Services & Resources / Wolfram Forums / MathGroup Archive
-----

MathGroup Archive 2011

[Date Index] [Thread Index] [Author Index]

Search the Archive

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

  • To: mathgroup at smc.vnet.net
  • Subject: [mg121708] Re: Integration error? Integrate[1/(x^3-1)]?
  • From: Daniel Lichtblau <danl at wolfram.com>
  • Date: Mon, 26 Sep 2011 20:05:51 -0400 (EDT)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • References: <201109260816.EAA08704@smc.vnet.net>

On 09/26/2011 03:16 AM, 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!
>

No. Both are correct antiderivatives (indefinite integrals, primitives). 
You can verify this by differentiating and checking that the result, in 
each case, is equivalent to the integrand.

The mathematical reason this can happen is that the two terms of 
interest differ by a (piecewise) constant. The Mathematica reason is 
that the Integrator, for reasons unknown to me, rather insists on using 
version 7 of Mathematica. I'll make inquiries about that.

Daniel Lichtblau
Wolfram Research





  • Prev by Date: Re: Fittings 2 sets of equations and 2 data sets with nonlinearmodelfit
  • Next by Date: Re: Bug with Sequence and Assignment by Part...
  • Previous by thread: Re: Integration error? Integrate[1/(x^3-1)]?
  • Next by thread: Re: Integration error? Integrate[1/(x^3-1)]?