Comment #2 on issue 2010 by mattpap: Integration with the full Risch Algorithm
http://code.google.com/p/sympy/issues/detail?id=2010
This is strong preliminary work, but a lot of work is still needed to make this usable and to cover cases that are currently not implemented. Here we can see the trade-off: heuristic Risch algorithm is simple to implement and can handle lots of special cases, but can't prove anything; on contrary Risch algorithm can prove that a function has (or not) an elementary integral, but is very complex and hard to implement.
Finally, I'm thinking there needs to be a way to differentiate between an unevaluated Integral (...). Any ideas?
I think that adding NonElementaryIntegral class would be sufficient. It would inherit from Integral class, but have noop _eval_integral(). There would be also additional classes for special cases, e.g. logarithmic or sine integrals (special pretty printing etc.).
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