Albert Rich schrieb:   
   >   
   > [...] Using the nonobvious piecewise-constant extraction sqrt(x^2)/x,   
   > followed by the substitution u=(x^2-1)^(1/4), Rubi 4.14 will return   
   >   
   >     Sqrt[x^2/(1+Sqrt[x^2-1])^2] * (1+Sqrt[x^2-1])/x *   
   >       EllipticF[2*ArcTan[(x^2-1)^(1/4)],1/2]   
   >   
   > which is real and continuous on the real line when the integrand is   
   > real.   
   >   
      
   I believe that:   
      
     SQRT(x^2/(1 + SQRT(x^2 - 1))^2)*(1 + SQRT(x^2 - 1))/x = x/SQRT(x^2)   
      
   FriCAS will probably squeal, but can Mathematica or Maple validate or   
   invalidate this simplification?   
      
   Martin.   
      
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