Re: Why does this happen?
- To: mathgroup at smc.vnet.net
- Subject: [mg78725] Re: [mg78668] Why does this happen?
- From: DrMajorBob <drmajorbob at bigfoot.com>
- Date: Sat, 7 Jul 2007 06:15:43 -0400 (EDT)
- References: <17887335.1183708613203.JavaMail.root@m35>
- Reply-to: drmajorbob at bigfoot.com
Both answers are wrong.
Log[1 + \[ExponentialE]^x/Sqrt[x]] > Log[\[ExponentialE]^x/Sqrt[x]] = x -
1/2 Log[x]. That's a positive increasing (and unbounded) function on 1/2
to Infinity, so the integral diverges, big time.
Mathematica version 6 "knows" the Integrate version doesn't converge, but
NIntegrate gets the same answer as you're showing -- with an (absurd)
error message:
NIntegrate::inumri: The integrand Log[1+\[ExponentialE]^x/Sqrt[x]] \
has evaluated to Overflow, Indeterminate, or Infinity for all \
sampling points in the region with boundaries {{0.,4.64782*10^14}}.
Bobby
On Fri, 06 Jul 2007 02:31:37 -0500, Budaoy <yaomengliang at gmail.com> wrote:
> I have a problem in calculating this integral shown below:
>
> Integrate[Log[1+Exp[x]/Sqrt[x]],{x,0,Infinity}]
> Pi^2/6
>
> N[%]
> 1.64493
>
> NIntegrate[Log[1+Exp[x]/Sqrt[x]],{x,0,Infinity}]
> 1.01799
>
> Where does this difference come from and which one is correct?
>
>
>
--
DrMajorBob at bigfoot.com