
Re: Incorrect symbolic improper integral
Posted:
Sep 30, 2009 7:33 AM


A follow  up to my previous post:
1. Of course, the simple form of the answer I gave is just
Pi*Exp[Abs[a]]
2. When I was talking about pole contributions, I meant for two exponential terms Exp[I*a*x] and Exp[I*a*x] (expanding the cosine) separately. The two terms always pick the opposite poles but give the same contribution. The single term never gets the contribution from both poles.
Regards, Leonid
On Tue, Sep 29, 2009 at 4:38 AM, jwmerrill@gmail.com <jwmerrill@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 resultif 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 > >

