On Saturday, July 6, 2013 10:28:30 AM UTC-10, clicl...@freenet.de wrote:
> Since Rubi manages to return the proper T1-based result already, it > shouldn't be hard to make it handle Charlwood's problem 41. It merely > needs to be taught to normalize integrands like COT(x)*COS(x)/ > SQRT(1 + SIN(x)) to their sine-only form. This would be just one > normalization among others performed regularly, and would only require > some twisting or minor extension of existing code, I guess.
Rather than blindly normalizing such integrands to their sine-only form and hoping for the best, it is safer to drive the degree of the cosine factor toward zero using the following hot new rule: If a^2-b^2=0 and m>0 is even, then
which is valid if a^2-b^2=0. The new rule will make it possible for the next version of Rubi to integrate a whole new class of expressions including the integrand in question, as well as the much more difficult one