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

**Follow-Ups**:**Re: Integrate 'learns'?***From:*Daniel Lichtblau <danl@wolfram.com>