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Re: Which symbolic method for this Integral ?

  • To: mathgroup at
  • Subject: [mg82863] Re: Which symbolic method for this Integral ?
  • From: Thierry Mella <thierry.mella at>
  • Date: Thu, 1 Nov 2007 05:22:55 -0500 (EST)
  • References: <fg6r2l$dsl$> <fg9nhg$l47$>

samuel.blake at wrote:

> So I'll give
> it a go using the good old method of substitution.
> It's late in Australia, so PLEASE check this!! I believe that using
> the substitutions
> u = 1 - x
> then
> t = Sqrt[u]
> then
> t = Sqrt[2] Sin[v]
> This will result in a trig rational integral which can be converted to
> a rational integral using the trick given in every calculus book. Then
> the rational integral can be calculated using the partial fraction
> method. I would not expect the answer to be as nice as that given by
> Mathematica, mainly because integrating a rational function using the
> partial fraction method does not produce an answer in the minimal
> algebraic extension field, whereas the Hermite reduction followed by
> Lazard-Rothstein-Trager-Rioboo algorithm will! Also, I assumed t =
> Sqrt[u] inverts to u = t^2 which causes further complications....


Thanks for your answer.

The substitutions that you suggest are the ones that I thought about
also ...

The problem to have a "clean" answer after calculating the rational
integral is to invert the substitutions and the result seems to be
"heavy" ...

But I'm an engineer, not a mathematician ... :-)



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