From: //noreply@axelvogt.de   
      
   Have not checked the test pages, but   
   > INT((1 + x^2)/((1 - x^2)*SQRT(1 + x^2 + x^4)), x)   
   >   = 1/SQRT(3)*ATANH(SQRT(3)*x/SQRT(1 + x^2 + x^4))   
      
   Maple 2016: in terms of elliptic functions   
      
   > INT((x^(3*a) + x^(2*a) + x^a)*(2*x^(2*a) + 3*x^a + 6)^(1/a), x)   
   >   = 1/(6*(a + 1))*x^(a + 1)*(2*x^(2*a) + 3*x^a + 6)^(1/a + 1)   
      
   Maple 2016: in terms of elementary functions   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)