How Can I Solve the Integration of (e^-x)/x Using Series?

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Discussion Overview

The discussion centers around the integration of the function \(\frac{e^{-x}}{x}\), exploring methods to solve this integral, including the potential use of series expansions and integration techniques. The conversation includes attempts to apply integration by parts and considerations of the limitations of these methods.

Discussion Character

  • Exploratory
  • Technical explanation
  • Homework-related

Main Points Raised

  • One participant asks how to solve the integral \(\int \frac{e^{-x}}{x} dx\).
  • Another suggests using integration by parts, but expresses doubt about its effectiveness.
  • A participant mentions that integration by parts may not lead to a solution in terms of elementary functions.
  • Some participants propose repeatedly applying integration by parts, but note that this leads to complications such as natural logarithms or higher-order terms.
  • A link to the Wikipedia page on the exponential integral is shared as a potential resource.
  • One participant claims to have solved the problem using series methods, although details are not provided.
  • There are multiple requests for assistance and expressions of frustration regarding the inability to find a solution.

Areas of Agreement / Disagreement

Participants express uncertainty about the effectiveness of integration by parts for this integral, with some suggesting it may not yield a solution in elementary terms. There is no consensus on a definitive method to solve the integral, and multiple approaches are discussed without resolution.

Contextual Notes

Some participants indicate that the problem may not be solvable using standard techniques, and the discussion includes references to series solutions, but these are not elaborated upon.

Who May Find This Useful

This discussion may be of interest to students or individuals seeking to understand advanced integration techniques, particularly in the context of special functions and series expansions.

ريمان
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how I can slove this intergation

((e)^-x)\x)

tank you
 
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what have you tried?

[tex]\int \frac{e^{-x}}{x}[/tex]? use integration by parts.
 
tank you master courtrigad

I tray but I don't get it

tank you
 
Let [tex]u = e^{-x}[/tex] and [tex]dv = \frac{1}{x}[/tex]
 
courtrigrad said:
Let [tex]u = e^{-x}[/tex] and [tex]dv = \frac{1}{x}[/tex]

That won't get you very far in evaluating the integral, I don't think parts will at all, I think I remember a post from a while ago that this can't be integrated in terms of elementary functions.
 
just do it multiple times
 
courtrigrad said:
just do it multiple times

And it still won't work very well, if you let dv=1/x then you get a natural log that will make things messy, and if you let u=1/x then you'll just get e-x/x2, e-x/x3 etc..
 
hi

and whit is the soultions

tank you
 
  • #10
hi

is there anybody can solve this proplem
 
  • #11
hi

waher is smart people in math

any genis here
 
  • #12
Just for your reference, ريمان, the people who help out here aren't here to do the problem for you or give you the answer outright. We'll just point you in the right direction/ correct what you did wrong and give you a boost. Please respect that.
 
  • #13
ريمان said:
how I can slove this intergation

((e)^-x)\x)

tank you
قبل ما تسءل٬ جرب ال سؤ ال
هذا السؤال لا تقدر أن تكمله

I think that was a little clearer.. :P My written Arabic's a little rusty though.

Taylor Series Solution بس تقدر تعمل
 
Last edited:
  • #14
hi اهلاً

I'm solve this problem befor some days by Series

are you know arabic
 
  • #15
ريمان said:
hi اهلاً

I'm solve this problem befor some days by Series

are you know arabic
ا, بس ما بعرف لغة الفصحى
 

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