%I #13 Jun 06 2017 10:32:30
%S 2,2,7,7,1,4,4,7,9,9,7,9,5,7,9,1,6,0,6,0,6,5,5,8,0,2,6,2,6,2,1,4,7,0,
%T 3,3,4,9,3,8,4,3,9,1,3,5,5,5,0,3,1,7,2,8,8,7,1,9,1,7,9,3,4,9,0,0,0,5,
%U 1,3,3,0,4,4,3,4,8,0,8,0,7,7,2,6,1,2,6,6,3,7,0,0,7,9,8,7,0,1,5,4,4,3,6,6,4
%N Decimal expansion of Integral_{0..Pi/2} x^2*tan(x)*log(sin(x)) dx (negated).
%C This integral appears in the expression of the 3rd moment of the distribution of the number of vertices of Goudsmit-Miles random polygonal cells.
%H Steven R. Finch, <a href="/A261710/a261710.pdf">Random Triangles V</a>, December 22, 2010, p. 9. [Cached copy, with permission of the author]
%H J. C. Tanner, <a href="http://www.jstor.org/stable/3213589">Polygons Formed by Random Lines in a Plane: Some Further Results</a>, Journal of Applied Probability, Vol. 20, No. 4 (Dec., 1983), pp. 778-787. See Eq. 7, p. 783.
%e -0.2277144799795791606065580262621470334938439135550317288719179349...
%t NIntegrate[x^2*Tan[x]*Log[Sin[x]], {x, 0, Pi/2}, WorkingPrecision -> 105] // RealDigits // First
%K nonn,cons,easy
%O 0,1
%A _Jean-François Alcover_, Aug 29 2015