can any one explain why this integral diverges ?

Question

integration of [(e^(-sqrt(t)))/sqrt(t)]dt from 0 to infinity

thanks

Answer 1

let u= sqrt(t)
du= 1/2sqrt(t) dt
dt= 2u du

int e^-u * 1/u * 2u du=2 int e^-u du

= -2e^-u eval 0 to inf= 2

check my thinking.

Answer 2

yeah the integration is right

but I was meaning that the integral is improper i.e. the function is not continuous at 0 neither at inf

so how could we evaluate the integration?

thanks for ur reply