%I #12 Feb 23 2022 22:22:42
%S 3,5,3,4,9,6,8,0,0,7,0,1,4,2,2,0,5,5,4,6,5,8,3,6,3,7,0,2,0,6,6,9,8,2,
%T 4,5,0,9,0,2,5,6,8,0,0,8,0,8,7,7,3,9,9,3,8,0,7,8,0,7,9,2,4,6,0,7,8,0,
%U 0,1,8,4,5,9,7,0,0,2,5,3,3,9,0,4,0,4,0,2,9,0,6,4,2,7,6,5,0,9,1,9,5,2,3,2,6
%N Decimal expansion of the definite integral of x^(1/x) for x = 0 to 1.
%H J. Sondow and D. Marques, <a href="http://ami.ektf.hu/uploads/papers/finalpdf/AMI_37_from151to164.pdf">Algebraic and transcendental solutions of some exponential equations</a>, Annales Mathematicae et Informaticae 37 (2010) 151-164; see Figure 5.
%e 0.3534968007014220554658363702066982450902568008087739938078079246078001845970...
%t RealDigits[ NIntegrate[x^(1/x), {x, 0, 1}, WorkingPrecision -> 128], 10, 111][[1]] (* _Robert G. Wilson v_, Mar 10 2013 *)
%o (PARI) intnum(x=exp(-lambertw(default(realbitprecision)*log(2)+2)),1,x^x^-1) \\ _Charles R Greathouse IV_, Feb 23 2022
%o (PARI) intnum(x=1e-9,1,x^x^-1) \\ good for up to 29 billion digits; _Charles R Greathouse IV_, Feb 23 2022
%Y Cf. A073229 (decimal expansion of e^(1/e)).
%K cons,nonn
%O 0,1
%A _Dylan Hamilton_, Nov 05 2010