一个反常积分估计式

An Estimate of an Improper Integral

类比于反常积分∫0+∞sit/tdt=2π,对积分∫x+∞cost/tdt做出估计.当x>0时,有∫+x∞cost/tdt=ln1/x-γ+o(x),其中γ为Euler常数.

Compared with the improper integral∫0^＋∞t/sintdt=π/2,we establish the following ∫0^＋∞t/costdt=ln1/x-＋0（x）where γ is Euler＇s constant.