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: firstname.lastname@example.org
- References: <email@example.com>
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]/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!