# [Maxima] Endless loop during definte integral

Richard Hennessy rich.hennessy at verizon.net
Tue Mar 31 10:58:29 CDT 2009

```Basically I was trying to verify an identity for diracdelta using thin spiking functions (let sigma approach 0).

(%i4) integrate(x*pwdelta(a*x-b),x);

(out4) b*(signum(x-b/a)+1)/(2*a*abs(a))

I can use a gaussian instead, so it's no big deal.

Rich

----- Original Message -----
From: "reyssat" <eric.reyssat at math.unicaen.fr>
To: "Richard Hennessy" <rich.hennessy at verizon.net>
Cc: "Maxima List" <maxima at math.utexas.edu>
Sent: Tuesday, March 31, 2009 3:38 AM
Subject: Re: [Maxima] Endless loop during definte integral

Richard Hennessy a écrit :
> I also noticed that it is not caused by the limits being inf and minf.
>
> assume(a>0,b>0,sigma>0,c<d)\$
> f2(x):=(2*sigma^(3/2))/(%pi*x^4+2*%pi*sigma*x^2+%pi*sigma^2)\$
> integrate(f2(a*x-b)*x^3,x,c,d);  /* loops long time */
>
> I am trying it and will let it run for a hour or two and see if I get an answer.
>
> Rich
>
>
>
This is enough to get stuck :
integrate(1/(x^4+x^2+1),x,c,c+1);

However,
integrate(1/(x^4+x^2+1),x,10,11);
and
integrate(1/(x^4+x^2+1),x);
are ok.

Maxima version: 5.17.1
Maxima build date: 19:10 12/18/2008
host type: i686-pc-mingw32
lisp-implementation-type: GNU Common Lisp (GCL)
lisp-implementation-version: GCL 2.6.8

Eric
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