LXIX. On some definite integrals

Solving Some Definite Integrals by Using Maple

This study uses the mathematical software Maple for the auxiliary tool to evaluate two types of definite integrals. We can obtain the closed forms of these two types of definite integrals by using differentiation with respect to a parameter and Leibniz differential rule. At the same time, we provide some definite integrals to do calculation practically. The research methods adopted in this stud...

Application of Parseval’s Theorem on Evaluating Some Definite Integrals

Abstract This paper uses the mathematical software Maple for the auxiliary tool to study six types of definite integrals. We can determine the infinite series forms of these definite integrals by using Parseval’s theorem. On the other hand, we provide some definite integrals to do calculation practically. The research methods adopted in this study involved finding solutions through manual calcu...

On Some Definite Integrals Involving the Hurwitz Zeta Function

We establish a series of integral formulae involving the Hurwitz zeta function. Applications are given to integrals of Bernoulli polynomials, log Γ(q) and log sin(q).

Some Definite Integrals Associated with the Riemann Zeta Function

Some Definite Integrals Involving Algebraic, Trigonometric and Bessel Functions

Some defin ite analytic integrals involving algebraic, trigonometric and Bessel functions which are needed in some electromagnetic calculations are proposed. The mathematical expansions are based on Mathematica (Wolfram) software and on some well known formulas. The agreement between the present expansion results and the numerical evaluation results is excellent.