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.