Albert Rich schrieb: > > On Wednesday, November 13, 2013 1:56:55 AM UTC-10, clicl...@freenet.de wrote: > > > I also notice now that the evaluations proposed for Examples 36a,b,c,d > > involve TAN(x/2) and friends, whereas your evaluations for Examples 38, > > 40, 41, 43 involve SIN(x)/(1+COS(x)) and friends instead. I propose to > > normalize in accordance with your policy for the entire Timofeev suite. > > (In fact, I like the latter choice more; in Example 36 I simply followed > > Timofeev, p. 355.) > > The antiderivatives for examples 36i in the current Timofeev Chapter 8 > pdf file at > > http://www.apmaths.uwo.ca/~arich/TimofeevChapter8TestResults.pdf > > are free of tan(x/2) and friends. Do you approve, and if so are there > antiderivatives for examples 38, 40, 41, and 43 free of > sin(x)/(1+cos(x)) and friends? >
The simplified antiderivatives for Examples 36a to 36d look nice and seem to be correct (I have checked only one). My answer to your question is: I don't think so. The same transformation could be used to get rid of the 2*#i*#e^x terms in Examples 38, 40, 41, 43, but TAN(x/2) = SIN(x)/(1+COS(x)) and friends would not vanish here (their sign would be inverted), and the gain in simplicity would be marginal.
The perfomance table has increased your pdf file-size from 350 to 1600 kByte, that's plain crazy. I am a bit curious what Mathematica and Maple return for integral 69 from Timofeev's Chapter 8.