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Re: Please explain this weird Integrate result

• To: mathgroup at smc.vnet.net
• Subject: [mg60152] Re: Please explain this weird Integrate result
• From: David Bailey <dave at Remove_Thisdbailey.co.uk>
• Date: Sun, 4 Sep 2005 03:02:22 -0400 (EDT)
• References: <dfbevv$inu$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Jose Reckoner wrote:
> 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?
> 
Hello,

You are doing indefinite integration which always produces a result that 
has an undetermined constant of integration! In maths classes you always 
have to write +C, or get a mark deducted. C can stand for any constant - 
including -1/2.

David Bailey
http://www.dbaileyconsultancy.co.uk