From: nma@12000.org   
      
   On 2/20/2021 6:51 PM, drhu...@gmail.com wrote:   
   > what is integral of x^x = ?   
   >   
   > mathHand.com   
   >   
      
   A known trick is to write x^x as exp(x*ln x), then   
   use   exp(u) = sum u^n/n!, n=0..infinity, and integrate   
   term by term, and sum. So you get   
      
     sum( integrate( (x*ln x)^n/n!  ,x) , n=0..infinity)   
      
   For one term only, Rubi gives   
      
   oneterm = Int[ x^n*Log[x]^n/n!, x];   
      
   (Gamma[1 + n, -((1 + n) Log[x])] Log[x]^n (-((1 + n) Log[x]))^-n)/((1 + n) n!)   
      
   But this has no closed form sum   
      
       Sum[oneterm, {n, 0, Infinity}];   
      
   --Nasser   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)