Re: Incorrect result for improper integral with MMA?

*To*: mathgroup at smc.vnet.net*Subject*: [mg8841] Re: [mg8773] Incorrect result for improper integral with MMA?*From*: seanross at worldnet.att.net*Date*: Mon, 29 Sep 1997 02:40:07 -0400*Sender*: owner-wri-mathgroup at wolfram.com

Chris Barker wrote: > > The command: > > Integrate[1/(x*Log[x]^2),{x,3,Infinity}] > > yields the result: I am not sure I understand the internal workings of Integrate and the internal difference between Integrate[f,x] and Integrate[f,{x,a,b}], but fi[a_]=Integrate[1/(x*Log[x]^2),x]/.x->a; fi[3]-fi[Infinity] returns a correct result. Also, Integrate[1/(x*Log[x]^2),{x,3,a}] returns a correct result for any finite a greater than three, including huge values where the integrand is extremely small. If I had to guess at a reason, it would be that there is no way that mathematica can know if a function is reasonably behaved on an interval that goes to infinity, so it defaults to a different behavior when Infinity is one of the limits.