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Rational function integration

  • To: mathgroup at smc.vnet.net
  • Subject: [mg14409] Rational function integration
  • From: lebigot at ens.fr (Eric Le Bigot)
  • Date: Sun, 18 Oct 1998 15:10:13 -0400
  • Organization: Ecole Normale Superieure, Paris
  • Sender: owner-wri-mathgroup at wolfram.com

  Hello,

  To my immense surprise, I've not been able to obtain from Mathematica
the result of *very simple integrations* of rational functions.
Furthermore, there seem to be some inconsistencies between different
results given by Mathematica...

  Does anybody know how to make Mathematica compute those integrals of
rational functions ? (the result is not that much interesting in
itself, but the method is: the expressions I actually want to compute
are simply some more complicated rational functions).

  EOL, who loves Mathematica, even though he is a bit disappointed this
time...


  Here is a notebook that gives further details:

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Cell[CellGroupData[{
Cell["Some problems with integrals of rational functions",
"Subsection"],

Cell["Easy integral:", "Text"],

Cell[CellGroupData[{

Cell[BoxData[
    RowBox[{"Integrate", "[", 
      RowBox[{\(1\/\(\[Epsilon]\^2 + \((0 - x)\)\^2\)\), ",", 
        RowBox[{"{", 
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            InterpretationBox[\(-\[Infinity]\),
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        \(Assumptions \[Rule] {Arg[\[Epsilon]\^2] == 0}\)}], "]"}]],
"Input"],

Cell[BoxData[
    \(\[Pi]\ \ at \(1\/\[Epsilon]\^2\)\)], "Output"] }, Open  ]],

Cell["\<\
The following integral is simply a translation of the previous one, \
and should give the same result, which is not the case:\ \>", "Text"],

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As strange as it is, removing the constraint gives a general \ result:\
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However, the following translated integral generates a condition, \
although it is the \"same\" as the previous one:\ \>", "Text"],

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-- 
-------------------------------------------------------------------------------

Eric-Olivier Le Bigot (EOL)
lebigot at lpan.jussieu.fr


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