"Nasser M. Abbasi" schrieb:   
   >   
   > How high a number "n" can your cas integrate this?   
   >   
   >         1/((1 + x^n)*(1 + x^2))   
   >   
   > Fricas 1.3.2 and Rubi 4.14.7 go up to n=18. Then after that, they   
   > return unevaluated.   
   >   
   > Mathematica gives an answer for higher than 18, but the result after   
   > 18 is in terms of Root objects. I tried up to n=100.   
   >   
   > Maple also can go higher than n=18, and it also gives results   
   > in terms of RootOf. Tried up to n=200. So to remove these Roots, one   
   > has to evaluate the answer numerically.  I assume this is why Rubi and   
   > Fricas stop at n=18.   
   >   
   > Any insight why 18 is the limit here? Is it due to some   
   > factorization done, which after n=18 produces polynomials that   
   > can't be solved exactly for higher order?   
   >   
      
   Derive 6.10 evaluates the integrals for n=1 through n=6 quickly. For   
   the n=7 integrand, factors containing ATAN functions are produced,   
   which bog the computation down. I have not tried to find out if Derive   
   would eventually finish, churn on forever, or exhaust its memory in   
   this case.   
      
   Martin.   
      
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