Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
2007
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 2007

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: Integrate

  • To: mathgroup at smc.vnet.net
  • Subject: [mg74078] Re: Integrate
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Thu, 8 Mar 2007 04:45:09 -0500 (EST)
  • Organization: The Open University, Milton Keynes, UK
  • References: <esls78$q0v$1@smc.vnet.net>

Michael Weyrauch wrote:
> Hello,
> 
> I seem to have a problem with Integrate using Mathematica 5.2 on a
> Windows PC.
> 
> In fact, I would like to integrate the following somewhat lengthy
> rational function of  t. (I use a replacement rule to save some typing)
> 
> rep={b1\[Rule]a1+t,b2\[Rule]a2+t,b3\[Rule]a3+t,b4\[Rule]a4+t}
> 
> \!\(test = \(-\(\((b3\ b4\ t13\^2\ \((\(-b2\)\ b4 + t24\^2)\) -
>                 b1\^2\ b3\ \((b2\ b4\^2 - b4\ t24\^2 +
>                       b3\ \((b4\^2 + t24\^2)\))\) +
>                 b1\ \((\(-b2\)\ b4\^2\ \((b3\^2 + t13\^2)\) +
>                       b3\^2\ b4\ t24\^2 + b4\ t13\^2\ t24\^2 +
>                       b3\ t13\^2\ \((b4\^2 +
>                             t24\^2)\))\))\)\/\(\((b1\ b3 - t13\^2)\)\^3\ \
> \((\(-b2\)\ b4 + t24\^2)\)\^2\)\)\) /. rep\)
> 
> If I try to determine the indefinite integral using
> 
> Integrate[test,t]
> 
> Mathematica never returns a result on my computer. It works hard, consumes eventually all memory of my computer ( I have up to 32 GB 
> on a Linux workstation) and eventually shuts down the kernel. But that takes very long!
> 
> However, the integral is actually relatively easily determined "by hand". The result is
> 
>  \!\(test3 = \(\((a1 + t)\)\ \((a3 + t)\)\ \((a4 + t)\)\)\/\(\((\(-t13\^2\) + \
> \((a1 + t)\)\ \((a3 + t)\))\)\^2\ \((t24\^2 - \((a2 + t)\)\ \((a4 + t)\))\)\)\
> \)
> 
> as can be verified by differentiation.
> 
> Since I have to do more of such integrals, it would be nice if I could get Mathematica to do the work. Does anyone have an idea what 
> could be done about that? Is there any trick or option in order to do such integrals using Mathematica?
> 
> Moreover, it would be nice to know what Mathematica is actually doing while it suffers through that calculation, it also does not 
> give me an error message.
> 
> Thanks for any help.
> 
> Michael Weyrauch
> 
> 
You can use the option *Assumptions* to pas assumptions to Integrate. 
For example,

Integrate[test, t, Assumptions ->
  {a1, a2, a3, a4, t13, t24} \[Element] Reals]

HTH,
Jean-Marc


  • Prev by Date: Re: analytic integration of InterpolatingFunction compositions
  • Next by Date: Re: Problem with Which
  • Previous by thread: Re: Integrate
  • Next by thread: Re: Integrate