Talk:Definite Integral to Infinity of Exponential of -a x by One minus Cosine x over x Squared

Possible mistake in Schaum
Schaum claims that:


 * $\ds \int_0^\infty \frac {e^{-a x} \paren {1 - \cos x} } {x^2} \rd x = \arccot a - \frac a 2 \map \ln {a^2 + 1}$

This is "obviously" wrong since for sufficiently large $a$, the LHS is positive and the RHS is negative, and the graphs on Desmos don't seem to align at all. (but they do with the $a \ln a$ term)

Could someone give a quick look over to make sure I haven't made a mistake? Caliburn (talk) 11:12, 6 August 2020 (UTC)


 * It wouldn't be the first mistake found in a Schaum manual. Even as an undergraduate we were warned not to take any result in one of those books as true without checking it.


 * I'll take a look at it in due course, probably over the weekend, unless someone gets there first. --prime mover (talk) 18:04, 6 August 2020 (UTC)