Date: Nov 15, 2013 6:11 PM
Author: Albert D. Rich
Subject: Re: The A. F. Timofeev symbolic integration test suite

On Friday, November 15, 2013 3:43:59 AM UTC-10, wrote:

>> Ok, for integrands of the form (c+d x)^n/(a+b x) when n is symbolic,
>> the next version of Rubi will return
>> (c+d*x)^n/(b*n*(b*(c+d*x)/(d*(a+b*x)))^n)*
>> 2F1(-n,-n,1-n,-(b*c-a*d)/(d*(a+b*x)))
> > The simpler equivalent rule derived using Euler's transformation is
>> not used since it is harder to simplify its derivative back to the
>> original integrand.

> But this is just an arbitrary property of the differentiator, right?
> Another differentiator may give the result you would now obtain by
> applying Euler's transformation first (and undoing it on non-elementary
> hypergeometrics that remain in the derivative).
> So your reason is no good reason; you are just bending to the dictate of
> WRI. I suggest that Rubi redefines 2F1 differentiation instead. The
> optimality of Rubi's antiderivatives determines the rules to which WRI
> must bend!
> I have spoken.
> Martin.

Ok, the Messiah has spoken. I modified the optimal antiderivatives for Timofeev Chapter 8 examples 6a.n, 6b.n and 14 in the test-suite to reflect use of Euler's transformation and posted the revised pdf file at

However, full credit is still given to those integrators that return valid, but suboptimal, antiderivatives for these problems.

Note that the revised pdf file also includes Chapter 8 test-suite results for various integrators, including the forthcoming version 4.3 of Rubi...