I think the reason to do expansion is in the case that the "inside" is not a
simple expression in x, but, say, an expression like (sin(x)+4*cos(x)). Then
you might consider doing the expansion and then treating the terms using
other techniques in the bag of tricks that constitutes Joel Moses' SIN
program.
It would probably be a mistake to expand ()^199 because you would be waiting
too long for the expansion. Certainly the value 6 is pretty much arbitrary.
The reason not to use the general formula is that it won't do some examples
that can be done by expansion. At least that is my supposition. Reading
Moses' online
thesis at MIT could be a check on this.
The notion that you have a form that looks like u*du or u^n*du in general
can demand more than simple pattern matching. You might need to factor the
integrand in some cases. Or maybe some effective method can be substituted
in the program for the hackish "test division" used by SIN. I once assigned
such a task in a grad class; I wrote a solution too; perhaps I can recreate
it.
RJF
> -----Original Message-----
> From: maxima-bounces at math.utexas.edu
> [mailto:maxima-bounces at math.utexas.edu] On Behalf Of Robert Dodier
> Sent: Tuesday, March 18, 2008 6:55 PM
> To: Raymond Toy (RT/EUS)
> Cc: Maxima List
> Subject: Re: [Maxima] Bug 1901044?
>
> On 3/17/08, Raymond Toy (RT/EUS) <raymond.toy at ericsson.com> wrote:
>
> > An example from bug 1901044 (from Barton):
> >
> > (%i1) integrate((5*x-2)^199,x);
> > (%o1) (5*x-2)^200/1000
> >
> > (%i2) integrate((5*x-2)^3,x);
> > (%o2) (125*x^4)/4-50*x^3+30*x^2-8*x
>
> > Any opinions on whether this is the right thing to do?
> And if so, why
> > 6, and not some other value? Or should we just use the general
> > formula always?
>
> OK by me to use the general formula for all cases.
>
> Thanks for looking into this.
>
> Robert
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