An Asymptotic Expansion

马上准备试一下用打字机打一张排版复古的数学小论文，所以把以前一个回答改成英文版，来适配打字机和铅字印刷的排版

In some problems in other fields, we need to obtain the asymptotic expansion of following integral. 

Make following substitution

to obtain a new integral

expand numerator into power series of 1/x

Then plug expansion into the integral and obtain