>>>>> "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