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Math Help - Simple Integral question w/ parts

  1. #16
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    Quote Originally Posted by Chris L T521 View Post


    Where are you stuck in the division process?

    --Chris
    Well, I guess the whole thing, like how do you get 1-\frac {1}{1+s^2}
    It's something to do with the s^2 right?
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  2. #17
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by matt3D View Post
    Well, I guess the whole thing, like how do you get 1-\frac {1}{1+s^2}
    It's something to do with the s^2 right?
    You take 1+s^2~|\overline{~~~~s^2}

    We see that s^2 goes into s^2 1 time.

    Thus, we should get

    .~~~~~~~~~~~~~~~~~~{\color{blue}1}
    {\color{magenta}1+s^2}~|\overline{~~~~~~~~~s^2}
    .~~~~~~~~~\underline{-(1+s^2)}
    .~~~~~~~~~~~~~~~~~{\color{red}-1}

    So our quotient will be {\color{blue}1}+\frac{{\color{red}-1}}{{\color{magenta}1+s^2}}=1-\frac{1}{1+s^2}, where -\frac{1}{1+s^2} is the remainder.

    Does this make sense?

    --Chris
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  3. #18
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    This is done by polynomial long division. Check the link here to see how it is done: Polynomial Long Division
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  4. #19
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    If you want to do it quickly without polynomial division:

    \frac{x^2}{x^2+1}

    Add one/subtract one: \frac{(x^2 + 1) - 1}{x^2+1}
    Split: \frac{x^2+1}{x^2+1} - \frac{1}{x^2+1}
    Cancel: 1 - \frac{1}{x^2+1}
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  5. #20
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by Chop Suey View Post
    If you want to do it quickly without polynomial division:

    \frac{x^2}{x^2+1}

    Add one/subtract one: \frac{(x^2 + 1) - 1}{x^2+1}
    Split: \frac{x^2+1}{x^2+1} - \frac{1}{x^2+1}
    Cancel: 1 - \frac{1}{x^2+1}
    Aha! I remember that trick now...I remember seeing it before...

    --Chris
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