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Math Help - Integration by partical fractions

  1. #1
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    Integration by partical fractions

    I have the following integral to evaluate and determine the values for A and B

    x + 1 / (x + 2) (x - 3) so I would have

    A/(x + 2) and B / (x-3) therefore


    x + 1 = A(x-3) + B (x+2)

    Equating the coefficients:
    A + B = 1

    -3A + 2B = 1

    THe answer the sample test gives for A is 1/5 !!! I could understand this if it were 3A not -3A Can someone please tell me am I going crazy or did the teacher make a mistake in the orginal problem and it should read

    x + 1/ (x +2)(x+3)????????? Please help THanks much
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  2. #2
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    A + B = 1 \: \: \iff \: \: A = 1 - B

    Substitute:
    -3(1-B) + 2B = 1
    -3 + 3B + 2B = 1
    5B  = 4
    B = \frac{4}{5}

    Plug back into your first equation:
    A + \left(\frac{4}{5}\right) = 1
    A = 1 - \frac{4}{5} = \frac{1}{5}
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