Integral from 0 to ∞ of x sech(x) ln(1 - sech(x) )

Notes:

Integral from 0 to ∞ of x log(1 - 1/cosh(x) )/cosh(x)
Integral from 0 to ∞ of x sech(x) log(1 - sech(x) )
Catalan constant G
Catalan's constant
Dirichlet beta(2)
Logarithmic integral
Integral with hyperbolic secant function
sech cosh
A = ∫ x from 0 to 1 of log(x) log((1–x)/(1+x))/(1+x²)
B = ∫ x from 0 to 1 of log(x) tan⁻¹(x)/(1–x²)
C = ∫ x from 0 to 1 of log(x) log(1+x²)/(1+x²)
D = ∫ x from 0 to 1 of log(x) log(1–x)/(1+x²)
A = 2Glog2 + 2B + C
A = 4B + π³/16
B = –π³/32 + ½Glog2 + D