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%I #11 Jun 08 2021 14:20:08
%S 6,0,3,7,5,8,1,1,0,6,3,0,9,5,9,8,1,7,0,2,6,7,4,3,6,8,9,2,6,5,0,2,6,7,
%T 4,6,7,5,5,0,3,9,8,2,8,5,8,8,8,6,8,6,2,7,1,7,5,1,8,0,4,9,0,1,3,5,5,8,
%U 7,4,2,2,1,2,7,0,1,6,0,6,7,4,0,9,7,6,9,3,5,9,7,6,6,7,5,9,9,6,8,2
%N Decimal expansion of integral_{0, Pi/4} log(sin(x))^3 dx.
%C Curiously, this integral from 0 to Pi/4 is far more difficult to evaluate by hand than the same integral from 0 to Pi/2.
%e -6.037581106...
%t (1/8)*((-Log[2]^2)*(Pi*Log[2] + 3*Catalan) - 4*Sqrt[2]*(6*HypergeometricPFQ[{1/2, 1/2, 1/2, 1/2, 1/2}, {3/2, 3/2, 3/2, 3/2}, 1/2] + HypergeometricPFQ[{1/2, 1/2, 1/2, 1/2}, {3/2, 3/2, 3/2}, 1/2]*Log[8])) // RealDigits[#, 10, 100] & // First
%t RealDigits[Integrate[Log[Sin[x]]^3,{x,0,Pi/4}],10,120][[1]] (* _Harvey P. Dale_, Jun 08 2021 *)
%Y Cf. A196878 (the same integral from 0 to Pi/2)
%K nonn,cons
%O 1,1
%A _Jean-François Alcover_, Mar 20 2013
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