Integral of 1/(sqrt(2)+sin(x))



>>>>> "Felix" == Felix E Klee <felix.klee@inka.de> writes:

    Felix> Hi,
    Felix> take a look at this:
    Felix>     (C133) integrand:1/(sqrt(2)+sin(x));
    Felix>     (D133) 1/(SIN(x)+SQRT(2))
    Felix>     (C134) integrate(integrand,x,0,2*%pi);
    Felix>     (D134) 2*%PI
    Felix>     (C135) defint(integrand,x,0,2*%pi);
    Felix>     (D135) 2*%PI
    Felix>     (C136) ldefint(integrand,x,0,2*%pi);
    Felix>     (D136) 0

    Felix> 2. Maxima returns a non continuous indefinite integral:
    Felix>        (C214) ratsimp(integrate(integrand,x));
    Felix>        (D214) 2*ATAN((SQRT(2)*SIN(x)+COS(x)+1)/(COS(x)+1))
    Felix>    Shouldn't integrate always return a continuous function when the
    Felix>    integrand is continuous?

In these kinds of integrals, don't you always have to be careful about
what branch of atan should be used?

This is probably why ldefint returns 0 since d214 is %pi/2 for both x
= 0 and x = 2*%pi.



Ray