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

• To: mathgroup at smc.vnet.net
• Subject: [mg121707] Re: Integration error? Integrate[1/(x^3-1)]?
• From: David Reiss <dbreiss at gmail.com>
• Date: Mon, 26 Sep 2011 20:05:41 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <j5pcpv$8j9$1@smc.vnet.net>

The results differ by a constant.  Hence they are the same
(integrationally speaking)....


On Sep 26, 4:23 am, Travis Ayres <tray... at gmail.com> 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!