Actually, MuPAD returns -cos(2*x)/4 as the indefinite integral.
-Alasdair
On 5/16/07, Stavros Macrakis <macrakis at alum.mit.edu> wrote:
>
> On 5/16/07, sen1 at math.msu.edu < sen1 at math.msu.edu> wrote:
> >
> > Agreed that this might be low on the list of things to do, but, isn't it
> > reasonable to
>
> have indefinite integrals return constants to show the non-uniqueness?...
>
> If so, how hard would it be to add constants to indefinite integrals?
>
>
> It would be trivial to implement if we decide to do it -- a couple of
> lines of code in $integrate and simpinteg. From the user's point of view,
> one complication might be a profusion of arbitrary constants, e.g.
>
> integrate(x+x^2,x) => x^2/2+x^3/3+%c1
>
> but
>
> integrate(x,x)+integrate(x^2,x) => x^2/2+x^3/3+%c2+%c3
>
> Also, it is curious that Maple 10 returns
> > sin(x)^2/2
> > while Mathematica 3.0 returns
> > -cos(x)^2/2
>
>
> Most integrals in computer algebra systems are not handled by lookup in a
> table of integrals, but are derived algorithmically. The details of the
> algorithm determine the result. As a general rule, they try to preserve
> the shape of the expression, so that the equivalent integral -cos(2*x)/4
> isn't generated, but even that is not guaranteed in general.
>
> >From this discussion, it seems that the indefinite integration and ode2
> > routines in maxima have little to do with each other.
>
>
> They have a lot to do with each other: the ode2 routines use integration
> as a subroutine.
>
> -s
>
>
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