OFFSET
1,2
LINKS
Paul J. Nahin, Inside interesting integrals, Undergrad. Lecture Notes in Physics, Springer (2020), (5.1.3).
Michael I. Shamos, Shamos's catalog of the real numbers, 2011. See p. 465.
FORMULA
From Amiram Eldar, May 21 2024: (Start)
Formulas from Shamos (2011):
Equals Integral_{x>=1} log(x^2-1)/(x^2+1) dx.
Equals Integral_{x>=0} x/(exp(x) + 2*exp(-x) - 2) dx.
Equals Integral_{x=0..Pi/2} (sin(x)-cos(x))/(sin(x)+cos(x)) * x dx.
Equals Integral_{x>=0} arccot(x)/(x+1) dx.
Equals Integral_{x=0..Pi/2} log(1+tan(x)) dx. (End)
EXAMPLE
1.46036211...
MAPLE
Pi/4*log(2)+Catalan ; evalf(%) ;
MATHEMATICA
RealDigits[Pi*Log[2]/4 + Catalan, 10, 120][[1]] (* Amiram Eldar, May 21 2024 *)
CROSSREFS
KEYWORD
cons,nonn
AUTHOR
R. J. Mathar, May 16 2024
STATUS
approved