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Math Help - [SOLVED] Integration problem

  1. #1
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    Question [SOLVED] Integration problem

    Hi guys,

    I need to integrate the following equation with respect to x.

    <br /> <br />
-ax + \frac{ab}{c-x}<br /> <br />

    where a,b and c are integers. I was advised to re-write the equation as

    <br /> <br />
-ax -ab\frac{-1}{c-x}<br /> <br />

    and i'm pretty confident in integrating the first part of the equation, but i dont know how to integrate the last part. I'm guessing that the answer will involve ln(?) but i dont know how to work out what its meant to be the log of, so if anybody could help me i will be truely thankful as i've been trying to work this out for a while, getting nowhere!

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  2. #2
    MHF Contributor
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    Quote Originally Posted by Kimmy4 View Post
    Hi guys,

    I need to integrate the following equation with respect to x.

    <br /> <br />
-ax + \frac{ab}{c-x}<br /> <br />

    where a,b and c are integers. I was advised to re-write the equation as

    <br /> <br />
-ax -ab\frac{-1}{c-x}<br /> <br />

    and i'm pretty confident in integrating the first part of the equation, but i dont know how to integrate the last part. I'm guessing that the answer will involve ln(?) but i dont know how to work out what its meant to be the log of, so if anybody could help me i will be truely thankful as i've been trying to work this out for a while, getting nowhere!

    Note that \frac{-1}{c-x} = \frac{1}{x-c} and the antiderivative of \frac{1}{x-c} is \ln{|x-c|}.
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  3. #3
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    Wow is it really that simple! I was thinking it was gonna be much more complicated than that! Thanks.



    so am i right in saying that the whole integral is

    <br /> <br />
\frac{-ax^2}{2} - abln(x-c)<br /> <br />

    Thanks again
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  4. #4
    MHF Contributor
    Joined
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    Quote Originally Posted by Kimmy4 View Post
    Wow is it really that simple! I was thinking it was gonna be much more complicated than that! Thanks.



    so am i right in saying that the whole integral is

    <br /> <br />
\frac{-ax^2}{2} - abln(x-c)<br /> <br />

    Thanks again
    Yes, that is the correct integral. Don't forget to add your constant.
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