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Math Help - indefinite integral

  1. #1
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    indefinite integral

    please see the attatchment...
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by bobby77
    please see the attatchment...
    ================================================== ===

    Which asks:

    Evaluate the indfinite integral:

    \int \frac{x^2-2x-3}{x-1}\ dx

    ================================================== ===


    Reduce the integrand to the sum of a linear term in x plus a constant
    divided by another linear term in x. This can be done either by inspection
    or synthetic division.

    Then the integral should be elementary

    RonL
    Last edited by CaptainBlack; December 10th 2005 at 09:12 AM.
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  3. #3
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    Right. So basically this will reduce down to something easily integratable. But you have to be careful that once you integrate the reduced function to indicate the point of discontinuity. I would start by factoring.
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by Jameson
    Right. So basically this will reduce down to something easily integratable. But you have to be careful that once you integrate the reduced function to indicate the point of discontinuity. I would start by factoring.
    The reduction process does not alter the position or nature
    of the singularity, in fact it makes it more obvious if anything.

    Also the position of the singularity is quite evident from
    the form of the integral.

    The nature of the singularity is that of: 1/x which has a
    singularity at 0, as does ln(|x|)+c, which is its indefinite integral.

    That you have to be careful when using this to construct a definite integral
    is something that has to be done for all integrals with singularities in the
    range of integration.

    (Also the use of the word elementary was slightly tongue in
    cheek - meaning has an indefinite integral expressible in terms
    of elementary functions)

    RonL
    Last edited by CaptainBlack; December 10th 2005 at 01:20 PM.
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  5. #5
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    Agreed. I was just making sure the poster realized that if he/she integrate the function over x=-1 to understand the problem.
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