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MathGroup Archive 2005

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Re: Please explain this weird Integrate result

  • To: mathgroup at smc.vnet.net
  • Subject: [mg60140] Re: [mg60116] Please explain this weird Integrate result
  • From: "David Park" <djmp at earthlink.net>
  • Date: Sun, 4 Sep 2005 03:02:03 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Elementary calculus. An indefinite integral always contains an arbitrary
constant - which Mathematica does not supply. -1/2 is a constant.

David Park
djmp at earthlink.net
http://home.earthlink.net/~djmp/

From: Jose Reckoner [mailto:reckoner at gmail.com]
To: mathgroup 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?





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