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