"Never forget to check that the output is a continuous function!"   
      
   Thus James H. Davenport reminded us in a conference presentation on the   
   "Complexity of Integration, Special Values, and Recent Developments" at   
   last year's International Congress on Mathematical Software.   
      
   Now, in a posthumous publication in the Institutiones Calculi Integralis   
   Tomus 4, pages 36 - 48, Leonhard Euler showed that:   
      
     SQRT(a + b*x^2 + c*x^4)/(a - c*x^4)   
      
   has an elementary antiderivative. In fact, the integrand is Goursat   
   pseudo-elliptic.   
      
   Does your favorite symbolic integrator then succeed in returning a (i)   
   real, (ii) elementary, and (iii) continuous result for:   
      
     INT(SQRT(1 - x^4)/(1 + x^4), x)   
      
   ? Yes, a simple such a solution does exist.   
      
   Martin.   
      
   PS: Derive 6.10 just returns the integral with its denominator factored   
   into real quadratics.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)