From: Albert_Rich@msn.com   
      
   On Monday, February 19, 2018 at 7:26:06 AM UTC-10, Nasser M. Abbasi wrote:   
   > Rubi 4.14.6  can integrate   
   >   
   >         (x Exp[x])/(1 - Exp[x])     (1)   
   >   
   > but not   
   >   
   >         (x Exp[x])/(1 - Exp[-x])    (2)   
   >   
   > I was just wondering why that is. Could not figure what changes   
   > in rules needed. Since the result are very similar (in terms   
   > of PolyLog, which Rubi supprts). For example, for (1) it   
   > gives   
   >   
   > In[59]:= rubi = Int[(x Exp[x])/(1 - Exp[x]), x]   
   > Out[59]= -x Log[1 - E^x] - PolyLog[2, E^x]   
   >   
   > But for (2) it does not evaluate it. Mathematica gives for (2)   
   >   
   > In[60]:= mma = Integrate[(x Exp[x])/(1 - Exp[-x]), x]   
   > Out[60]= E^x (-1 + x) + x Log[1 - E^x] + PolyLog[2, E^x]   
   >   
   > thanks   
   > --Nasser   
      
   Thank you for reporting this embarrassing deficiency in Rubi. The just   
   released version 4.14.7 includes a new rule which algebraically expands your   
   example integrand into x*E^x+x/(1-E^(-x)). This sum is then integrated in 7   
   steps using existing rules.   
      
   Among other enhancements, Rubi 4.14.7 can find elementary antiderivatives for   
   integrands of the form x/((c+d*x^3)*sqrt(a+b*x^3)) when   
   b*c-4*a*d=0, or b*c+8*a*d=0, or b*c-2*(5+3*sqrt(3))*a*d=0.  These   
   pseudo-elliptic integrals are discussed in the sci.math.symbolic thread "More   
   teething help".   
      
   I am still trying to find optimal antiderivatives for when   
   b*c-2*(5-3*sqrt(3))*a*d=0. The best so far has 3 arctan(h) terms, but involves   
   the imaginary unit. Maybe some system or person can do better...   
      
   Albert   
      
   --- SoupGate-Win32 v1.05   
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