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Trig substitution integral

  1. Feb 3, 2010 #1
    1. The problem statement, all variables and given/known data
    evaluate the integral using the indicated trig substitution. sketch the corresponding right triangle.

    integral of(1/(x^2 sqrt(x^2 - 9))

    2. Relevant equations

    integral of(1/(x^2 sqrt(x^2 - 9))

    3. The attempt at a solution
    at first glance this seemed really easy, and i tried doing it without the given trig substitution of 3sec(theta), but i just got confused. i made the triangle with 3 on the hypotenuse and x on the leg opposite theta. then i said x = 3sin(theta) (because i have a value for the hypotenuse and the opposite) and from there i have no idea what to do. Also, im discouraged because the book tells you to use 3sec(theta) which is driving me insane because i have no idea why i would use sec at all. thanks for you help.
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Feb 3, 2010 #2
    The hint is infact very useful.

    you have:


    using the substitution x = 3sec[tex]\theta[/tex]
    you will get a simple integral.

    substitute this into the integral. BUT... you have to first find dx/d[tex]\theta[/tex] in order to substitute something for dx (in terms of d[tex]\theta[/tex])

    so after the substitution, what do you get?
    (You might like to remember also the identity (sec[tex]\theta[/tex])^2-1=tan([tex]\theta[/tex])^2)
  4. Feb 3, 2010 #3


    Staff: Mentor

    Since the radical contains x2 - 9, you want x on the hypotenuse and 3 on one leg, and sqrt(x2 - 9) on the other leg.
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