Published 2005-05-07
Keywords
- integrals,
- rational functions
Copyright (c) 2025 Scientia Series A: Mathematical Sciences
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How to Cite
An elementary evaluation of a quartic integral. (2005). Scientia Series A: Mathematical Sciences, 11, 1-12. https://revistas.usm.cl/scientia/article/view/51
Abstract
We provide an elementary evaluation for the integral
\[N_{0.4}(a; m) = \int_{0}^{\infty} \frac{dx}{(x^4 + 2ax^2 + 1)^{m+1}}\]
where \(m \in \mathbb{N} and a \in (-1, \infty)\)
\[N_{0.4}(a; m) = \frac{2^{m+3/2}}{(a+1)^{m+1/2}}\pi P_m(a)\]
\({for } P_m(a) \text{ a polynomial in } a.\)
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