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%I #12 Sep 27 2015 11:18:52
%S 3,0,6,0,1,8,0,5,9,9,8,4,3,5,8,5,5,6,2,5,5,6,9,3,3,4,3,6,8,5,0,4,9,6,
%T 4,0,0,3,2,1,2,7,6,1,2,9,0,5,4,0,5,3,6,0,9,4,4,3,4,0,4,3,0,5,7,6,3,0,
%U 8,6,4,7,6,2,0,9,7,2,0,7,1,9,5,9,8,3,0,4,5,1,5,4,1,8,1,2,0,7,3,0,9,9,5,9,3
%N Decimal expansion of Integral_{0..1} log(1-x)*log(x)^2 dx (negated).
%H M. Jung, Y. J. Cho, J. Choi, <a href="http://dx.doi.org/10.4134/CKMS.2004.19.3.545">Euler sums evaluatable from integrals</a>, Commun. Korean Math. Soc. 19 (2008), 545-555.
%F Equals -6 + Pi^2/3 + 2 zeta(3).
%F Equals Integral_{0..Pi/2} log(cos(x)^2) * log(sin(x)^2)^2 * sin(2x) dx.
%e -0.30601805998435855625569334368504964003212761290540536094434 ...
%t RealDigits[Integrate[Log[1 - x]*Log[x]^2, {x, 0, 1}] , 10,
%t 105] // First
%o (PARI) -(-6 + Pi^2/3 + 2*zeta(3)) \\ _Michel Marcus_, Sep 27 2015
%Y Cf. A152416 (Integral_{0..1} log(1-x)*log(x) dx), A262606 (Integral_{0..1} log(1-x)^2*log(x)^2 dx).
%K nonn,cons,easy
%O 0,1
%A _Jean-François Alcover_, Sep 26 2015