Hello,
With Maxima 5.18.1, I get the following behavior:
Maxima 5.18.1 http://maxima.sourceforge.net
Using Lisp ECL 9.4.1
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) integrate(sin(x)/(cos(x))^2,x);
1
(%o1) ------
cos(x)
(%i2) integrate(cos(x)/(sin(x))^2,x,%pi/6,%pi/4);
Is sin(x) positive, negative, or zero?
--Mike