Integral of an exponential function

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Homework Help Overview

The discussion revolves around solving an integral involving an exponential function, specifically focusing on integration techniques applicable to the problem presented in an image link.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the use of integration by parts and question the implications of their chosen substitutions. There is also a consideration of convergence related to the integral.

Discussion Status

The conversation includes various suggestions for approaches, such as integration by parts, and participants are exploring different interpretations of the integral's behavior. There is no explicit consensus, but guidance on potential methods has been provided.

Contextual Notes

Some participants note the importance of checking convergence, indicating that this aspect is under consideration in the context of the integral being discussed.

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Homework Statement



Hey guys.

How do I solve this integral?

http://img816.imageshack.us/img816/208/68315659.png

I've not been doing this for a long time :)

Thanks a lot.


Homework Equations





The Attempt at a Solution

 
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Show some work, and explain what tools you have to work with. Definite integrals can be computed in many ways.
 


You can use integration by parts. Using u = e^-t and dv = t^-2 dt
 


JetteroHeller said:
You can use integration by parts. Using u = e^-t and dv = t^-2 dt

Yeah, but then I'll get some kind of Ln(t)*e^-t, no?
 


Actually you may want to check convergence.
 


I was actually thinking:
you perform integration by parts once to reduce t^2 to t.
Result is that one of the terms is integral((e^-t)/t)
Rewrite that term to become integral(1/te^t)

use the following identity from integral tables: integral(ue^u) = (u-1)e^u
the rest is taking limits.
 

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