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