Will it converge?

Calculus Level 3

Which of the following integrals converge?

I. \(\displaystyle{\int_0^\infty \frac{\ln(x)}{x^2 + 1} \, dx}\)

II. \(\displaystyle{\int_1^\infty \frac{1}{(x-1)^2} \, dx}\)

III. \(\displaystyle{\int_0^{\pi/2} \sqrt{\tan(x)} \, dx}\)

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