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A dozen integrals: Russell-style
Tewodros Amdeberhan, Victor Moll
On June 15, 1876, the Proceedings of the Royal Society of London published a paper by Mr. W. H. L. Russell entitled "On certain integrals". The paper starts with "The following are…
The Laplace transform of the digamma function: an integral due to Glasser, Manna and Oloa
Tewodros Amdeberhan, Victor H. Moll
We provide an analytic expression for the Laplace transform of the digamma fuction. This complements work of L. Glasser, D. Manna and O. Oloa on this question. The Laplace transfor…
The integrals in Gradshteyn and Ryzhik. Part9: Combinations of logarithms, rational and trigonometric functions
Tewodros Amdeberhan, Victor H. Moll, Jason Rosenberg +2
The classical table of integrals by I. S. Gradshteyn and I. M. Ryzhik contains many definite integrals where the integrand is the product of a rational function times the logarithm…
The integrals in Gradshteyn and Ryzhik. Part 7: Elementary examples
Tewodros Amdeberhan, Victor H. Moll
The classical table of integrals by I. S. Gradshteyn and I. M. Ryzhik contains some elementary integrals. We discuss their evaluations.
A formula for a quartic integral: a survey of old proofs and some new ones
Tewodros Amdeberhan, Victor H. Moll
We discuss several existing proofs of the value of a quartic integral and present a new proof that evolved from rational Landen transformations.
The integrals in Gradshteyn and Ryzhik. Part 5: Some trigonometric integrals
Tewodros Amdeberhan, Luis Medina, Victor H. Moll
We present evalauations and provide proofs of definite integrals involving the function x^p cos^n x. These formulae are generalizations of 3.761.11 and 3.822.1, among others, in th…