I recall having done this integral a long time ago, but I can't remember how I actually did it. Does anyone have any ideas? Anything (for example contour integration) goes, but I'd prefer an elegant change-of-variables method. The integral in question is
$I(v,w) = \int_{\mathbb{R}^+} \frac{ds}{s} \left[e^{-vs} - e^{-ws} \right] = \int_{\mathbb{R}^+} \frac{ds}{s} \left[e^{-s} - e^{-(w/v)s} \right].$
for $v,w \geq 0.$
Wolfram Alpha doesn't immediately recognize it, but I believe that the answer is proportional to $\ln(w/v).$ Thanks in advance!