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Decimal expansion of the triple integral int Integral_{z = 0..1} int Integral_{y = 0..1} int Integral_{x = 0..1} (x*y*z)^(x*y*z) dx dy dz.
The double integral int Integral_{y = 0..1} int Integral_{x = 0..1} (x*y)^(x*y) dx dy equals int Integral_{x = 0..1} x^x dx, which is listed as A083648.
The triple integral is most conveniently estimated from the identity int Integral_{z = 0..1} int Integral_{y = 0..1} int Integral_{z = 0..1} (x*y*z)^(x*y*z) dx dy dz = (1/2)*sum Sum_{n >= 1..inf} (-1)^(n+1)*(1/n^n + 1/n^(n+1)).
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digits = 103; 1/2*NSum[ (-1)^(n+1)*(1/n^n + 1/n^(n+1)), {n, 1, Infinity}, WorkingPrecision -> digits+10, NSumTerms -> 100] // RealDigits[#, 10, digits]& // First (* Jean-François Alcover, Feb 15 2013, from formula *)
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_Peter Bala (pbala(AT)talktalk.net), _, Mar 04 2012
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