How to prove that the following integral doesn't converge? $$\int_0^\infty \frac{1}{(\ln^4x + \ln^2x)\ln^2(1-x^{1/3})^2(x + \sqrt{x} + 1)}dx$$
I suppose it doesn't converge because of quick growth rate of function at $x = 0$, but I can't prove that.
2026-05-14 03:45:09.1778730309
Does the integral converge
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Hint: $0$ is not the problem for convergence. Consider what's happening at $1$ instead.