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Math Help - Integration Troubles

  1. #1
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    Integration Troubles

    I'm working on a Linear Coefficients problem of the form G(ax+by):

    (3x-2y-6)dx-(2y-3x+2)dy=0

    I've managed to reduce it to the following,

    \int dx\ = \int -dz\frac{2-z}{5z-18}\\

    where z = 3x-2y

    But I don't know how to finish this. I've scanned the table integrals in my book to no avail and I'm not sure how I'd use u substitution. Please lead me down the right path.
    Last edited by Talwar; February 25th 2009 at 10:56 PM.
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  2. #2
    MHF Contributor matheagle's Avatar
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    Divide, it's basic partial fractions.
    You'll get 1+{something\over 5z-18}

    BUT there's something wrong, where is dy?
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  3. #3
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    Sorry. I left it out. It's fix'd now.

    As for the partial fractions, I think I figured it out. I used u-sub:

    u = 5z-18

    du = 5dz

    z = {u\over z}+{18\over 5}

    dz = {du\over 5}

    And as long as I don't screw up the algebra, it should work. Thanks. ^_^
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  4. #4
    MHF Contributor matheagle's Avatar
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    Quote Originally Posted by Talwar View Post
    Sorry. I left it out. It's fix'd now.

    As for the partial fractions, I think I figured it out. I used u-sub:

    u = 5z-18

    du = 5dz

    z = {u\over z}+{18\over 5}

    dz = {du\over 5}

    And as long as I don't screw up the algebra, it should work. Thanks. ^_^
    What is z = {u\over z}+{18\over 5} supposed to be?
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