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12-21.

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. Use integration by parts. Let and .
    Then and .

    Use integration by parts on the integral in Step 2.
    Let and .
    Then and .

    Use algebra to get the original integral expression by itself.

  1. Use partial fraction decomposition.

  1. Rewrite the denominator of the integrand using Steps 1 and 2.
    You should recognize the integrand as a form of the derivative of a special function.