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