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Math Help - Integral

  1. #1
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    Integral

    Integral

    ∫[(x-1)^(-3/2) ][(2-x)^(-1/2)]dx
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  2. #2
    Math Engineering Student
    Krizalid's Avatar
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    Hey galactus

    It should be -\frac32 from the beginning
    Last edited by Krizalid; December 20th 2007 at 10:06 AM.
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  3. #3
    Eater of Worlds
    galactus's Avatar
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    Let's try this again.

    \int\frac{1}{(x-1)^{\frac{3}{2}}\sqrt{2-x}}dx

    Let u=\sqrt{2-x}, \;\ 2-u^{2}=x, \;\ -2udu=dx

    Make the subs and get:

    -2\int{(1-u^{2})^{\frac{-3}{2}}}du

    Let u=sin{\theta}, \;\ du=cos{\theta}d{\theta}

    -2\int{(1-sin^{2}{\theta})^{\frac{-3}{2}}cos{\theta}}d{\theta}

    -2\int{sec^{2}{\theta}}d{\theta}

    -2tan{\theta}

    Resub:

    -2tan(sin^{-1}u)

    \frac{-2u}{\sqrt{1-u^{2}}}

    Resub:

    \boxed{\frac{-2\sqrt{2-x}}{\sqrt{x-1}}}
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