clicliclic@freenet.de wrote:   
   >   
   > oldk1331@gmail.com schrieb:   
   > >   
   > > > > I think there is no symbolic result for   
   > > > > "integrate((1 + x)/((1 + x + x^2)*(a + b*x^3)^(1/3)), x)".   
   > > > > When a,b are integers, FriCAS can give symbolic results.   
   >   
   > > > Wow - we could all become world-famous if this proves to be the   
   > > > first parametrized algebraic integrand with this property!   
   > >   
   > > Can you be more clear with that?  Just to clarify, I test a,b with   
   > > some prime numbers, and FriCAS always gives result.   
   > >   
   >   
   > You appeared to be contemplating the violation of a principle supported   
   > by extensive observation:   
   >   
   > Let f(p,x) be an algebraic function in both arguments; if, with respect   
   > to x, f(p,x) possesses an elementary antiderivative for an infinite   
   > number of complex parameter values p, then it possesses a single   
   > symbolic elementary antiderivative F(p,x) that holds for all complex   
   > values of p.   
   >   
   > Proof (or disproof) of the principle is left to our top experts in   
   > symbolic integration theory.   
   >   
      
   Look at   
      
   http://koutschan.de/conf/ICMS16/davenport.pdf   
      
   starting from page 25.  It seems that we need to limit   
   how parameter is choosen, otherwise there is a   
   couterexample.  The claim appeared as a theorem, but   
   recently couterexample was discovered, so there   
   remain some work to find correct statement.  IIUC   
   the case when you substitute integers is considerd   
   to be proved.   
      
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