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.