Axel Vogt schrieb: > > 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. > > > > 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
Oh dear, yes, this is a hypergeometric three-eff-two.