Integration of exponentials with a fractional power?

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Discussion Overview

The discussion revolves around the integration of exponential functions with fractional powers, specifically focusing on the expression e^(-t/T). Participants seek clarification on the rules and methods applicable to such integrals.

Discussion Character

  • Exploratory, Technical explanation, Homework-related

Main Points Raised

  • One participant requests an explanation of the integration rule for exponentials with fractional powers, specifically e^(-t/T).
  • Another participant asks for clarification on the variable of integration.
  • A third participant suggests that the integration may involve a simple substitution, proposing u = t/T and providing the corresponding differential relationship.
  • A comment highlights a concern regarding the sharing of document files, suggesting that direct answers are preferable.

Areas of Agreement / Disagreement

The discussion does not appear to reach a consensus, as participants are still exploring the integration method and clarifying the context of the problem.

Contextual Notes

There is an assumption about the variable of integration that remains unaddressed, and the discussion does not clarify the specific conditions under which the proposed substitution would be valid.

jamesd2008
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Could anyone explain to me the rule when Integrating of exponentials with a fractional power?

e.g. ue to the power of -t/T. ue^-t/T

Thanks in advance
 
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jamesd2008 said:
Could anyone explain to me the rule when Integrating of exponentials with a fractional power?

e.g. ue to the power of -t/T. ue^-t/T

Thanks in advance
Welcome to PF,

What are we integrating with respect to?
 
Think it is this,
 

Attachments

Many people will not open "doc" files because they are notorious for viruses. Please just answer the question.

It looks to me like this just requires a simple substitution. Assuming you are integrating with respect to t, to integrate e^(t/T), let u= t/T. Then du= dt/T or dt= du/T.
 

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