OFFSET
1,1
COMMENTS
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.
EXAMPLE
-6.037581106...
MATHEMATICA
(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
RealDigits[Integrate[Log[Sin[x]]^3, {x, 0, Pi/4}], 10, 120][[1]] (* Harvey P. Dale, Jun 08 2021 *)
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Jean-François Alcover, Mar 20 2013
STATUS
approved