The code for rational function integration in Maxima has been
replaced in the commercial macsyma. Basically, if the denominator
of the rational fraction does not factor over the integers,
then newer solution methods have been discovered. These are
actually kind of clumsy with sum over "rootof" expressions, but
the answer is formally correct. Mupad uses these methods.
There are other, probably better for many users, ways for expressing the
answer.. e.g. finding approximate roots in the complex plane
in this case (where the denominator has no extra parameters).
If the derivative doesn't come back with the same answer,
after simplification, then there may also be a bug in
the procedures.
RJF
Daniel Duparc wrote:
>
> The same results were given by Maxima 5.4:
>
> [daniel@georgette ~]$ maxima
> GCL (GNU Common Lisp) Version(2.3) ven avr 28 22:31:35 CEST 2000
> Licensed under GNU Library General Public License
> Contains Enhancements by W. Schelter
> Maxima 5.4 ven avr 28 22:31:31 CEST 2000 (with enhancements by W. Schelter).
> Licensed under the GNU Public License (see file COPYING)
> (C1) integrate(1/(1+x+x^5),x);
>
> / 2
> [ x - 4 x + 5
> I ------------ dx 2 x + 1
> ] 3 2 2 5 ATAN(-------)
> / x - x + 1 LOG(x + x + 1) SQRT(3)
> (D1) ----------------- - --------------- + ---------------
> 7 14 7 SQRT(3)
> (C2)
>
> The true answer is (given for example by MuPAD 1.4.2):
>
> *----* MuPAD 1.4.2 -- The Open Computer Algebra System
> /| /|
> *----* | Copyright (c) 1997 - 1999 by SciFace Software
> | *--|-* All rights reserved.
> |/ |/
> *----* Licensed to: Daniel Duparc
>
> Type ?demo, ?topics, ?news or ?changes for further information.
>
> >> int(1/(1+x+x^5),x);
>
> / 1/2 \
> 1/2 | 2 3 (x + 1/2) |
> 5 3 atan| ---------------- | 2 /
> \ 3 / ln((x + 1/2) + 3/4) |
> ------------------------------- - -------------------- + sum|
> 21 14 \
>
> / 2 3 4
> | 5941 X2 3284 X2 54096 X2 216384 X2
> X2 ln| x + ------- - -------- + --------- - ---------- +
> \ 625 625 625 625
>
> \ \
> | 2 3 |
> 256/625 |, X2 = RootOf(- 12 X3 - 23 X3 + 161 X3 - 1 ) |
> / /
>
> Bests regards.
> ----
> Daniel Duparc <dduparc@club-internet.fr>
> 29 av. de la Commune de Paris
> 94400 Vitry sur Seine (France)
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