"Nasser M. Abbasi" schrieb:   
   >   
   > [...]   
   >   
   > One such example in the Hearn test file. #281   
   >   
   > Int[Sqrt[9 - 4*Sqrt[2]]*x - Sqrt[2]*Sqrt[1 + 4*x + 2*x^2 + x^4],x]   
   >   
   > Your input file says there is no known anti-derivative. So Rubi   
   > does not solve it, and it got an A using the rule above.   
   >   
   > But Maple and Mathematica solved this (result too large to post).   
   >   
      
   This integral is the only such case from the 12 named suites.   
      
   Being obviously elliptic, the integral is expressible in terms of the   
   canonical elliptic integrals. But the necessary factorization of the   
   radicand into real quadratics is really awkward:   
      
   x^4 + 2*x^2 + 4*x + 1 = (x + 1)*(x^3 - x^2 + 3*x + 1) = 1/27*(x + 1)   
     *(3*x - (6*SQRT(33) - 26)^(1/3) + (6*SQRT(33) + 26)^(1/3) - 1)   
     *(9*x^2 + 3*((6*SQRT(33) - 26)^(1/3) - (6*SQRT(33) + 26)^(1/3) - 2)*x   
      + 2*(233 - 39*SQRT(33))^(1/3) + 2*(39*SQRT(33) + 233)^(1/3)   
      - (6*SQRT(33) - 26)^(1/3) + (6*SQRT(33) + 26)^(1/3) + 9)   
      
   as it involves cube roots of square roots.   
      
   I therefore suggest to just comment this entry out; in fact, such   
   appears to be the fate already of another integral from Anthony Hearn's   
   suite, for which I originally counted 285 distinct entries.   
      
   To remind one of the situation, the model antiderivative could perhaps   
   be set to a placeholder like "awkward".   
      
   Martin.   
      
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