Evaluate the following integral from 0 to infinity

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SUMMARY

The integral evaluated from 0 to infinity, represented as ∫(e^(-ax) - e^(bx)) / x dx, is discussed with the conditions a, b > 0 and a < b. Participants suggest exploring residue calculus for evaluation, although some have not yet learned this technique. The possibility of using integration by parts is also considered as an alternative method for solving the integral.

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  • Introduction to complex analysis concepts, particularly residue calculus
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Evaluate the following integral from 0 to infinity. (see attached for better picture)

e^(-ax)-e^(bx)
------------------ dx
x

Remarks:

a , b > 0
a < b
 

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Have you tried residue calculus?
 


No, we have not learned how to calculate integrals with residue calculus just yet.

Do you think it's possible with integration by parts?
 

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