Re: Re: Incorrect symbolic improper integral

*To*: mathgroup at smc.vnet.net*Subject*: [mg103692] Re: [mg103645] Re: [mg103586] Incorrect symbolic improper integral*From*: DrMajorBob <btreat1 at austin.rr.com>*Date*: Fri, 2 Oct 2009 08:26:03 -0400 (EDT)*References*: <30167826.1254225639354.JavaMail.root@n11>*Reply-to*: drmajorbob at yahoo.com

> Wolfram|Alpha also gets Pi/E -- they need to update their version! > No... Pi/E is correct, as other posts have pointed out. Bobby On Thu, 01 Oct 2009 05:38:47 -0500, Curtis Osterhoudt <cfo at lanl.gov> wrote: > 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 >> >> >> >> > > -- DrMajorBob at yahoo.com