OFFSET
0,2
FORMULA
Equals Pi^2/54 - PolyGamma(1, 2/3)/9. - Vaclav Kotesovec, Oct 31 2021
EXAMPLE
-0.15766014916783233039054467406996221822374946546295676913413604497322566...
MATHEMATICA
RealDigits[Integrate[x*Log[x]/(1 + x + x^2), {x, 0, 1}], 10, 100][[1]] (* Amiram Eldar, Oct 31 2021 *)
RealDigits[Pi^2/54 - PolyGamma[1, 2/3]/9, 10, 100][[1]] (* Vaclav Kotesovec, Oct 31 2021 *)
PROG
(SageMath)
RealField(25)(numerical_integral(x*log(x)/(1+x+x^2), 0, 1)[0])
(PARI) intnum(x=0, 1, x*log(x)/(1+x+x^2)) \\ Michel Marcus, Oct 31 2021
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Dumitru Damian, Oct 31 2021
STATUS
approved