Infinite Serieshard
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Apply the Integral Test to n=2n(n2+1)ln(n2+1)\sum_{n=2}^{\infty} \frac{n}{(n^2+1) \ln(n^2+1)}. Evaluate the improper integral 2xdx(x2+1)ln(x2+1)\int_2^{\infty} \frac{x \, dx}{(x^2+1) \ln(x^2+1)} and determine convergence.