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