Incorrect result for improper integral with MMA?

*To*: mathgroup at smc.vnet.net*Subject*: [mg8773] Incorrect result for improper integral with MMA?*From*: barker at inreach.com (Chris Barker)*Date*: Thu, 25 Sep 1997 12:26:07 -0400*Organization*: San Joaquin Delta College*Sender*: owner-wri-mathgroup at wolfram.com

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? E-mail responses gladly accepted.