Martin and Nasser, FYI:   
      
   For the problem   
       integrate((a + b*x)/((3 + x^2)*(1 - x^2)^(1/3)), x)   
   and   integrate((a + b*x)/((3 - x^2)*(1 + x^2)^(1/3)), x),   
      
   both fricas and mma can do the later part in elementary functions:   
   namely   
       integrate((b*x)/((3 + x^2)*(1 - x^2)^(1/3)), x)   
      
   For the first part, mma gives result contains AppellF1, fricas can do   
       integrate(1/((3 + x^2)*(1 - x^2)^(1/3)), x)   
   but gives a very long but elementary result.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)