integrate(sqrt(1-cos(x)^2), x) gives cos(x)



Hello,

can anyone explain this obviously wrong behavior?

(%i1) integrate(sqrt(1-cos(x)^2),x);
(%o1)                               cos(x)
(%i2) trigsimp(sqrt(1-cos(x)^2));
(%o2)                             abs(sin(x))
(%i3) integrate(abs(sin(x)),x);
                                /
                                [
(%o3)                          I abs(sin(x)) dx
                                ]
                                /

Seems like "integrate" does some additional simplification of the input function which leads to a wrong result.

Even if it somehow simplified it to sin(x) instead of abs(sin(x)), the result would still have the wrong sign, because it should be -cos(x) then, and not cos(x).

Kind regards,
David Scherfgen