Date: Sep 26, 2013 5:13 PM
Author: Albert D. Rich
Subject: Re: Rubi 4.1 and the Timofeev test suite

On Thursday, September 26, 2013 7:17:06 AM UTC-10, clicl...@freenet.de wrote:

> Albert Rich schrieb:
> > Your perfectionist credentials remain impeccable! Chapter 9 of the
> > Timofeev test suite, revised as you suggested, is now available at

>
> > http://www.apmaths.uwo.ca/~arich/TimofeevChapter9TestResults.pdf
>
> Wasn't as perfect as you thought! Here's the next iteration on example
> #49 from Timofeev's Chapter 9:
>
> INT(ASIN(SQRT((x - a)/(x + a))), x)
> = - 2*a*(SQRT((x - a)/(x + a))/SQRT(2*a/(x + a)))
> + (x + a)*ASIN(SQRT((x - a)/(x + a)))
>
> I notice that Timofeev (p. 422) gives an evaluation incompatible with
> the above: it doesn't differentiate back to something as simple as his
> integrand, so one may conclude he made the mistake rather than the
> typesetter.


I just posted revised Timofeev Chapter 9 test suite problems and results incorporating the above change at

http://www.apmaths.uwo.ca/~arich/TimofeevChapter9TestResults.pdf

which of course required reducing the grades for problem #49 from 2 to 1 for all the systems tested.

Perhaps Timofeev assumes a different definition for the derivative of the arcsine and arccosine functions which results in what we consider to be invalid antiderivatives...

Albert