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>