From: nma@12000.org   
      
   I tried Rubi, Mathematica and Maple, and none can integrate this   
      
      int( tanh(x)/(1+tan(x)),x)   
      
   Maple was able to give partial answer:   
      
   -(1/2+I*(1/2))*x+(1/2+I*(1/2))*ln((exp(x))^2+1)+   
       int(((exp(x))^2-1)/(((exp(I*x))^2+I)*((exp(x))^2+1)), x)   
      
   It looks like complex contour integration is required to finish   
   this?   
      
   looking at the Taylor series of tanh(x)/(1+tan(x)) expanded   
   around 0, for few terms:   
      
   Series[Tanh[x]/(1 + Tan[x]), {x, 0, 6}]   
      
   x - x^2 + (2 x^3)/3 - x^4 + (22 x^5)/15 - (82 x^6)/45   
      
   Is there a closed form for the anti-derivative to   
   tanh(x)/(1+tan(x)) or how would one go about trying to   
   find one? Can different CAS above solve this? (I did   
   not try sage/maxima etc...)   
      
   --Nasser   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)