Does $$\int_0^1 \sqrt[3]{\ln\left(\frac{1}{x}\right)} \mathrm{d}x$$ converge? WA says it is equal to $\Gamma(4/3)$, however calculating the antiderivative seems approachless to me and can't compare to other functions. I would appreciate any help. Thanks.
2026-05-14 17:50:39.1778781039
Convergence of $\int_0^1 \sqrt[3]{\ln(1/x)} \mathrm{d}x $
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Hint: Substitute $x=e^{-t}$ in the integral. You should end up with
$$\int_0^{\infty} dt \, e^{-t} \,t^{1/3}$$