Albert Rich schrieb: > > Chapter 8 of Timofeev's book discusses the integration of expressions > involving exponentials, logarithms and hyperbolic functions. I > transcribed the 109 example problems in the chapter. The integrands > and candidate optimal antiderivatives are available as a pdf file at > > http://www.apmaths.uwo.ca/~arich/TimofeevChapter8TestResults.pdf > > The problems from Chapter 8 and the other chapters of Timofeev's book > are also available in machine readable form at > > http://www.apmaths.uwo.ca/~arich/ > > expressed in Axiom, Maple, Mathematica and Maxima syntax. If you > find and would like to contribute significantly better > antiderivatives than the ones shown in the pdf file, please post them > on sci.math.symbolic. >
I propose to add evaluations for generic exponents n to Examples 3, 5a, 5b, 6a, 6b (p. 346), as was done for Example 97 (p. 377); such as:
The duplication +-r can be omitted since r is allowed to be negative. Example 14 involves eighth (4 occurences) or sth (1 occurence) roots; in view of Example 12, I suggest to use s (it looks like the typesetter needed better eyeglasses). Again the duplication +-r can be omitted.
The hypergeometric evaluation of Example 33 (p. 355) can be simplified to:
I suggest to replace #i by -#i in the evaluation of Example 43 for conformity with Examples 38, 40, and 41.
Integrand 61 (p. 365) was meant to read 1/(a +- b*COSH(x)), but the duplication is pointless once b is allowed to be negative. Isn't it better here to write SQRT(a^2 - b^2) for SQRT(a - b)*SQRT(a + b) inside and outside ATANH since a^2 - b^2 is positive when both a - b and a + b are not? The duplication of Example 63 is pointless for your result, but not for Timofeev's evaluation - provided he got it right, which I didn't check.
Timofeev's evaluation of Example 93b (p. 377) is funny.
The integrand 96a must have been meant to involve SQRT(a^2 +- LN(x)^2); the cases SQRT(LN(x)^2 - a^2) of Example 95a and SQRT(a^2 + LN(x)^2) of Example 96a are omitted in your suite. I propose to split these integrands into a1 and a2 (or similar).
I noticed these points by scanning your file visually and checking against the book only where I had doubts; no systematic comparison was made - but should eventually be made.