Determine the positive values of p for which the following integral converges and those for which it diverges:
integral from 3 to infinite of: [(x^(2p))*sqrt(2x +7) + 3] dx / [(x^(7p/4) +2)*sqrt(x^(3p) + 2)]
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Hmm... Treat the integrand as a series and see if this gives you any intuition through rational equations.