calculus

Calculate the following integral:

∫ dx / x(1 - √x)^2

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  1. I bailed out after whole page of messy attempts using integration by parts.

    http://integrals.wolfram.com/index.jsp?expr=1%2F%28x%281-x%5E%281%2F2%29%29%5E2%29&random=false

    Wolfram's answer assumes that log x is ln(x)

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  2. hmmm. Doesn't look too bad.
    u = 1-√x
    x = (1-u)^2
    dx = -2(1-u) du

    dx/(x(1-√x)^2)
    = -2(1-u) du / ((1-u)^2 * u^2)
    = -2 /((1-u)*u^2) du
    = -2/u^2 -2/u + 2/(u-1) du
    = 2(1/u + ln(1-u) - ln(u))

    Now substitute u = 1-√x to get back to x

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  3. Thanks Reiny and Steve. Now to pass the exam!

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