From: fateman@cs.berkeley.edu   
      
   I suspect that part of the problem in getting   
   back via differentiation may be that antiderivatives   
   computed using any of the purely algebraic methods   
   are not cognizant of branch cuts or discontinuities   
   at all. I think this analysis-related stuff is deserving of   
   serious consideration, but demanding that some Risch-based   
   procedure produce an optimal (e.g. continuous if possible)   
   antiderivative may not be a "debug this"   but "can we make   
   another pass over the answer".   
      
   It's not that the Risch algorithm(?) is too hard, but that   
   it is not computing what you want...   
      
   Returning to the integrand via differentiation putting you   
   on the wrong side of a branch cut?  Whose fault is that if   
   differential algebra doesn't even have that concept?   
   RJF   
      
      
      
   On 10/1/2015 7:59 AM, Waldek Hebisch wrote:   
   > clicliclic@freenet.de wrote:   
   >>   
   >> Waldek Hebisch schrieb:   
   >>>   
   >>> clicliclic@freenet.de wrote:   
   >>>>   
   >>>> I have stumbled across a familar bug in the integrator of the FriCAS   
   >>>> version running at   
   >>>> :   
   >>>   
   >>> This was version 1.2.6.  However, in this case 1.2.7 behaves the   
   >>> same.   
   >>>   
   >>>> the antiderivative of ACOS(x^2 - SQRT(1 - x^2)), though computed   
   >>>> instantly, does not differentiate back. [...]   
   >>>   
   .....   
      
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