Re: Distribution and Integral
- To: mathgroup at smc.vnet.net
- Subject: [mg59878] Re: Distribution and Integral
- From: David Bailey <dave at Remove_Thisdbailey.co.uk>
- Date: Wed, 24 Aug 2005 06:32:05 -0400 (EDT)
- References: <deeo66$2vq$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
ms_usenet at gmx.de wrote: > Hello, > > to apply further rules on simpler integrals (rules for the integration > by parts), I would like to distribute the integral over its summands. > This works if it is an integral alone, but doesn't if there is a factor > (because the head is Integrate in the first, and Times in the latter > case?): > > \!\(Distribute[ > t \(\[Integral]\_x1\%x2\((f[x] + > g[x])\) \[DifferentialD]x\)]\[IndentingNewLine] > Distribute[\[Integral]\_x1\%x2\((f[x] + g[x])\) \[DifferentialD]x]\) > > Out[695]= > \!\(t\ \(\[Integral]\_x1\%x2\((f[x] + g[x])\) \[DifferentialD]x\)\) > Out[696]= > \!\(\[Integral]\_x1\%x2 f[x] \[DifferentialD]x + \[Integral]\_x1\%x2 g[ > x] \[DifferentialD]x\) > > How could I get the distribution in the latter case? Because f and g > can have variable structure, I haven't found a simple rule with > patterns. A hint to simplify the original problem, integration by > parts, would be appreciated too! > > Best Regards, > Martin > Hello, One useful way to manipulate integrals and derivatives in specific ways is to use a private notation - say Integral rather than Integrate and then you can define your own functions to manipulate expressions involving these without any complications from Mathematica, because it doesn't know anything about your notation. Then when you need to do so, you can use something like expr /. Integral->Integrate to 'activate' your notation. David Bailey http://www.dbaileyconsultancy.co.uk