Calculation and Application of a Class of Infinite Integrals 
of Irrational Functions Based on the Idea of Reduction

Xin Chen; Jianhong Zhuang

doi:10.70711/wef.v3i2.7833

Calculation and Application of a Class of Infinite Integrals of Irrational Functions Based on the Idea of Reduction

Xin Chen, Jianhong Zhuang

Abstract

The method of reduction is an effective mathematical thinking approach and serves as an important concept and technique for solving mathematical problems. Based on the idea of reduction, a class of infinite integrals of irrational functions as?(0-?)dx/?((a+x)x)?( ? > 1 , a > 0 ) are studied and a novel substitution method for convergent ones is proposed. Furthermore, the integrands are extended to a more general form to demonstrate the universality of the given substitution approach. Application examples of this type of integrals in calculating the expectation and variance of random variables are also provided.

Keywords

Reduction; Infinite Integral; Irrational Function; Substitution

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DOI: http://dx.doi.org/10.70711/wef.v3i2.7833

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