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Math Help - Simple Integration - PLEASE HELP???

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    Exclamation Simple Integration - PLEASE HELP???

    Integration of (9x^2-2x)/(6x^3-2x^2) respective to x.

    I keep on getting 3/4 * ln(x^2-3) + c

    Is that right???? Could someone please show me how to get the right answer if it's wrong?
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  2. #2
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    Quote Originally Posted by xwrathbringerx View Post
    Integration of (9x^2-2x)/(6x^3-2x^2) respective to x.

    I keep on getting 3/4 * ln(x^2-3) + c

    Is that right???? Could someone please show me how to get the right answer if it's wrong?
    Use the substitution u = 3x^3 - x^2 so that \frac{du}{dx} = 9x^2 - 2x.


    Therefore

    \int{\frac{9x^2 - 2x}{6x^3 - 2x^2}\,dx} = \frac{1}{2}\int{\frac{1}{u}\,\frac{du}{dx}\,dx}

     = \frac{1}{2}\int{\frac{1}{u}\,du}

     = \frac{1}{2}\ln{|u|} + C

     = \frac{1}{2}\ln{|3x^3 - x^2|} + C.
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