Evaluate the following integral:

  1. Let
    and let

  2. Hence,
    and let

  3. Using the formula for integration by parts

    we get

  4. Now we can use integration by parts again to compute the following integral

  5. Let
    and let

  6. Hence,
    and let

  7. Finally we get

  8. We can now use the above result to finish solving the problem:

  9. It is easy to see that the integral obtained ( marked in red ) is the same as the original integral. Let us combine both integrals on the left hand side:

  10. Acknowledgment: The java applet which is used on this page to display the equations in the discussion above is HotEqn from the Virtual Control Lab.

    This page and the javascript used on this page was written by Marek Szapiel.