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Which of the following integrals converge?
I. ∫0∞ln(x)x2+1 dx\displaystyle{\int_0^\infty \frac{\ln(x)}{x^2 + 1} \, dx}∫0∞x2+1ln(x)dx
II. ∫1∞1(x−1)2 dx\displaystyle{\int_1^\infty \frac{1}{(x-1)^2} \, dx}∫1∞(x−1)21dx
III. ∫0π/2tan(x) dx\displaystyle{\int_0^{\pi/2} \sqrt{\tan(x)} \, dx}∫0π/2tan(x)dx
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