On the Results of Coffy and Moli

Abstract

The primary aim of this article is Generalization leading to search of integrals of the type∫ 𝒍𝒐𝒈𝑷 𝒍𝒐𝒈𝑸 𝒅𝒙 = ∫ 𝑭𝑮 𝒏𝒅𝒙 where both P, Q are functions of x only and also verification of results by using new trend. In this direction of verification, converting integrals into ordinary differential equations and finding the solutions, has significant trend and fresh impetus in the recent years. In this paper, along with the generalization of integrals, formation of ordinary differential equations and their solutions were also listed. Here in this article we obtained significant differential equations based on integrals of Russell [1], type. In the first part, generalizations of preliminary lemmas along with new integrals of logarithmic integrand were evaluated on the lines Mark Coffy [4]. Then first order linear differential equations were obtained for such integrals, to verify the truth of the solutions.