# KH and Riemann integrals example

I am looking for examples that demonstrate how the KH integral is more "powerful" than the Riemann integral (i.e. can integrate more functions than the Riemann integral). For example, $1/\sqrt{x}$ is not Riemann-integrable on $[0,1]$, but is KH-integrable. However, this function can be handled easily as an improper integral. What would be examples of functions that are KH-integrable yet cannot be handled even as improper (Riemann) integrals?

• It doesn't seem very different to the Riemann-Stieltjes integral – reuns Aug 21 '17 at 1:23
• @reuns - what do you mean? – Frank Aug 23 '17 at 22:46
• That the KH integral isn't so common, while you'll find many results about the Riemann-Stieltjes integral – reuns Aug 23 '17 at 22:52