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
|