Integration of exponentials with a fractional power?

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SUMMARY

The discussion focuses on the integration of exponential functions with fractional powers, specifically the function e^(-t/T). The key method for integrating this function involves a substitution technique where u = t/T, leading to du = dt/T. This substitution simplifies the integration process, allowing for a straightforward calculation of the integral with respect to t.

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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,
 

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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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