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Homework Help: I have problems with integrating this

  1. Oct 8, 2006 #1
    I have problems with integrating this... :(

    [tex]
    \int_{0}^{x}\frac{1}{\sqrt{a^2 - b/x}}dx
    [/tex]

    I have tried substituting 1/x with u and so on... But it doesn't seem to work :(

    Thanks in advance!
     
  2. jcsd
  3. Oct 8, 2006 #2

    acm

    User Avatar

    1/Sqrt(a^2 - b/x)
    1/sqrt(a^2x - b)/Sqrt(x)
    Sqrt(x)/ Sqrt(a^2x - b)
    Let u = a^2x - b
    du/dx = a^2
    du/a^2 = dx
    u+b/a^2 = x
    Integral becomes - (1/a)Sqrt(u+b) * 1/Sqrt(u) * du/a^2
    1/a^3 + 1/a^3sqrt(b/a) du
     
  4. Oct 8, 2006 #3
    Thank you :)

    (By the way, I think you meant 1/a^3[sqrt((u+b)/u)] for the last part, right?)
     
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