Chapter 5 of Timofeev's book discusses the integration of expressions involving trig functions. I transcribed the 121 problems in the chapter and attempted to find optimal antiderivatives for them. They are available as a pdf file at
expressed in Axiom, Maple, Mathematica and Maxima syntax.
Timofeev book contains numerous typographical errors, and he does not seem to distinguish between (z^m)^(1/n) and z^(m/n). Also some of the problems require huge, non-elementary antiderivatives which were surely not his intent. If based on Timofeev proposed antiderivative you can determine his true intentions or you know of a more optimal antiderivative, please let me know so I can revise the test suite.