find-f-t-0-e-x-ln-1-e-tx-dx-with-t-gt-0-2-let-u-n-0-e-x-ln-1-e-nx-dx-find-lim-n-u-n-

Question Number 37243 by math khazana by abdo last updated on 11/Jun/18

f i n d f (t) = \int_{0}^{\infty} e^{x} l n (1 + e^{- t x}) d x w i t h t > 0 .

2) l e t u_{n} = \int_{0}^{\infty} e^{x} l n (1 + e^{- n x}) d x

f i n d {l i m}_{n \to + \infty} u_{n} .