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Working problem 3 ways

  1. Jun 26, 2005 #1
    I have to work this problem 3 ways, and I've gotten two, but am not sure about the third way.

    integral (x/sqrt(x^2-9))dx
    the first way I worked by setting u = x^2 - 9
    the second way I worked by setting x = 3sec(theta)
    but the third way I have no clue, the book gave us a hint: Let x^2 - 9 = (sin(theta))^2

  2. jcsd
  3. Jun 26, 2005 #2
    Do exactly what you did with x = 3sec(theta), but this time with the identity x^2 - 9 = (sin(theta))^2.

    x = sqrt((sin(theta)^2)+9);
    dx = sin(theta)cos(theta)(((sin(theta)^2)+9)^-.5) d(theta)

    Plug that in (and the x^2 value) and solve; you answer should come up to be sin(theta) + C. Then all you need to do is change back in terms of x.
    Last edited: Jun 26, 2005
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