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Question about Improper Integrals

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Please see the attached file for the fully formatted problems.

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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Solution Summary

Improper integrals are investigated. The solution is detailed and well presented.

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