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I have to calculate an integral from x0 > 0 to infinity of a function like ln (F(x)) / x where F(x) is a function which tends to 1 for x going to infinity. Since the integrand goes to zero very slowly, I am trying to calculate the asymptotic expansion of the integral by taking the power series of the integrand and integrating term by term. Unfortunately F(x) is a very messy function, so it's difficult to do the calculations by hand. What is the best way of using Mathematica for this type of calculation? Thanks.