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Examine the integrals below. Consider the multiple tools available for integrating and use the best strategy. After evaluating each integral, write a short description of your method.

  1. Use integration by parts.
    Let and .

  2. Use substitution.
    Let .

  3. You should recognize the integrand as the derivative of an inverse trigonometric function.

    This is an improper integral, so a limit will need to be used to evaluate it.
    The symmetry of the graph can also be used to evaluate the integral.

  4. Review the first Fundamental Theorem of Calculus.