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Please explain this weird Integrate result

• To: mathgroup at smc.vnet.net
• Subject: [mg60116] Please explain this weird Integrate result
• From: "Jose Reckoner" <reckoner at gmail.com>
• Date: Sat, 3 Sep 2005 02:06:03 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

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?

• Follow-Ups:
  • Re: Please explain this weird Integrate result
    • From: stephen layland <layland@wolfram.com>