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Math Help - partial fractions decomposition problem

  1. #1
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    partial fractions decomposition problem

    can someone solve

    ∫ (4dx)/(x-2x-3)

    i don't think this equation diverges i think the denominator is 10 and not 4 but i am not sure
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  2. #2
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    Quote Originally Posted by cummings15 View Post
    can someone solve

    ∫ (4dx)/(x-2x-3)

    i don't think this equation diverges i think the denominator is 10 and not 4 but i am not sure
    \frac{4}{(x+1)(x-3)} = \frac{A}{x+1} + \frac{B}{x-3}

    4 = A(x-3) + B(x+1)

    let x = 3 ... B = 1

    let x = -1 ... A = -1

    \frac{4}{(x+1)(x-3)} = \frac{1}{x-3} -\frac{1}{x+1}

    now you can integrate the right side ...
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  3. #3
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    Quote Originally Posted by cummings15 View Post
    can someone solve

    ∫ (4dx)/(x-2x-3)

    i don't think this equation diverges i think the denominator is 10 and not 4 but i am not sure
    \frac{4}{x^2-2x-3} = \frac{4}{(x+1)(x-3)}

    Now find A and B such that \frac{4}{(x+1)(x-3)} =\frac{A}{x+1} +\frac{B}{x-3}
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  4. #4
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    would it be

    4ln l(x-3)(x+1)l +c
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  5. #5
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    No. Skeeter had already worked out that the coefficients A and B are 1 and -1 so the integral is 4(ln|x-3|- ln|x+1|)+ C.
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  6. #6
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    so then i can distribute and get

    4ln l(x-3)(x+1)l + C
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