On 21.01.2013 19:55, firstname.lastname@example.org wrote: > > Wanting to refresh my knowledge of the capabilties of the Reduce algebra > system, I have recently browsed the website. The system comes with the > 'algint' package by J. Davenport which boosts the integrator > capabilities for algebraic functions. The package documentation > > <http://www.reduce-algebra.com/docs/algint.pdf> > > introduces the example integrand sqrt(sqrt(a^2 + x^2) + x)/x. A correct > antiderivative for this is > > 2*(sqrt(sqrt(a^2 + x^2) + x) > - sqrt(a)*atanh(sqrt(sqrt(a^2 + x^2) + x)/sqrt(a)) > - sqrt(a)*atan(sqrt(sqrt(a^2 + x^2) + x)/sqrt(a))) > > The antiderivative printed in the documentation, however, is either very > wrong or garbled beyond recognition. > > Martin.
Maple 16 returns 2*sqrt(2*x)*hypergeom([-1/4, -1/4, 1/4],[1/2, 3/4],-a^2/x^2) May be right, but not that 'usefull' w.r.t. your result