The algorithm is an implementation of Manual Bronstein's poor man's integrator (which is, as Kalevi notes, the parallel Risch algorithm). See http://www-sop.inria.fr/cafe/Manuel.Bronstein/pmint/. If someone has a copy of Maple, I'd be interested to see if the original pmint can do this integral. If you want to learn more about the algorithm, I believe it is very similar to the one described in the last chapter of his book.
The parallel Risch algorithm can compute algebraic integrals, but it's somewhat luck based, as the ability to do so depends on how the algebraic expressions happen to be represented in the system (algebraic functions don't have unique representations, e.g., sqrt(x) = x/sqrt(x)). I wouldn't be surprised if SymPy changed the way it autosimplified x/sqrt(x) if it broke many integrals and made some other integrals start working. Hence the inability to compute an answer is far from a proof of nonelementaryness, but answers sometimes can be found and verified to be correct. And by the way, the example itself comes from Bronstein's paper, "Symbolic Integration Tutorial" (or at least I assume it does, unless Bronstein and Wikipedia both took it from some third source). Aaron Meurer On Thu, Feb 19, 2015 at 12:57 PM, Kalevi Suominen <[email protected]> wrote: > > > Sympy currently uses the parallel Risch algorithm for this function. > The full Risch algorithm for functions with nonrational algebraic terms is > not implemented. > > -- > You received this message because you are subscribed to the Google Groups > "sympy" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To post to this group, send email to [email protected]. > Visit this group at http://groups.google.com/group/sympy. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sympy/8182f914-e2c1-4f6b-845c-60823a077d0c%40googlegroups.com. > > For more options, visit https://groups.google.com/d/optout. -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sympy. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/CAKgW%3D6JeKHZ9Hmyzk%3D-oUUW6nJ6uQWDcnc_DxHfLQxWKOfXZ%3Dw%40mail.gmail.com. For more options, visit https://groups.google.com/d/optout.
