Re: Incorrect symbolic improper integral
- To: mathgroup at smc.vnet.net
- Subject: [mg103705] Re: Incorrect symbolic improper integral
- From: Mariano Suárez-Alvarez <mariano.suarezalvarez at gmail.com>
- Date: Sat, 3 Oct 2009 09:02:09 -0400 (EDT)
- References: <200909291138.HAA25632@smc.vnet.net> <h9vflr$e6v$1@smc.vnet.net>
On Sep 30, 8:33 am, Daniel Lichtblau <d... at wolfram.com> wrote:
> jwmerr... at gmail.com wrote:
> > 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
>
> > [...]
>
> Pi/E is correct. For one thing, it agrees with NIntegrate. For another,
> you can find and verify correctness of an antiderivative, observe it
> crosses no branch cuts, and take limits at +-infinity to verify the
> definite integral.
>
> Moreover I do not replicate your parametrized result.
>
> In[20]:= Integrate[Cos[a*x]/(1+x^2), {x,-Infinity,Infinity},
> Assumptions -> Element[a,Reals]] // InputForm
> Out[20]//InputForm= Pi/E^Abs[a]
>
> I got that result, or something equivalent, in every Mathematica version
> I tried going back to 4. I may have missed some point releases. Also it
> could be a timing-dependent problem, particularly if you are running
> version 6 (where it seems to be much slower than other versions).
What is a 'time-dependent problem' in this context?
-- m