I)/3)*PolyLog[2, (-1)^(1/4)]
  which seems to be Mathematica's final answer.

  I am happy that the results are equivalent, but puzzled about what has
been saved, and where, to generate this difference. Did Mathematica ask the
audience or phone a friend? Can anyone enlighten me?

  Tony Harker



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