Hello, question: does the integral [tex]\int_0^\infty \frac{\sin(x)}{x^a}[/tex] converge (in the sense of Lebesgue principal value) for all [tex]a \in (0;2)[/tex]? For a=1/2, it's the Fresnel integral, but other than that, I'm not sure how to approach this.(adsbygoogle = window.adsbygoogle || []).push({});

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# Integrability of sin(x)*x^(-a)

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