Subject: Incorrect integration of rational functions
From: Anton Voropaev
Date: Fri, 23 Apr 2010 22:50:33 +0400
integrate(1/(2-x^4),x,0,1)
returns incorrect complicated expression while
integrate(1/((2^(1/2)-x^2)*(2^(1/2)+x^2)),x,0,1)
works.
THE INPUT:
display2d : false;
I1 : integrate(1/(2-x^4),x,0,1);
I2 : integrate(1/((2^(1/2)-x^2)*(2^(1/2)+x^2)),x,0,1);
[I1,I2], numer;
THE INPUT AND THE OUPUT:
Maxima 5.19.2 http://maxima.sourceforge.net
Using Lisp GNU Common Lisp (GCL) GCL 2.6.8 (aka GCL)
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
The function bug_report() provides bug reporting information.
(%i1) display2d : false;
(%o1) false
(%i2) I1 : integrate(1/(2-x^4),x,0,1);
(%o2) %i*(log((sqrt(2)*(97*2^(7/2)-463*2^(9/4)+21*2^(3/4)+854)
+283*2^(13/4)-227*2^(7/4)-427*2^(3/2)-399)
/1153)
/2^(19/4)
+log(-(sqrt(2)*(-1827*2^(7/2)+4423*2^(9/4)+12701*2^(3/4)-21282)
+3095*2^(13/4)+9069*2^(7/4)-10857*2^(3/2)-31679)
/3583)
/2^(19/4)+log(2^(7/4)+2^(3/2)+2^(5/4)+3)/2^(19/4)
-log(-2^(7/4)+2^(3/2)-2^(5/4)+3)/2^(19/4))
-log((sqrt(2)*(97*2^(7/2)-463*2^(9/4)+21*2^(3/4)+854)
+283*2^(13/4)-227*2^(7/4)-427*2^(3/2)-399)
/1153)
/2^(19/4)
-log(-(sqrt(2)*(-1827*2^(7/2)+4423*2^(9/4)+12701*2^(3/4)-21282)
+3095*2^(13/4)+9069*2^(7/4)-10857*2^(3/2)-31679)
/3583)
/2^(19/4)+log(2^(7/4)+2^(3/2)+2^(5/4)+3)/2^(19/4)
-log(-2^(7/4)+2^(3/2)-2^(5/4)+3)/2^(19/4)
(%i3) I2 : integrate(1/((2^(1/2)-x^2)*(2^(1/2)+x^2)),x,0,1);
(%o3) atan(1/2^(1/4))/2^(7/4)-log(-2^(7/4)+2^(3/2)-2^(5/4)+3)/2^(11/4)
(%i4) [I1,I2], numer;
(%o4) [2.7755575615628914E-15*%i+0.36396463394057,0.57183362703471]