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Re: Incorrect symbolic improper integral

• To: mathgroup at smc.vnet.net
• Subject: [mg103645] Re: [mg103586] Incorrect symbolic improper integral
• From: Curtis Osterhoudt <cfo at lanl.gov>
• Date: Thu, 1 Oct 2009 06:38:47 -0400 (EDT)
• Organization: LANL
• References: <30167826.1254225639354.JavaMail.root@n11> <200909300903.FAA09670@smc.vnet.net>
• Reply-to: cfo at lanl.gov

  Yes, Jason is obviously using 7.0.0. I use that version on a linux machine, and get what he reported. Wolfram|Alpha also gets Pi/E -- they need to update their version!


> From: jwmerrill at gmail.com [mailto:jwmerrill at gmail.com] 
> 
> 
> Below is a definite integral that Mathematica does incorrectly.
> Thought someone might like to know:
> 
> In[62]:= Integrate[Cos[x]/(1 + x^2), {x, -\[Infinity], \[Infinity]}]
> 
> Out[62]= \[Pi]/E
> 
> What a pretty result--if it were true. The correct answer is \[Pi]*Cosh
> [1], which can be checked by adding a new parameter inside the
> argument of Cos and setting it to 1 at the end:
> 
> In[61]:= Integrate[Cos[a x]/(1 + x^2), {x, -\[Infinity], \[Infinity]},
>   Assumptions -> a \[Element] Reals]
> 
> Out[61]= \[Pi] Cosh[a]
> 
> Regards,
> 
> Jason Merrill
> 
> 
> 
> 


-- 
==================================
Curtis Osterhoudt
cfo at remove_this.lanl.and_this.gov
PGP Key ID: 0x4DCA2A10
==================================

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  • Re: Re: Incorrect symbolic improper integral
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>