Re: Incorrect result for improper integral with MMA?

*To*: mathgroup at smc.vnet.net*Subject*: [mg8820] Re: Incorrect result for improper integral with MMA?*From*: Paul Abbott <paul at physics.uwa.edu.au>*Date*: Fri, 26 Sep 1997 00:33:43 -0400*Organization*: University of Western Australia*Sender*: owner-wri-mathgroup at wolfram.com

Chris Barker wrote: > The command: > > Integrate[1/(x*Log[x]^2),{x,3,Infinity}] > > yields the result: > > \!\(\* > RowBox[{ > \(Integrate::"idiv"\), \( : \ \), > "\<"Integral of \!\(1\/\(x\\ \(Log[x]\)\^2\)\) does not converge on \ > \!\({3, \*InterpretationBox[\"\\[Infinity]\", DirectedInfinity[1]]}\)."\>"}]\) > > i.e. the integral does not converge. However, analytic techniques seem > to indicate that the integral does indeed converge to 1/ln(3). Mimicing > the analytic procedures step by step with mma also yields 1/ln(3). Am I > being stupid, or is mma wrong? Mathematica easily computes the indefinite integral -- from this you will see why the integral does not converge on [3,Infinity). Cheers, Paul ____________________________________________________________________ Paul Abbott Phone: +61-8-9380-2734 Department of Physics Fax: +61-8-9380-1014 The University of Western Australia Nedlands WA 6907 mailto:paul at physics.uwa.edu.au AUSTRALIA http://www.pd.uwa.edu.au/~paul God IS a weakly left-handed dice player ____________________________________________________________________