#3078 bad result of integrate(1/cos(x),x) and integrate(1/sin(x),x)

[lanride]

integrate(1/cos(x),x) gives log(sin(x)+1)/2-log(sin(x)-1)/2 and
integrate(1/sin(x),x) gives log(cos(x)-1)/2-log(cos(x)+1)/2
in both cases sin(x)-1<0 and cos(x)-1<0 and undefined for log().
Correct values should be 1-sin(x) and 1-cos(x).

[Jaime E. Villate]

You're restricting yourself to the real domain, while Maxima is working in the complex domain. The configuration variable logabs allows you to get the results you expected:

(%i7) logabs:true$

(%i8) integrate(1/cos(x),x);
            log(abs(sin(x) + 1))   log(abs(sin(x) - 1))
(%o8)       -------------------- - --------------------
                     2                      2