Open
Description
See this comment, discussion in #13364, the supposed fix at https://sourceforge.net/p/maxima/bugs/2520/, this ask.sagemath question, and so forth.
E.g. this is annoying (but apparently right)
(%i1) load(abs_integrate);
(%i3) display2d:false;
(%o3) false
(%i4) integrate(abs(sin(x)),x);
(%o4) 4*(abs(sin(x))*(atan(sin(x)/(cos(x)+1))/2
+sin(x)/((cos(x)+1)*(2*sin(x)^2/(cos(x)+1)^2+2)))
/abs(cos(x)+1)
-(signum(1/(cos(x)+1))*signum(sin(x))*log(2*sin(x)^2/(cos(x)+1)^2+2)
-signum(1/(cos(x)+1))*signum(sin(x))*log(sin(x)^2/(cos(x)+1)^2+1)
+signum(1/(cos(x)+1))*signum(sin(x))
*(2*sin(x)*atan(sin(x)/(cos(x)+1))/(cos(x)+1)
-log(2)))
/4)
but it doesn't do the definite integral at all, even the easy ones where abs does nothing on the interval!
Upstream: Reported upstream. Developers acknowledge bug.
CC: @slel
Component: calculus
Keywords: abs_integrate
Stopgaps: #12731
Author: Frédéric Chapoton
Reviewer: Vincent Delecroix
Issue created by migration from https://trac.sagemath.org/ticket/17511