Albert Rich schrieb: > > The 84 integration problems in the Timofeev Chapter 1 test suite and > their optimal antiderivatives is now available as a pdf file at > > http://www.apmaths.uwo.ca/~arich/TimofeevChapter1TestResults.pdf > > Also shown in the file are the test scores on each problem earned by > various integrators. The bottom line totals were as follows: > > Rubi 4.2 Mathematica 9 Derive 6.1 Maple 17 Maxima 5.28 > Totals: 168 161 158 161 158 > Percent: 100% 95.8% 94.0% 95.8% 94.0% >
You have replaced "+-" by "+" in examples #14 and #15 on p. 26. In your place I would prefer if Timofeev's choice of integrands (inasmuch as they can be inferred from the printed book at all) were not modified in any way, lest you open yourself to accusations of having introduced a selection bias which compromises the strict neutrality of the test suite - Timofeev couldn't have known about the systems tested, but you do. Hence I suggest to duplicate these integrands to "+" and "-" versions and to split the example numbers into 14a/b and 15a/b. In fact, integral tables and symbolic integrators often distinguish between expressions like b^2*SIN(x)^2 + a^2 and b^2*SIN(x)^2 - a^2, although the evaluations in these two cases are not much affected (which fact is worth noting too).
This being a matter of principle, the choice of model antiderivatives is often just a matter of taste. In examples #16 and #56 you list the simpler but discontinuous ATAN evaluations. Are you retracting your statement of June 18 that "continuity of antiderivatives trumps compactness"?
In the evaluation of example #59, -4 + 4*SIN(x)^2 may be simplified to -4*COS(x)^2, and the evaluation of example #70 can (accidentally?) be written more compactly as 1/48*SIN(2*x)^3 - 1/64*SIN(4*x) + x/16.
Finally a more detailed explanation why ATANH(1-2*x^2) in your evaluation of example #42 from Chapter 9 is bad: The vast majority of people being presented with an integrand like x^2*ASEC(x)/(x^2-1)^(5/2) do attach meaning to it for real x with |x| > 1 only. Similarly, they attach meaning to ATANH(1-2*x^2) for real 1-2*x^2 with |1-2*x^2| < 1 only. Your antiderivative is consequently meaningless to them - and this group is likely to include almost all of Professor Charlwood's students.