Simply this exponential integral

Question

I am trying to simplify of this:

$$\int_{0}^{\infty} \frac{1-e^{-x}}{x}e^{-\lambda x}\,dx.$$

Maybe I should separate these equation into two exponential integral function? But it will ended up with infinite minus infinite? please give me some help or advices, thanks!

I haven't tried it but you probably can separate the integral into two indefinite integrals, and evaluate them separately — john, Oct 12 '15 at 06:01

John Dawkins · Accepted Answer · 2015-10-11T17:36:55.797

2

Write ${1-e^{-x}\over x}$ as $\int_0^1 e^{-tx}\,dt$, reverse the order of integration in the resulting double integral, then integrate.

edited Oct 11 '15 at 17:36

answered Oct 11 '15 at 16:53

John Dawkins

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Yes, thanks! Now fixed. – John Dawkins Oct 11 '15 at 17:37
thanks a lot! I really appreciate that! – KennyYang Oct 12 '15 at 06:03

Simply this exponential integral

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