
Re: Charlwood Fifty test results
Posted:
Jul 5, 2013 7:46 PM


On Friday, July 5, 2013 11:15:41 AM UTC10, clicl...@freenet.de wrote:
> Nice. Only for Charlwood's problem 44 does Rubi 4.1 (complex domain) > fall behind Derive 6.10 (real domain). I am not surprised that problems > 3 and 45 are not handled by Rubi. But why is problem 41 untractable? > > Martin.
Thanks for your compliment of the Charlwood Fifty test results I posted. Problem #41 is
integrate(log(sin(x)) sqrt(1+sin(x)), x)
Rubi starts correctly (I think) using integration by parts that gives the log free integral
integrate(cos(x) cot(x)/sqrt(1+sin(x)), x)
Unfortunately Rubi and the other systems tested cannot determine that its antiderivative is
2 cos(x)/sqrt(1+sin(x)) ? 2 arctanh(cos(x)/sqrt(1+sin(x)))
Obviously since its antiderivative is a function of cos(x)/sqrt(1+sin(x)), the log free integral above can be integrated by making the substitution u=cos(x)/sqrt(1+sin(x)) yielding the trivial integral
integrate(22/(1u^2), x)
Any ideas how a rulebased system like Rubi should ?know? to make that substitution?
Albert

