cosh integral incorrect because of abs_integrate #14591
Description
See this ask.sagemath question.
sage: a = integrate(sqrt(1-1/4*cosh(x)^2),x)
sage: a.full_simplify()
cosh(x)
Not that I'm an expert here, but at any rate, viewed as real functions this makes no sense, though perhaps on some branch it does. This happens because
Maxima 5.29.1 http://maxima.sourceforge.net
using Lisp ECL 12.12.1
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) domain:complex;
(%o1) complex
(%i2) display2d:false;
(%o2) false
(%i3) B:integrate(sqrt(1-cosh(x)^2/4),x);
(%o3) 'integrate(sqrt(1-cosh(x)^2/4),x)
(%i4) trigsimp(B);
(%o4) 'integrate(sqrt(-(cosh(x)^2-4)/4),x)
(%i5) fullratsimp(B);
(%o5) 'integrate(sqrt(-(cosh(x)^2-4)/4),x)
(%i6) load(abs_integrate);
(%o6) "/Users/.../sage-5.9.rc1/local/share/maxima/5.29.1/share/contrib/integration/abs_integrate.mac"
(%i7) trigsimp(B);
(%o7) cosh(x)
(%i8) fullratsimp(B);
(%o8) cosh(x)
I'm not sure we want to unload abs_integrate but we need to figure something out here.
Upstream: Reported upstream. No feedback yet.
CC: @sagetrac-tmonteil @gagern
Component: calculus
Keywords: abs_integrate
Stopgaps: #12731
Issue created by migration from https://trac.sagemath.org/ticket/14591