13
$\begingroup$

Today I had an exam and I mixed up the integration by parts formula. The question was to integrate $$ \int\nolimits_0^\infty \frac{e^{-at} - e^{-bt}}{t} \text{d}t $$

I will try solve this again with the right formula when I arrive home. I would appreciate if somebody could tell me the solution so I can double check and maybe give a hint to another way of solving this instead of integration by parts (if possible).

  • 2
    Hint: Write the integrand as an integral over [a,b], then switch the order of integration.2011-09-06
  • 0
    I actually asked this question a couple of weeks ago: http://math.stackexchange.com/questions/56304/integrate-difference-of-exponentials2011-09-06
  • 0
    I guess this is a duplicate then, but @Ragib's answer is different (from robjohn's) and also nice.2011-09-06
  • 0
    [Another related question.](https://math.stackexchange.com/questions/61828)2017-10-31

2 Answers 2