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Examine the integrals below. Consider the multiple tools available for integrating and use the best strategy for each part. Evaluate each integral and briefly describe your method.

  1. This is an improper integral because has a vertical asymptote at .

    Rewrite properly (with limits) before evaluating.

  1. Use integration by parts after you rewrite the integrand as .
    Let and .
    Then and .
    Warning: You will have to use -substitution to evaluate the integral.