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Math Help - Integrate this using partial fraction

  1. #1
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    Integrate this using partial fraction

    how do i integrate this

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

    I have to split this into partial fraction but I don't know how

    \frac{1}{(3x^2-1)^2(1-x^2)} =\frac{Ax+B}{(1-x^2)} + \frac{Cx+D}{(3x^2-1)^2}?
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by charikaar View Post
    how do i integrate this

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

    I have to split this into partial fraction but I don't know how

    \frac{1}{(3x^2-1)^2(1-x^2)} =\frac{Ax+B}{(1-x^2)} + \frac{Cx+D}{(3x^2-1)^2}?
    Note that 3x^2-1=\left(\sqrt{3}x-1\right)\left(\sqrt{3}x+1\right) and 1-x^2=\left(1-x\right)\left(1+x\right).

    So we have \frac{1}{\left[(\sqrt{3}x+1)(\sqrt{3}x-1)\right]^2(1+x)(1-x)}=\frac{A}{\sqrt{3}x-1}+\frac{B}{(\sqrt{3}x-1)^2}+\frac{C}{\sqrt{3}x+1} +\frac{D}{(\sqrt{3}x+1)^2}+\frac{E}{1+x}+\frac{F}{  1-x}

    This is going to get quite messy...feel free to post back when you get stuck!
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