Re: Incorrect symbolic improper integral
- To: mathgroup at smc.vnet.net
- Subject: [mg103617] Re: Incorrect symbolic improper integral
- From: Erik Max Francis <max at alcyone.com>
- Date: Wed, 30 Sep 2009 05:01:28 -0400 (EDT)
- References: <h9srop$p7s$1@smc.vnet.net>
jwmerrill 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
>
> 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]
I get different answer with Mathematica 7 on Linux:
In[1]:= Integrate[Cos[x]/(1 + x^2), {x, -\[Infinity], \[Infinity]}]
Out[1]= \[Pi]/E
In[2]:= Integrate[Cos[a x]/(1 + x^2), {x, -\[Infinity], \[Infinity]},
Assumptions -> a \[Element] Reals]
Out[2]= E^-Abs[a] \[Pi]
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