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Re: Please explain this weird Integrate result

• To: mathgroup at smc.vnet.net
• Subject: [mg60131] Re: Please explain this weird Integrate result
• From: "Steve Luttrell" <steve_usenet at _removemefirst_luttrell.org.uk>
• Date: Sun, 4 Sep 2005 03:01:53 -0400 (EDT)
• References: <dfbevv$inu$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

These are INdefinite integrals, so the integrals are modulo an additive 
constant.

Steve Luttrell

"Jose Reckoner" <reckoner at gmail.com> wrote in message 
news:dfbevv$inu$1 at smc.vnet.net...
>
> 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?
>