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Thread: Find all primitives to root fraction

  1. #1
    Junior Member TriForce's Avatar
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    Find all primitives to root fraction

    Find all primitives to f(x) by using substitution:
    $$t=\sqrt(\frac{x-1}{x+1})$$
    $$f(x)=\int\frac{3}{(x+1)^2}\sqrt(\frac{x-1}{x+1})dx$$

    I have problem finding dt and dx.
    Last edited by TriForce; Mar 13th 2018 at 06:07 AM.
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  2. #2
    MHF Contributor
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    Re: Find all primitives to root fraction

    $t = \sqrt{\dfrac{x-1}{x+1}}$

    $dt = \dfrac{1}{2}\left( \dfrac{x-1}{x+1} \right)^{-1/2}\dfrac{2}{(x+1)^2}dx$

    So, you wind up with:

    $\displaystyle \int 3t^2dt$
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  3. #3
    Junior Member TriForce's Avatar
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    Re: Find all primitives to root fraction

    Nice, just figured out how you did it.
    Last edited by TriForce; Mar 13th 2018 at 06:39 AM.
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