From: Albert_Rich@msn.com   
      
   On Saturday, March 8, 2014 4:22:30 AM UTC-10, clicl...@freenet.de wrote:   
      
   > My interest in Example 44 (like the similar but simpler 62, 64, 66, and   
   > 118) was mostly in the asymmetric LN evaluation. Please fuse the ATAN's   
   > in numbers 62, 64, 66 as you see fit; I find no continuity problems:   
   >    
   > ATAN(1 + SQRT(2)*SQRT(TAN(x))) - ATAN(1 - SQRT(2)*SQRT(TAN(x)))   
   >  = ATAN((TAN(x) - 1)/(SQRT(2)*SQRT(TAN(x)))) + pi/2   
   >   
   > [...]   
      
   I revised the optimal antiderivatives for examples 62, 64, 66, 90, 91, 112 and   
   118 of Chapter 5 of the Timofeev integration test suite unifying arctangents   
   as you suggested, and posted the results on the Rubi website at   
      
   http://www.apmaths.uwo.ca/~arich/   
      
   Note that the derivative of each side of the above equation are equal, so the   
   unified arctangents can be used for antiderivatives.  However, the two sides   
   are not always equal assuming standard CCW (counter-clockwise) continuity is   
   used along the    
   arctangent's branch cut on the imaginary line. Interestingly the equation IS   
   everywhere valid in Derive, since Derive uses CW continuity on the   
   arctangent's branch cut...   
      
   Albert   
      
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