#3528 abs_integrate causes integral of sqrt(1+2*sin(x)^2) to give spurious results

[Robert Dodier]

Without abs_integrate, integrate returns a noun expression for sqrt(1+2*sin(x)^2):

(%i2) integrate (sqrt(1+2*sin(x)^2), x);
                           /
                           [           2
(%o2)                      I sqrt(2 sin (x) + 1) dx
                           ]
                           /
(%i3) integrate (sqrt(1+2*sin(x)^2), x, 0, %pi);
                           %pi
                          /
                          [              2
(%o3)                     I    sqrt(2 sin (x) + 1) dx
                          ]
                          /
                           0

After loading abs_integrate, I get spurious results:

(%i4) load (abs_integrate);
(%o4) /usr/local/share/maxima/branch_5_42_base_151_gaadbaa6/share/contrib/inte\
gration/abs_integrate.mac
(%i5) integrate (sqrt(1+2*sin(x)^2), x);
               (2 sin(3 x) + 6 sin(x)) false - sin(3 x) + 3 sin(x)
(%o5)        - ---------------------------------------------------
                                        5/2
                                     3 2
(%i6) integrate (sqrt(1+2*sin(x)^2), x, 0, %pi);
(%o6)                                  0

It seems possible that the definite integral is computed from the incorrect antiderivative, so that's something to verify:

(%i7) ev(%o5, x=%pi) - ev(%o5, x=0);
(%o7)                                  0

Originally reported on mailing list 2019-02-19: "integrals and sage"

Version info:

Maxima version: "branch_5_42_base_151_gaadbaa6"
Maxima build date: "2018-11-20 22:45:52"
Host type: "i686-pc-linux-gnu"
Lisp implementation type: "CLISP"
Lisp implementation version: "2.49 (2010-07-07) (built 3605610186) (memory 3751771554)"

[Dima Pasechnik]

a similar wrong result with abs_integrate loaded, with ECL-compiled Maxima, doing integrate(sqrt(1+cos(x)^2),x);

[Barton Willis]

Fixed by Commit [3ca423] . Closing ticket.