Question: so I have integrated the function ln(n)/3n and I got 1/6 times ln^2(n) and now I don't know how to tell why this means the

so I have integrated the function ln(n)/3n and I got 1/6 times ln^2(n) and now I don't know how to tell why this means the series is divergent. can you explain how by using the integral test, after integrating it you should know if it is convergent or divergent?

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