What is $$\int_0^\infty e^{-t}\log tdt?$$
Plugging into Wolfram Alpha yields that it's $-\gamma$, where $\gamma$ is Euler's constant. How can we get it? Maybe by some contour integration?
Asked
Active
Viewed 147 times
3
-
1http://en.wikipedia.org/wiki/Euler-Mascheroni_constant will explain where this constant appears (a lot of places). – Claude Leibovici Nov 30 '13 at 07:42
-
Take a look at the right hand side of the page, under Related, and you'll see there several questions asking the exact same thing you're asking. Click on them, and read their answers. – Lucian Nov 30 '13 at 08:22