Bob Baker wrote:
> dlakelan at street-artists.org <mailto:dlakelan at street-artists.org> wrote:
>
> > Also, by performing the transformations mentioned by others I found
> that
> > the integrand is the same as:
> >
> > (cos(5 x) + sqrt(cos(2 x) - 8 cos(x) + 7)
> > (sqrt(2) cos(4 x) - 4 sqrt(2) cos(3 x) + sqrt(2) cos(2 x) + 2 sqrt(2))
> > - 8 cos(4 x) + 14 cos(3 x) - 8 cos(2 x) + cos(x))
> > /(2 cos(2 x) - 16 cos(x) + 14)
> >
> > the procedure:
> > ratsimp(trigreduce(subst(lambda([s], ''(exponentialize(sinh('s)))),
> > sinh, integrand(1,3))));
> >
> > however, maxima still can't integrate this.
>
> You're right, since f(x) was a log() and shows up inside some exp() in
> the integrand, quite a bit of simplification is possible. I suppose
> the authors of the paper said to themselves, "Our form is more compact
> and matches our derivation, so why simplify it--let Mathematica do
> that." It appears to have worked, although I don't have an
> independent check on most of the results they gave.
>
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For what it's worth, I tried your function in Mathematica 3.0 and it
cranked for a long time and then gave up with an "out of memory" message.
-sen