From: Albert_Rich@msn.com   
      
   On Tuesday, October 15, 2019 at 6:16:30 AM UTC-10, clicl...@freenet.de wrote:   
      
   > I remember that no computer algebra system was found able to confirm   
   > the identity:   
   >   
   >   2*pi*SQRT(1 - z) = SQRT(z - 1)*(2*LN(- SQRT(z - 1)) - LN(z - 1))   
   >   
   > for arbitrary complex z. [...]   
      
   Substituting z+1 for z in this identity and rearranging terms yields the   
   identity   
      
       log(-sqrt(z)) = log(z)/2 - pi*sqrt(z)/sqrt(-z)   
      
   valid for arbitrary complex z.  More generally the identity   
      
       log(-z^n) = n*log(z) - pi*sqrt(z)/sqrt(-z)   
      
   appears to be valid for arbitrary complex z provided n is positive (someone   
   please confirm).   
      
   Perhaps computer algebra systems and Rubi should use this identity to   
   normalize integrands involving dependent logarithms; thereby making the second   
   integration problem in Welz_problems.txt trivial.   
      
   Albert   
      
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