If we consider the integral , it is once seen to be an infinite and improper integral. This integral is infinite because the upper limit of integration is infinite and it is improper because is a point of infinite discontinuity of the integrand, if , where is either real number or real part of a complex number. This integral is known as Euler’s Integral. This is of a great importance in mathematical analysis and calculus. The result, i.e., integral, is defined as a new function of real number , as .