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

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  • Subject: [mg121702] Integration error? Integrate[1/(x^3-1)]?
  • From: Travis Ayres <trayres at>
  • Date: Mon, 26 Sep 2011 04:16:18 -0400 (EDT)
  • Delivered-to:

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:^3-1%29&random=false
-(ArcTan[(1 + 2*x)/Sqrt[3]]/Sqrt[3]) + Log[-1 + x]/3 - Log[1 + x +

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!

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