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Integration error? Integrate[1/(x^3-1)]?

• To: mathgroup at smc.vnet.net
• Subject: [mg121702] Integration error? Integrate[1/(x^3-1)]?
• From: Travis Ayres <trayres at gmail.com>
• Date: Mon, 26 Sep 2011 04:16:18 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com

The indefinite integral of 1/(x^3-1) with respect to x.
In input form, put into Mathematica 8:
Integrate[1/(x^3 - 1), x]
Gives result:
-(ArcTan[(1 + 2*x)/Sqrt[3]]/Sqrt[3]) + (1/3)*Log[1 - x] - (1/6)*
  Log[1 + x + x^2]

Computing online with the Wolfram integrator:
http://integrals.wolfram.com/index.jsp?expr=1%2F%28x^3-1%29&random=false
Gives:
-(ArcTan[(1 + 2*x)/Sqrt[3]]/Sqrt[3]) + Log[-1 + x]/3 - Log[1 + x +
x^2]/6

Look at the (1/3)*Log[1-x] term.
Mathematica 8 gives me Log[1-x], the online integrator gives the
answer Log[x-1].
The answers are exactly the same in all other terms. I ran across this
because I was trying the tutorials, and I noticed my answer was
different than the result in the tutorial even.

Is this an error?
Thanks all!

• Follow-Ups:
  • Re: Integration error? Integrate[1/(x^3-1)]?
    • From: Daniel Lichtblau <danl@wolfram.com>
  • Re: Integration error? Integrate[1/(x^3-1)]?
    • From: Heike Gramberg <heike.gramberg@gmail.com>