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I have a problem with getting the exact value of this integral : $\int_{x}^{+\infty}\frac{e^{-t}}{t}dt$

Any help would be much appreciated.

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    Thank you for you remarks. I am really sorry for let you feel that i am not polite. But, it s juste my first time to post on.2012-05-30

1 Answers 1

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Did you try WolframAlpha?

integrate e^(-t)/t, t=x..infinity 

yields $\log (x)+\Gamma (0,x)$ for $x>0$. When a result is specified in terms of a special function like this, it's probably not exactly computable. Nonetheless, you can generate numerical approximations easily enough.

log(x) + gamma(0,x) at x=3 

or look at a plot

plot log(x) + gamma(0,x) 

enter image description here

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    @Bassem No, no, not at all! I just think that it is generally useful to point out to someone how they might find things out for themselves in the future - and I'm certainly not one of the downvoters of the question, either.2012-05-30