Finding convergence or divergence of an integral?

Hello, I've been really struggling on determining the convergence/divergence of this integral with strong evidence. I have to use a test of some sort to show evidence, such as the Integral Test, but I have been having troubles deciding if this test is the best... If there's anyone good with Calc II, I could really use some guidance. This is the last problem on my homework set that I am stuck on.

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