Evaluate the following integral from 0 to infinity

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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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