Why is $x^a \sin(x)$ Lebesgue-integrable on $[0,\infty[$? It's obviously measurable, so why $\int |f|<\infty$... You can divide the integral by the period of sine, but I don't know how to cope with $x\to0$...
EDIT: $-2<a<-1$
2026-04-02 11:06:03.1775127963
Lebesgue integrability of $x^a \sin(x)$ on $[0,\infty[$
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