Re: Distribution and Integral
- To: mathgroup at smc.vnet.net
- Subject: [mg59844] Re: Distribution and Integral
- From: "Jens-Peer Kuska" <kuska at informatik.uni-leipzig.de>
- Date: Wed, 24 Aug 2005 06:30:11 -0400 (EDT)
- Organization: Uni Leipzig
- References: <deeo66$2vq$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Hi, and expandIntegrand = Verbatim[Integrate][a_.*(b_ + c_), {x_, x1_, x2_}] /; FreeQ[a, x] :> a*Integrate[b, {x, x1, x2}] + a*Integrate[c, {x, x1, x2}] t*Integrate[f[x] + g[x], {x, x1, x2}] /. expandIntegrand will not help ypu ? Regards Jens <ms_usenet at gmx.de> schrieb im Newsbeitrag news:deeo66$2vq$1 at smc.vnet.net... | 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 |