Re: Integrate 'learns'?

*To*: mathgroup at smc.vnet.net*Subject*: [mg106331] Re: Integrate 'learns'?*From*: Bill Rowe <readnews at sbcglobal.net>*Date*: Fri, 8 Jan 2010 04:18:13 -0500 (EST)

On 1/7/10 at 2:28 AM, a.harker at ucl.ac.uk (Tony Harker) wrote: >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? Using: In[2]:= $Version Out[2]= 7.0 for Mac OS X x86 (64-bit) (February 19, 2009) with a fresh session I get the second result with no warning message. I believe Integrate like several other built-in functions caches intermediate computations. The second time the same code is executed, this cache of intermediate results are available. As a consequence, the time to get the second result will be shorter. And in this case have a different form. You didn't state what the warning message said. My guess is that if you were to change some of the options for Integrate, you would get the second result with no warning message the first time you executed the code. But since I don't get the warning message on my system, I've no way to determine if this is really the case or what options should be changed.