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Re: Which symbolic method for this Integral ?

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

samuel.blake at maths.monash.edu.au 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....

Hello,

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 ... :-)

Thanks,

Thierry