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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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Take a look at this wolframalpha.com/input/… – Norbert May 25 '12 at 12:09
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I downvoted because "I need it as soon as possible" is not what I want to see on this site. – Asaf Karagila May 25 '12 at 12:09
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Bassem, welcome to Math.SE. Whenever you ask a question please provide as much info as possible on what you have done, where you got the problem from etc. Also, try to be polite - people are here to help you and are often willing to do so. – AD. May 25 '12 at 12:20
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@Asaf: Maybe you regard OP's "I need it as soon as possible" as a claim that we have to answer his question asap. I regard it as the need OP have and don't assume he thinks I have to do anything. All in all, I think that before downvoting the question, such comment as AD should be better appreciated. – Ilya May 25 '12 at 12:23
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@Asaf: I certainly agree to disagree and I do respect your point of view. Just wanted to warn you about cascades of downvoters caused by a 1st downvote to questions of new users, asked not in the lines of MSE. Challenge to outrace is accepted, but I won't take it serious, so most likely you win :) anyway, I respect your point of view and don't want to convince you I'm right. – Ilya May 25 '12 at 12:48
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1 Answer

up vote 5 down vote

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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What's $\Gamma(0,x)$? Is it the same as $\Gamma(x)$? – Stefan Smith May 26 '12 at 1:23
@user20520 If you enter the code I suggested, you'll see that $\Gamma(a,x)$ refers to the incomplete Gamma function and you'll see pointers to more information. – Mark McClure May 26 '12 at 1:46
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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. – Bassem May 30 '12 at 20:12
@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. – Mark McClure May 30 '12 at 20:24

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