Albert Rich schrieb: > > Chapter 9 of Timofeev's book discusses the integration of expressions > involving inverse trig functions. I transcribed the problems in the > chapter and tested various systems on them. The test results, > problems and answers are available as a pdf file at > > http://www.apmaths.uwo.ca/~arich/TimofeevChapter9TestResults.pdf > > Note the dramatic improvement of the recently released version 4.2 of > Rubi over previous versions. > > The 61 problems from Chapter 9 are also available in machine readable > form at > > http://www.apmaths.uwo.ca/~arich/ > > expressed in Axiom, Maple, Mathematica and Maxima syntax. The > antiderivatives in these test file are only a first approximation at > being optimal. Please let me know if you find and would like to > contribute significantly better ones. >
This should help CAS programmers help improve their integrators :). Strange that Derive 6.10 can handle example #53 while Rubi 4.2 cannot :(. And Rubi 4.0 even returned incorrect results for examples #30 and #35.
I suggest to replace ArcSin[1/x] by ArcCsc[x] throughout the file, and ArcCos[1/x] by ArcSec[x]. Sqrt[-1+x^2]/Sqrt[1-1/x^2] appears repeatedly and can be simplified to Sqrt[x^2].
I will insert the Chapter 9 data into our performance table once the FriCAS results are also known.
And now everybody is waiting for Peter Luschny to finish Chapter 7 (120 trigonometric integrands). But who is going to transcribe the examples from Chapter 8 (109 exponential and hyperbolic integrands)?