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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. Use integration by parts.
    Let and .

  1. Use substitution.
    Let .

  1. 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.

  1. Review the first Fundamental Theorem of Calculus.