On 5 December 2014 at 20:48, 'Martin R' via sage-devel < sage-devel@googlegroups.com> wrote: > > A famous example is > > integrate(x/sqrt(x^4+10*x^2+-96*x-71),x) > > which Mathematica won't do, although it is elementary, i.e., has a > solution in terms of elementary functions: > > > log((x^6+15*x^4+-80*x^3+27*x^2+-528*x+781)*(x^4+10*x^2+-96*x+-71)^(1/2)+(x^8 > +20*x^6+-128*x^5+54*x^4+-1408*x^3+3124*x^2+10001))/8 >
That is pretty interesting, I would've treated this as an elliptic integral without thinking about it twice. I have two questions: - I imagine if you calculate it as an elliptic integral (say, using the Weierstrassian functions) you would end up with elliptic invariants g1 and g2 with special values that make the elliptic integral collapse to an elementary function? - The factorization of the polynomial in the integrand yields a suspiciously symmetrical form in the factors, is that the reason why the integral can be evaluated with elementary functions? Sorry for the OT! Francesco. -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at http://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
