The exponential integral function Ei(x) is given as an indefinite integral of an elementary expression. This allows a second-order linear differential equation for the function to be constructed, which is of conventional form. A limitless number of differential equations can be derived from the original by elementary transformations, and many integrals are given by applying the method of fragments to some of these transformed equations. Results are presented here both for simple transformations and other transformations obtained by solving simple Riccati equations. Some of the Integrals are presented combine Ei(x) with Bessel functions, modified Bessel functions and Whittaker functions. All results have been checked by differentiation using Mathematica.

指数积分函数 Ei( x ) 作为基本表达式的不定积分给出。这允许构造函数的二阶线性微分方程，这是常规形式。可以通过初等变换从原始微分方程中推导出无数的微分方程，并且通过对这些变换方程中的一些应用片段法来给出许多积分。此处给出了简单变换和通过求解简单 Riccati 方程获得的其他变换的结果。提出了一些积分，将 Ei( x ) 与贝塞尔函数、修正的贝塞尔函数和惠特克函数结合起来。所有结果均已使用 Mathematica 通过微分检查。