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grrrrrrrrrrrrr: int(x^x)

Axel Vogt 5906 Maple
June 29 2010
1 
  restart; interface(version); Digits:=14;

    Classic Worksheet Interface, Maple 12.02, Windows, Dec 10 2008 Build ID 377066

  f:= x -> (x+1)^(x+1);
  simplify(int(f(x),x)): 
  F:=unapply(%,x);
                                        (x + 1)
                       f := x -> (x + 1)


                            (x + 1)            (x + 1)
                     (x + 1)        x + (x + 1)        - 1
           F := x -> -------------------------------------
                                     x + 2

but 

 f(1) = D(F)(1); evalf(%);

                         4 = 8/3 ln(2) + 29/9
                         4. = 5.0706147037154

and that is due to a problem in 'simplify':

  int(f(x),x);
  fdiff(%, x=1);

                  x hypergeom([1, -x - 1], [2], -x)
                           5.0706147037154

Edited, since I was too hasty (see Alejandro below): it should read as
and that is not due to a problem in 'simplify

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