From: nma@12000.org   
      
   fyi, Just trying Rubi 4.7 on this problem I saw   
      
   Int[ x^2/(x Sin[x] + Cos[x])^2, x]  it did not give an answer.   
      
   Wondering if a new rule is needed?  Mathematica gives   
      
   (-x Cos[x] + Sin[x])/(Cos[x] + x Sin[x])   
      
   and Maple also solves it   
      
   int(x^2/(x*sin(x)+cos(x))^2,x);   
   (x*tan((1/2)*x)^2-x+2*tan((1/2)*x))/(2*x*tan((1/2)*x)-tan((1/2)*x)^2+1)   
      
      
   Same for this   
      
   Int[x/(Cos[x] + Sin[x]), x], no answer. Mathematica 10.02 gives   
      
   Integrate[x/(Cos[x] +  Sin[x]), x]   
   (1/(2 Sqrt[2]))(-\[Pi] ArcTanh[(-1 + Tan[x/2])/Sqrt[2]] +   
      2 ((\[Pi]/4 + x) (Log[1 - (-1)^(1/4) E^(I x)] - Log[1 +   
   E^(1/4 I (\[Pi] + 4 x))]) + I (PolyLog[2, -(-1)^(1/4) E^(I x)]   
   - PolyLog[2, E^(1/4 I (\[Pi] + 4 x))])))   
      
   Maple 18.02 could not do it either.   
      
   --Nasser   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)