> Other combinations, seem too hard. For example   
   >   
   >        x^2 / (x Cos[x] + Cos[x])^2   
   >        x^2 / (x Sin[x] - Cos[x])^2   
   >        x^2 / (x Cos[x] + Sin[x])^2   etc...   
   > (Can your CAS do any of the above three?)   
      
   Those integrals can be proven to have no elementary   
   anti derivative by FriCAS.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)