From: nma@12000.org   
      
   can your CAS find integral of arctanh(t)*ln(t)/(t-1) ?   
      
   I tried Maple, Rubi, Fricas, mupad, and Mathematica.   
      
   Tried definite integration from t=0..1 and indefinite also.   
      
   Numerically the value is   
      
   NIntegrate[ArcTanh[t] Log[t]/(t - 1), {t, 0, 1}]   
   0.855136058   
      
   When the denominator is just "t", only Mathematica is able   
   to solve indefinite:   
      
   Integrate[ArcTanh[t] Log[t]/t, t]   
   (1/2)*((-Log[t])*PolyLog[2, -t] + Log[t]*PolyLog[2, t] + PolyLog[3, -t] -   
   PolyLog[3, t])   
      
   It also can find the definite integral (Maple can also)   
      
   Integrate[ArcTanh[t] Log[t]/t, {t, 0, 1}]   
   -((7 Zeta[3])/8)   
      
   Fricas gives "failed" on the above   
      
   (9) -> integrate(atanh(t)*log(t)/t,t=0..1)   
       (9)  "failed"   
      
      
   But What about when (t-1) in denominator? can CAS find   
   closed form solution? Either definite or indefinite?   
      
   I do not know is this has analytical antiderivative or not.   
   I am just asking.   
      
   Thanks,   
   --Nasser   
      
   --- SoupGate-Win32 v1.05   
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