I have converted the 61 examples from Chapter 9 of Timofeev's book to Derive format and made a visual comparison of your evaluations with those in the book. Thus I discovered that two integrands (and their antiderivatives) must be corrected: in example #45 a misprinted (x^2-1)^(3/2) must be replaced by (x^2-1)^(5/2), and in example #46 your ACSC(x)^2 must be replaced by ACSC(x)^4, as is actually printed. Timofeev's evaluations correctly differentiate back to the revised integrands.
For reasons of quality, uniformity, conciseness, and aesthetics, I also propose to: - replace 2*ATANH((1 + 2*x^2)) by LN(1 + 1/x^2) in examples #4, #33, #34 and #35 to get rid of the imaginary offset. - replace 2*ATANH((1 - 2*x^2)) by LN(1 - 1/x^2) in example #42 for the same reason and to get rid of bad branch cuts. - express ACSC as ASEC in example #47 since this is the rule for all other examples. - change SQRT(2 - COSH(x)^2) to SQRT(1 - SINH(x)^2) in example #57 because the second radicand looks more natural. - move the piecewise constant x/SQRT(x^2) into ATANH and simplify to ATANH(1/SQRT(x^2)) in examples #40, #41 (and the old #45). - move the piecewise constant x/SQRT(x^2) into ACOTH and simplify to ATANH(1/SQRT(x^2)) in example #43. - remove a constant term from the evaluation of example #36 as you see fit. - perhaps replace SQRT(x^2)/x by x/SQRT(x^2) in examples #37, #38, #43, #47 and #53, as the latter form is used elsewhere. In the same vain, simplify SQRT(x^2)/x^3 to 1/(x*SQRT(x^2)) in example #38, (simplify SQRT(x^2)/x^2 to 1/SQRT(x^2) in the old example #46), simplify SQRT(x^2)/x^3 to 1/(x*SQRT(x^2)) and SQRT(x^2)/x^5 to 1/(x^3*SQRT(x^2)) in example #47, and simplify SQRT(x^2)/x^2 to 1/SQRT(x^2) and SQRT(x^2)/x^4 to 1/(x^2)^(3/2) in example #48.
The Derive file incorprating these changes is appended. For examples involving dilogarithm functions, Timofeev's original evaluations in terms of simpler integrals are included as well.
Derive 6.10 cannot evaluate examples #6, #46, #47, #48, #49 and #50 if the integration variable is declared real (which is the default setting); additionally it cannot evaluate examples #5, #38, #39, #40, #41, #42, #44, #45, #53, #55, #56, #57 and #59 if the variable is declared complex. These results are in accord with your score table.
Derive's implementation of the dilogarithm function being very rudimentary, it also fails to evaluate any of the corresponding examples. Also note that the double DILOG antiderivatives in the Derive file rely on the Mathematica definition of the ATAN or ATANH functions, which is incompatible with Derive's definitions.
Hurray! If the present transcription rate can be kept up, from some time next year onward, the integrators of this world will thenceforth be judged by their Timofeev Index!