Can I Integrate e^[1 / (1 + t)] dt Numerically?

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Discussion Overview

The discussion revolves around the numerical integration of the function e^[1 / (1 + t)] dt. Participants explore the challenges of finding an anti-derivative for this function and draw comparisons to other integrals.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested, Mathematical reasoning

Main Points Raised

  • One participant inquires about how to integrate e^[1 / (1 + t)] dt.
  • Another participant asserts that the function does not have a nice anti-derivative and suggests numerical integration as a solution.
  • There is a comparison made to the integral of (sinx / x) dx, indicating a potential similarity in the lack of a simple anti-derivative.
  • A participant provides a more complex expression involving the exponential integral function (Ei) as a long answer to the integration question.
  • Further discussion touches on the relationship between the exponential integral (Ei) and the sine integral (Si), suggesting a deeper connection between these functions.
  • Participants express varying opinions on the brevity of the answers provided, with some suggesting that the short answer may not fully capture the complexity of the problem.

Areas of Agreement / Disagreement

Participants generally agree that numerical integration is the appropriate approach due to the absence of a simple anti-derivative. However, there are differing views on the complexity of the integration process and the adequacy of the answers provided.

Contextual Notes

The discussion includes references to specific mathematical functions and integrals, but does not resolve the underlying complexities or assumptions related to the integration of the given function.

irony of truth
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How do I integrate this? e^[1 / (1 + t)] dt?
 
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Short answer: Numerically.
There exist no nice anti-derivative to this function.
 
I see... so this could be the same case as that of (sinx / x) dx...
 
Long answer:
[tex]\allowbreak \left( 1+x\right) e^{\frac 1{1+x}}+\func{Ei}\left( 1,-\frac 1{1+x}\right) +C[/tex]

Daniel.
 
irony of truth said:
I see... so this could be the same case as that of (sinx / x) dx...

Yes,there is a connection between Ei (exp.integral) and Si (sinus integral).

Daniel.

P.S.Chack the wolfram site for more.
 
dextercioby said:
Long answer:
[tex]\allowbreak \left( 1+x\right) e^{\frac 1{1+x}}+\func{Ei}\left( 1,-\frac 1{1+x}\right) +C[/tex]

Daniel.
I'd rather say apparently short answer..
 
Yes,"apparently" is a well placed word...:wink:

Daniel.

P.S.Anyways,the # of characters from the code is much bigger than the # of letters from "numerically"...
 

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