From: Albert_Rich@msn.com   
      
   On Wednesday, October 4, 2017 at 6:21:59 AM UTC-10, clicl...@freenet.de wrote:   
      
   > 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.   
      
   3D plots of the absolute value of the difference of the two sides of the   
   equation with x replaced by x+y i over various ranges of x and y indicates   
   your belief is probably correct.   
      
   However, I hesitate to have Rubi return   
      
     x/Sqrt[x^2]*EllipticF[2*ArcTan[(x^2-1)^(1/4)],1/2]   
      
   as the optimal antiderivative of 1/(x^2-1)^(3/4) since the host CAS cannot   
   verify it correct.  But I will certainly put it in the code as a comment.   
      
   Albert   
      
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