Related papers: The integrals in Gradshteyn and Ryzhik. Part 12: S…
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…
We present the evaluation of some definite integrals in the classical table by I. S. Gradshteyn and I. M. Ryzhik where the integrand is a combination of powers, exponentials and logarithms.
We present the evaluation of a family of logarithmic integrals. This provides a unified proof of several formulas in the classical table of integrals by I. S. Gradshteyn and I. M. Rhyzik.
We describe methods to evaluate elementary logarithmic integrals. The integrand is the product of a rational function and a linear polynomial in ln x.
There have been many works on proving the integrals in the table of integrals compiled by Gradshteyn and Ryzhik, and in this paper we prove some doubly logarithmic integral identities in the Gradshteyn and Ryzhik table.
We present the evaluation of a family of exponential-logarithmic integrals. These have integrands of the form P(exp(x),ln(x)) where P is a polynomial. The examples presented here appear in sections 4.33, 4.34 and 4.35 in the classical table…
The classical table of integrals by I. S. Gradshteyn and I. M. Ryzhik contains some elementary integrals. We discuss their evaluations.
Many integrals in the classical table by Gradshteyn and Ryzhik can be evaluated in terms of the digamma function (= the logarithmic derivative of the gamma function). Some of them are presented here.
The table of Gradshteyn and Ryzhik contains many entries that are related to elliptic integrals. We present a systematic derivation of some of them.
The need to evaluate Logarithmic integrals is ubiquitous in essentially all quantitative areas including mathematical sciences, physical sciences. Some recent developments in Physics namely Feynman diagrams deals with the evaluation of…
We review a special technique for evaluating challenging integrals by providing a number of examples. Many of our examples prove integrals from the popular table of Gradshteyn and Ryzhik.
An elementary proof of an entry in the table of integrals by Gradshteyn and Rhyzik is presented.
The well known table of Gradshteyn and Ryzhik contains indefinite and definite integrals of both elementary and special functions. We give proofs of several entries containing integrands with some combination of hyperbolic and trigonometric…
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 the classical table of integrals by I. S. Gradshteyn and I. M.…
We present the evaluation of definite integrals in the classical table by I. S. Gradshteyn and I. M. Ryzhik that can be reduced to the beta function.
The logarithmic integral no. 4.325.7 from Gradshteyn and Ryzhik's tables of integrals was first evaluated by Malmst\'en. Recently, Blagouchine used contour integration methods to evaluate a family of logarithmic integrals that contains this…
We present a systematic derivation of some definite integrals in the classical table of Gradshteyn and Ryzhik that can be reduced to the gamma function.
We present a systematic study of integrals over [0,1] where the integrand is of the form Q(x) log log 1/x. Here Q is a rational function.
The table of Gradshteyn and Rhyzik contains some trigonometric integrals that can be expressed in terms of the beta function. We describe the evaluation of some of them.
Logarithmic integrals revisited. We consider integrals of the form $\int_0^1 \ln{\ln{(\frac{1}{x})}}R{(x)}{\rm d}x$ again, where $R{(x)}$ is a rational function, and we will explain a way to obtain their values.