From: peter.luschny@gmail.com   
      
   Hi all,   
      
   I'm much better in finding integrals than in solving them,   
   therefore I ask here where the experts on this subject seem   
   to sit in a row like migratory birds in autumn on the   
   telephone wires.   
      
   I have no problem to calculate the value, and indeed it is   
   utterly trivial to solve this integral by numerical approximation.   
      
   But I am interested in everything else which could be said about   
   this integral and possible transformations of this integral.   
      
   Of course integrability in elementary terms is one of these   
   questions (I think it is not).   
      
   The question remains why it is worth dealing with this integral.   
   This much can be disclosed (so as not to spoil the fun): the   
   value on the definite interval (-oo..+oo) is the quotient of   
   two famous constants, which implies a bunch of some interesting   
   new formulas.   
      
   This is the integral in Maple parlance:   
      
       int( -log((z^2+1/4)^(1/4))*sech(Pi*z)^2, z = -infinity..infinity)   
      
   Thanks,   
   Peter   
      
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