Your tests of the SymPy integrator reveal a glaring weakness in the algebraic arena (most of Charlwood; Timofeev 124, 154-159, 165), and a lesser one in the rational trigonometric arena (Charlwood 37; Timofeev 108, 114-117, 131, 162). So SymPy's Risch implementation doesn't really cover trigonometric functions yet. Also Sympy's trigonometric simplification fails to confirm many valid antiderivatives.
> > > PS: How about contributing a chapter of the Timofeev suite yourself? > > Hm, my Russian is a little bit rosty, Genosse Martin!
No knowledge of Russian is needed to copy mathematical expressions from a 20th century Russian book, and your appeal to comradeship doesn't make this fact disappear. Some knack for mathematical puzzle solving is needed, however, to undo any misprints in Timofeev's integrands with the help of his evaluations. The "examples" for Chapter 5 start near the bottom of page 202, for integral #4 you turn pages until you reach the next example section on page 208. Subsequent sections start on pages 211, 213, 219, 223, and so on.