# [Maxima] bug report

David Billinghurst dbmaxima at gmail.com
Sat Jun 2 17:56:44 CDT 2012

```On 3/06/2012 1:56 AM, Raymond Toy wrote:
> On 6/2/12 4:32 AM, Jaime Villate wrote:
>> On 06/02/2012 05:28 AM, Raymond Toy wrote:
>>> On 6/1/12 6:20 PM, Robert Dodier wrote:
>>>> On 2012-06-01, Банков Дмитрий<bankov_dmitrii at mail.ru>   wrote:
>>>>
>>>>> integrate(sin(a*x^3)/x, x, 0, +inf);
>>>>> maxima result: 0;
>>>>> correct result: %pi * abs(a) / 6 / a;
>>>> Thanks for this info. I confirm that it happens w/ Maxima 5.27.0.
>>> How did you get this?  I tried it with the current git version and I get
>>>
>>> gamma(1/3)/6/a^(1/3)
>>>
>>> when a>   0.
>>>
>>> Looking at the code in defint.lisp, I see maxima has a special routine
>>> (scaxn) to handle this type of integral.  integrate(sin(a*x^n),x,0,inf)
>>> ->   gamma(1/n)/a^(1/n)/n*sin(%pi/2/n).
>>>
>>>
>> ??
>> I got the most recent git master snapshot yesterday and compiled it with
>> SBCL, CCL, GCL, CLisp and ECL
>> and I also get the wrong 0 result
>>
>> Maxima branch_5_27_base_65_g08552c3_dirty http://maxima.sourceforge.net
>> using Lisp CLISP 2.49 (2010-07-07)
>> Dedicated to the memory of William Schelter.
>> The function bug_report() provides bug reporting information.
>> (%i1) integrate(sin(a*x^3)/x, x, 0, +inf);
>> (%o1) 0
> Well that's interesting.  On my mac with sources from just now, cmucl,
> ccl, and clisp don't give 0.  Maxima asks for the sign of a (pos) and
> returns gamma(1/3)/6/a^(1/3), which I think is right.  Which differs
> from what the original poster said should be the correct value.
>
> Someone else is going to have to debug this.
>
> Could you check to see if scaxn is called?  It is on my systems.  If it
> isn't, then that would be the problem.
>
> Ray
windows (cygwin)

Maxima branch_5_27_base_95_gf40c188 http://maxima.sourceforge.net
using Lisp CLISP 2.48 (2009-07-28)
(%i1) :lisp (trace scaxn)
;; Tracing function SCAXN.
(SCAXN)
(%i1) integrate(sin(a*x^3)/x,x,0,+inf);
1. Trace: (SCAXN '((MTIMES SIMP) ((MEXPT SIMP) \$X -1) ((%SIN SIMP)
((MTIMES SIMP) \$A ((MEXPT SIMP) \$X 3)))))
1. Trace: SCAXN ==> NIL
(%o1)                                  0

```