I am trying to pinpoint the following bug:

sage: integral(sqrt(1+cos(x)^2),x) 
-1/24*sin(3*x) + 1/8*sin(x)


which is incorrect. One would think that maxima is returning a wrong 
answer, but if we ask directly to maxima, it leaves the integral as it is:

sage: f = sqrt(1+cos(x)^2)
sage: maxima.integrate(f._maxima_(),x)
'integrate(sqrt(cos(_SAGE_VAR_x)^2+1),_SAGE_VAR_x)

which is the same result we get with sympy and fricas, and even by maxima 
itself:

Maxima 5.41.0 http://maxima.sourceforge.net
using Lisp ECL 16.1.2
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(sqrt(1+cos(x)^2),x);
                            /
                            [         2
(%o1)                       I sqrt(cos (x) + 1) dx
                            ]
                            /

 So something strange is going on when we call maxima internally to compute 
that integral. I have tried to trace it, but I got lost in the 
intrincancies of the maxima interface.

Does somebody know what exactly is causing this discrepancy? 

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