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



On Sunday 27 April 2003 00:19, Raymond Toy wrote:
> > A correct result would be something like
> >     (if (remainder(u-%pi,2*%pi) = 0) then 0 else d214)
> >     + 2*%pi*entier((u-%pi) / (2*%pi))
>
> Perhaps so, but that goes against decades (centuries?) of mathematical
> literature where such things are assumed away.  :-) I don't think you'll
> find any table of integrals that goes to this extreme.  You're just
> supposed to know. :-)
>
> Should we also add that unknown constant of integration?

Actually some books state that the indefinite integral of f(x) is the set of 
all functions F(x) with F'(x)=f(x). Ok, it might not be desirable to 
implement such a definition in a CAS but then it should be made clear what 
indefinite integration means in a particular CAS. In Maxima it seems to be 
defined as follows:

    integrate(f(x),x) returns *an* antiderivative of f that is defined
    everywhere except at single points.

Adding this to the documentation would clarify things and surely avoid 
trouble for newbies.

Felix