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

*To*: mathgroup at smc.vnet.net*Subject*: [mg121716] Re: Integration error? Integrate[1/(x^3-1)]?*From*: Heike Gramberg <heike.gramberg at gmail.com>*Date*: Mon, 26 Sep 2011 20:07:18 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <201109260816.EAA08704@smc.vnet.net>

An indefinite integral is unique up to an additive constant. Since Log[1-x] is equal to Log[x-1] plus or minus Pi I (try for example Log[1-x] /. x->4 which should give Pi I + Log[3]) the two answers are equally valid. Heike. On 26 Sep 2011, at 10:16, Travis Ayres wrote: > 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! >

**References**:**Integration error? Integrate[1/(x^3-1)]?***From:*Travis Ayres <trayres@gmail.com>