Evaluate the following integral from 0 to infinity

[mrdad123]

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

 

[hunt_mat]

Have you tried residue calculus?

 

[mrdad123]

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

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