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Math Help - partial fraction

  1. #1
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    partial fraction

    integral ( (2x^{2}-x-20) / (x^{2} + x - 6) dx

    since the powers from the demon and numer are the same, i have to divide...
    got it to be 2 remainder -3x-8
    so:
    -3x-8 / (x+3)(x-2) = A/(x+3) + B/(x-2)
    =
    -3x-8 = A(x-2) + B(x-3)

    plugged in 2 for x: B = -11/5
    plugged in -3 for x: A = -1/5

    int (-1/5)/(x+3) + int (-11/5)/(x-2)
    =
    (-1/5)ln|(x+3)| - (11/5)ln|(x-2)| +C

    i got that to be the answer, but its wrong. can someone explain what i am doing wrong?
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  2. #2
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    well i redid it got:

    B = -14/5
    A = -1/5

    int (-1/5)/(x+3) + int (-14/5)/(x-2)
    =
    (-1/5)ln|(x+3)| - (14/5)ln|(x-2)| + C

    answer is still wrong.
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  3. #3
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    earboth's Avatar
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    Quote Originally Posted by viet View Post
    well i redid it got:

    B = -14/5
    A = -1/5

    int (-1/5)/(x+3) + int (-14/5)/(x-2)
    =
    (-1/5)ln|(x+3)| - (14/5)ln|(x-2)| + C

    answer is still wrong.
    Hi,

    remember the division had a result which you have forgotten to use:

    int((2x-x-20)/(x+x-6))dx = int(2 + (-1/5)/(x+3) + (-14/5)/(x-2))dx = 2x - (1/5)*ln|x+3| - (14/5)*ln|x-2| + C

    As you may probably know you can collect those ln-terms.

    EB
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