Exploring Integrals Involving Logarithmic Function by Different Methods

Siyang Wang

2025

Abstract

This paper focuses on the theoretical development and applications of integral and logarithmic functions, with the research background covering the historical evolution of mathematical analysis and modern interdisciplinary demands. From the foundational work to modern scientific and engineering applications, the integral serves as a core tool for quantifying continuous variables. The logarithmic function, due to its data compression and computational simplification characteristics, has become a universal language across multiple disciplines. The paper emphasizes addressing the systematization of integral methods for logarithmic functions, involving the solution of complex integral expressions and the handling of improper integrals. The research method combines classical mathematical tools with innovative techniques: through integration by parts, linear variable substitution and the residue theorem. L'Hôpital's rule and partial fraction decomposition are utilized to handle limits and integrals with logarithms in the denominator. The research indicates that the combination of integral and logarithmic functions provides mathematical support for fields. The significance of the paper lies in integrating theory and application, strengthening the universality of integral techniques, and building a rigorous framework for modelling complex continuous systems and solving practical problems, promoting the in-depth application of mathematical tools in scientific and technological innovation.

Paper Citation

in Harvard Style

Wang S. (2025). Exploring Integrals Involving Logarithmic Function by Different Methods. In Proceedings of the 2nd International Conference on Innovations in Applied Mathematics, Physics, and Astronomy - Volume 1: IAMPA; ISBN 978-989-758-774-0, SciTePress, pages 104-108. DOI: 10.5220/0013814800004708

in Bibtex Style

@conference{iampa25,
author={Siyang Wang},
title={Exploring Integrals Involving Logarithmic Function by Different Methods},
booktitle={Proceedings of the 2nd International Conference on Innovations in Applied Mathematics, Physics, and Astronomy - Volume 1: IAMPA},
year={2025},
pages={104-108},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0013814800004708},
isbn={978-989-758-774-0},
}

in EndNote Style

TY - CONF

JO - Proceedings of the 2nd International Conference on Innovations in Applied Mathematics, Physics, and Astronomy - Volume 1: IAMPA
TI - Exploring Integrals Involving Logarithmic Function by Different Methods
SN - 978-989-758-774-0
AU - Wang S.
PY - 2025
SP - 104
EP - 108
DO - 10.5220/0013814800004708
PB - SciTePress