If Sage passes problems of integrating non-analytic functions to the
current version Maxima, then maybe Sage is
committing an error (too). Determining when the argument of abs() is
zero to do piecewise integration
is, in general, recursively undecidable, proved in a 1968 theorem by
Daniel Richardson.
I suppose Maxima could do better; though I tried this problem in the
(last commercial) Macsyma and got 162 also.
Maxima is clever enough to know it can't do this alternative,
integrate(x*(if x^2-9 < 0 then 9-x^2 else x^2-9),x,-6,0).
RJF
David Joyner wrote:
> Hi:
>
> FYI, here is a bug recently discovered by a Sage user named Pong:
>
>
> Maxima 5.16.3 http://maxima.sourceforge.net
> Using Lisp CLISP 2.46 (2008-07-02)
> Distributed under the GNU Public License. See the file COPYING.
> Dedicated to the memory of William Schelter.
> The function bug_report() provides bug reporting information.
> (%i1) integrate(x*abs(x^2-9),x,-6,0);
> (%o1) 162
>
>
> HTH, David Joyner
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