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Math Help - Integration with partial fractions

  1. #1
    DBA
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    Integration with partial fractions

    How do I start with this one?
    <br />
\int \frac {5x^{2}-3} {x^2-9}<br />

    Since nominator and denominator are x^2 I have to divide them, right?
    I am not sure how to do that.

    Thanks for any help.
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  2. #2
    Ted
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    Quote Originally Posted by DBA View Post
    How do I start with this one?
    <br />
\int \frac {5x^{2}-3} {x^2-9}<br />

    Since nominator and denominator are x^2 I have to divide them, right?
    I am not sure how to do that.

    Thanks for any help.
    Yes start by Long Division.
    Actually, there is another solutions without devide.
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  3. #3
    DBA
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    Hello, thanks for answering. Can you please explain how to do so?
    That was my problem, actually...
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  4. #4
    Ted
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    Quote Originally Posted by DBA View Post
    Hello, thanks for answering. Can you please explain how to do so?
    That was my problem, actually...
    Ohhh..You do not know to do the long division ?
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  5. #5
    MHF Contributor
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    You could do it this way:

    \int \frac {5x^{2}-3} {x^2-9} dx =

    \int \frac {5x^{2}-45 + 42} {x^2-9} dx =

    \int \frac {5(x^2 - 9)}{x^2 - 9} dx + \int \frac {42}{x^2 - 9} dx=

    \int 5 dx + \int \frac {42}{x^2 - 9} dx

    Then use an appropriate substitution on the second integral.
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