Improper Integrals Question

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Explain why the integral is improper and determine whether it diverges or converges. Evaluate the integral if it converges.

integral (1 / ((x-3)^3/2)) dx

Determine whether the improper integral diverges or converges. Evaluate the integral if it converges.

integral xe^(-x/2) dx

integral (x^3 / (x^2 + 1)^2) dx

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