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%I #6 Apr 07 2015 08:29:13
%S 7,8,1,1,9,7,0,3,1,1,0,8,6,5,5,9,1,5,1,0,7,4,3,2,8,1,4,3,4,8,2,9,9,5,
%T 0,5,7,7,6,6,9,7,3,9,0,9,6,2,1,7,8,6,0,3,9,8,0,9,2,6,0,2,6,8,4,3,2,4,
%U 2,3,4,0,8,2,2,1,7,0,4,5,9,3,2,9,0,2,4,2,9,3,5,3,9,1,5,8,7,3,3,7,9,1,3
%N Decimal expansion of Integral_{x=0..1} x*exp(x^3) dx.
%D Jonathan M. Borwein, Matthew P. Skerritt, An Introduction to Modern Mathematical Computing, Springer Science & Business Media, 2011, p. 89.
%F Equals (1/6)*(1 + i*sqrt(3))*(Gamma(2/3, -1) - Gamma(2/3)).
%F The simpler similar integral Integral_{x=0..1} x*exp(x^2) dx equals (e-1)/2 = 0.85914...
%e 0.7811970311086559151074328143482995057766973909621786...
%t int3 = (1/6)*(1 + I*Sqrt[3])*( Gamma[2/3, -1] - Gamma[2/3]); RealDigits[N[int3, 103] // Chop] // First
%o (PARI) intnum(x=0, 1, x*exp(x^3)) \\ _Michel Marcus_, Apr 07 2015
%Y Cf. A073006 (gamma(2/3)).
%K nonn,cons,easy
%O 0,1
%A _Jean-François Alcover_, Apr 07 2015