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Serret's Integral

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Serret's integral is given by

int_0^1(ln(x+1))/(x^2+1)dx=1/8piln2
(1)
=0.272198...
(2)

(OEIS A102886; Serret 1844; Gradshteyn and Ryzhik 2000, eqn. 4.291.8; Boros and Moll 2004, p. 243).

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References

Boros, G. and Moll, V. Irresistible Integrals: Symbolics, Analysis and Experiments in the Evaluation of Integrals. Cambridge, England: Cambridge University Press, 2004.Gradshteyn, I. S. and Ryzhik, I. M. Tables of Integrals, Series, and Products, 6th ed. San Diego, CA: Academic Press, 2000.Serret, M. J. A. "Sur l'intégrale int_0^1(ln(1+x))/(1+x^2)dx." J. Math. Pures Appl. 9, 436, 1844.Sloane, N. J. A. Sequence A102886 in "The On-Line Encyclopedia of Integer Sequences."

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Serret's Integral

Cite this as:

Weisstein, Eric W. "Serret's Integral." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SerretsIntegral.html

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