On Friday, September 23, 2016 at 1:55:30 AM UTC+8, clicl...@freenet.de wrote:   
   >   
   > ... which doesn't sound promising. But I see that I should have been   
   > specific. So, how does FriCAS 1.3.0 react to:   
   >   
   >   INT(1/(x^3 - 3*x^2 + 7*x - 4)^(1/3), x) = ?   
   >   
   >   INT(1/(x*(3*x^2 - 6*x + 5)^(1/3)), x) = ?   
   >   
   >   INT((1 - x^3)^(1/3)/(2 + x), x) = ?   
   >   
   >   INT((2 + x)/((1 + x + x^2)*(2 + x^3)^(1/3)), x) = ?   
   >   
   > All four are 'detuned' versions of pseudo-elliptics considered earlier.   
      
   FriCAS can prove No. 1,2,4 do not have elementary integral in   
   a few seconds with "setSimplifyDenomsFlag(true)".   
      
   For No. 3, FriCAS gives an error:   
      integrate: implementation incomplete (residue poly has multiple non-linear   
   factors)   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)