Re: Why does this happen?
- To: mathgroup at smc.vnet.net
- Subject: [mg78701] Re: Why does this happen?
- From: Bill Rowe <readnewsciv at sbcglobal.net>
- Date: Sat, 7 Jul 2007 06:03:12 -0400 (EDT)
On 7/6/07 at 3:31 AM, yaomengliang at gmail.com (Budaoy) 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?
Neither of these can be correct. The integrand is clearly
unbounded as x increases to infinity. That is Exp[x]/Sqrt[x] is
clearly a positive real for x > 0 and an exponential grows
faster than a square root.
You didn't say what version of Mathematica you were using. I
assume it is not version 6 since on my machine doing either
NIntegrate or Integrate with this integrand generates an error
message stating the integral does not converge on the specified
integration interval.
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