```Date: Aug 6, 2013 7:51 PM
Author: clicliclic@freenet.de
Subject: Rubi 4.1 and the Timofeev test suite

clicliclic@freenet.de schrieb:> > The following table summarizes the data made available for the example> integrals in Timofeev's 1948 book. To simplify the accounting, the> numbers of examples represent the actual numbers of distinct> integrands; for chapters where this has not yet been determined, the> total of Timofeev's numbered examples is given instead:> >  ch. ex's  Der.   Fri.   Mpl    MMA    Rubi   etc. etc.>            6.10   1.21    17     9     4.1> ------------------------------------------------------->   1   86    83     86     85     86     84>   2   90     -      -      -      -      ->   3   12    12     12     12     12     12>   4  132     -      -      -      -      ->   5  120     -      -      -      -      ->   6   26     -      -      -      -      ->   7   11     9     11     11     11      8>   8  109     -      -      -      -      ->   9   59     -      -      -      -      -> ------------------------------------------------------->      100%  95.4%  100%   99.1%  100%   95.4%> > The Winners so far are FriCAS 1.21 and Mathematica 9!> > It should be noted that some FriCAS results do not hold for all values> of the integration variable (and/or parameters in the integrand).> > I will let matters rest at this point until new chapters or revised> data become available.> I thought it would be instructive to list those integrals Rubi 4.1 failson: Timofeev's example 29 from Chapter 1:INT(TAN(x)*TAN(x - a), x) = 1/TAN(a)*LN(1 + TAN(a)*TAN(x)) - xTimofeev's example 64 from Chapter 1:INT(ASIN(x/a)^(3/2)/SQRT(a^2 - x^2), x) = 2/5*ASIN(x/a)^(3/2)*ATAN(x/SQRT(a^2 - x^2)) = 2/5*(a/SQRT(a^2 - x^2))*SQRT(1 - (x/a)^2)*ASIN(x/a)^(5/2)Timofeev's example 6 from Chapter 7:INT(x*SIN(x)^3/COS(x)^4, x) = x*(1/(3*COS(x)^3) - 1/COS(x)) - SIN(x)/(6*COS(x)^2) + 5/6*ATANH(SIN(x))Timofeev's example 10 from Chapter 7:INT((2*x + SIN(2*x))/(x*SIN(x) + COS(x))^2, x) = - 2*COS(x)/(x*SIN(x) + COS(x))Timofeev's example 11 from Chapter 7:INT((x/(x*COS(x) - SIN(x)))^2, x) = (x*SIN(x) + COS(x))/(x*COS(x) - SIN(x))In my view, the first two failures are deplorable but understandable,while the third one must be counted as a bug. The last two are simply tobe expected. Timofeev's book can be found at:  <http://www.math-life.com/jdownloads/view.download/27/279.html>Martin.
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