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?