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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?
> 
>