Will it converge?

Calculus Level 3

Which of the following integrals converge?

I. ∫0∞ln⁡(x)x2+1 dx\displaystyle{\int_0^\infty \frac{\ln(x)}{x^2 + 1} \, dx}

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

III. ∫0π/2tan⁡(x) dx\displaystyle{\int_0^{\pi/2} \sqrt{\tan(x)} \, dx}

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Henry Maltby by Henry Maltby
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