antispam@math.uni.wroc.pl schrieb:   
   >   
   > clicliclic@freenet.de wrote:   
   > >   
   > > I would address the unresolved algebraic quantities in your results by   
   > > moving the boundary up to which explicit radicals are introduced: Not   
   > > only quadratics should be resolved, but also quartics resolvable into   
   > > nested square roots, as detected from a cubic resolvent that factors   
   > > rationally. They are distinguished by their Galois group as well.   
   >   
   > That is a possibility.  But I am coming to conclusion that for   
   > most purposes 'rootSum' is better.   
      
   I would certainly also prefer a symmetric rootsum() expression over   
   your current asymmetric use of %%-objects. However, not only for the   
   roots of a the present special kind of quartic, either construct   
   destroys the closed-form character of an antiderivative and should   
   thereby lower its quality grade like any other non-elementary function   
   that is in fact elementary. Compare the grading in Albert's post "Who is   
   fastest AND optimal?" of Wed, 27 Apr 2016 15:45:46 -0700 (PDT).   
      
   >   
   > > As so often in FriCAS antiderivatives, the ATAN terms are complicated by   
   > > splitting (compare Albert's single "optimal" term) as well as halving,   
   > > the latter also introducing artificial radicals. Thus, your ATAN   
   > > quadruplet (as rewritten by Derive):   
   >    
   > > on doubling per ATAN(w) = ATAN(2*w/(1-w^2))/2 shrinks to:   
   >   
   > Replacing ATAN(w) by ATAN(2*w/(1-w^2))/2 seems undesirable   
   > in general because in many cases '2*w/(1-w^2)' is bigger   
   > than 'w' and because it complicates branching behaviour.   
   > Going in opposite direction is desirable if it can be done   
   > for free, but in this case leads to extra complicated   
   > roots...   
   >   
   > > where the first and third terms have become identical and where no   
   > > radical but SQRT(SIN(x)^5/COS(x)) remains, guaranteeing unconditional   
   > > validity. Continuity of the antiderivative on the real axis, however,   
   > > has suffered in the process.   
   > >   
      
   In fact, irrespective of any doubling or halving, your quadruplet can   
   be replaced by a single ATAN term since its derivative agrees with four   
   times the derivative of its first or third term alone. That's a lot of   
   needless repetition, a lot of heavy baggage being lugged along.   
      
   Martin.   
      
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