Re: Incorrect symbolic improper integral
- To: mathgroup at smc.vnet.net
- Subject: [mg103630] Re: [mg103586] Incorrect symbolic improper integral
- From: "David Park" <djmpark at comcast.net>
- Date: Wed, 30 Sep 2009 05:03:55 -0400 (EDT)
- References: <30167826.1254225639354.JavaMail.root@n11>
Jason, In Mathematica 7.0.1.0 I obtain for the second integral: Integrate[Cos[a x]/(1 + x^2), {x, -\[Infinity], \[Infinity]}, Assumptions -> a \[Element] Reals] % /. a -> 1 E^-Abs[a] \[Pi] \[Pi]/E Also, utilizing the symmetry about zero, this is the same answer given in Gradshteyn & Ryzbik, 3.723, 2. David Park djmpark at comcast.net http://home.comcast.net/~djmpark/ 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