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)