Re: Please explain this weird Integrate result
- To: mathgroup at smc.vnet.net
- Subject: [mg60133] Re: [mg60116] Please explain this weird Integrate result
- From: Bob Hanlon <hanlonr at cox.net>
- Date: Sun, 4 Sep 2005 03:01:56 -0400 (EDT)
- Reply-to: hanlonr at cox.net
- Sender: owner-wri-mathgroup at wolfram.com
Indefinate integration has an implied constant of integration so any results that differ by a constant are equivalent. The different forms resulted in a different sequence of operations that arrived at different but equivalent results. Bob Hanlon > > From: "Jose Reckoner" <reckoner at gmail.com> To: mathgroup at smc.vnet.net > Date: 2005/09/03 Sat AM 02:06:03 EDT > Subject: [mg60133] [mg60116] Please explain this weird Integrate result > > > Expand[Integrate[(2*x)/(2*x - 1), x]] > > gives > > -1/2 + x + Log[-1 + 2*x]/2 > > But, > > Expand[Integrate[1 + 1/(-1 + 2*x), x]] > > gives > > x + Log[-1 + 2*x]/2 > > even though > > (2*x)/(2*x - 1) == 1 + 1/(-1 + 2*x) > > Where did the extra -1/2 in the first result come from? > >