Physicist here. I am trying to rigor up some naive steps in my computations. Consider the following $$ \lim_{\delta\to0}\int_{\delta}^adx\,\frac{\cos(bx)-1}{x^{3/2}\log\frac{1}{x}} $$ where $1>a>0$ and $b>0$. I know that we can Lebesgue integrate all Riemann integrable functions, but the one above is an improper integral. Can we still see it as a Lebesgue integral? if so, why?
2026-04-09 04:03:02.1775707382
Can the following improper integral be seen as a Lebesgue integral?
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