When I saw $$\int_0^\infty\frac{|\sin t|}{t}\;dt$$ integral I remembered Laplace transform and complex analysis but I couldn't find anything. Is this integral bounded (convergent) and if it is what is it's value? I cannot do anything.
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1This integral diverges, as you can see from $\int_0^\infty \frac{|\sin(x)|}{x}\ge \sum_{k=0}^\infty\frac{1}{(k+1)\pi}\int_{k\pi}^{(k+1)\pi}|sin(x)|dx=\frac{2}{\pi}\sum\frac{1}{k+1}=\infty$ – Apr 07 '20 at 13:30
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1See this question – MPW Apr 07 '20 at 13:31