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8 April 2024 Simplified method of evaluating integrals of powers of natural logarithm using permutation
Redentor D. Isles, Monalissa M. Isles
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Proceedings Volume 13090, International Conference on Computer Application and Information Security (ICCAIS 2023); 1309009 (2024) https://doi.org/10.1117/12.3026785
Event: International Conference on Computer Application and Information Security (ICCAIS 2023), 2023, Wuhan, China
Abstract
This paper presents a simpler method of evaluating integrals of powers of natural logarithm. A reduction formula is derived to evaluate the integral of the nth power of natural logarithm. The reduction formula is then repeatedly applied until a generalized formula is derived. The exponents and coefficients of the derived formula showed very recognizable patterns. The exponents of the logarithmic terms are in decreasing order while the coefficient of each term is a permutation.
(2024) Published by SPIE. Downloading of the abstract is permitted for personal use only.
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Redentor D. Isles and Monalissa M. Isles "Simplified method of evaluating integrals of powers of natural logarithm using permutation", Proc. SPIE 13090, International Conference on Computer Application and Information Security (ICCAIS 2023), 1309009 (8 April 2024); https://doi.org/10.1117/12.3026785
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KEYWORDS
Mathematics
Differential equations
Engineering
Inspection
Roads
Transform theory
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