The integrals in Gradshteyn and Ryzhik. Part9: Combinations of logarithms, rational and trigonometric functions

Abstract

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 of another rational function. We begin the systematic evaluation of these integrals.

arXiv comment16 pages

References in corpus (3)

• The integrals in Gradshteyn and Rhyzik. Part 2: Elementary logarithmic integrals
• The integrals in Gradshteyn and Ryzhik. Part 5: Some trigonometric integrals
• The integrals in Gradshteyn and Ryzhik. Part 6: the beta function

Cited by in corpus (4)

• Some sums over the non-trivial zeros of the Riemann zeta function
• The integrals in Gradshteyn and Ryzhik. Part 12: Some logarithmic integrals
• The Laplace transform of the digamma function: an integral due to Glasser, Manna and Oloa
• Laplace transforms based some novel integrals via hypergeometric technique