$$f(t)=\int_{0}^{+\infty}\sin(x^t) \ dx, t\in\mathbb{R}$$
I need to find out for which $t \in \mathbb{R}$ this integrals exists (meaning it doesn't diverge) as Riemann-integral at first and then as Lebesgue-integral.
2026-03-26 16:07:10.1774541230
$t \in \mathbb{R}$ s.t. $f(t)=\int_{0}^{+\infty}\sin(x^t) \ dx, t\in\mathbb{R}$ exists
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