Hi Nasser:   
      
   The first one indeed fails,  maybe because of variables 'a', 'b'.   
      
   The last two can be computed: in FriCAS, especially when   
   dealing with algebraic function integration,   
      
       setSimplifyDenomsFlag(true)   
      
   speeds up things a lot.   
      
   So integrate((1 - x^3)^(1/3)/(1 + x),x) finishes in 1.5s and   
   integrate((1 - x^3)^(1/3)/(1 - x + x^2),x) finishes in 5.5s.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)