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Math Help - integral

  1. #1
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    integral

    im not sure how to integrate this

    \int\frac{1}{x^2(x^2+1)}

    i had this on a test and i got it wrong
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  2. #2
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by acosta0809 View Post
    im not sure how to integrate this

    \int\frac{1}{x^2(x^2+1)}

    i had this on a test and i got it wrong
    Partial fraction decomp is how I'd do it.
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  3. #3
    o_O
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    A couple of ways to do this one.

    Notice that: \frac{1 {\color{red}\  + \ x^2 \ - \ x^2}}{x^2 \left(x^2 + 1\right) } = \frac{1 + {\color{red}x^2}}{x^2 \left(x^2 + 1\right)} - \frac{{\color{red}x^2}}{x^2\left(x^2 + 1\right)} = \frac{1}{x^2} - \frac{1}{1+x^2}

    So your itnegral is the same as: \int \left( \frac{1}{x^2} - \frac{1}{1+x^2}\right) \ dx

    which is a lot easier. You could've gotten the same thing if you did something along the lines of partial fraction decomposition if you aren't comfortable with the 'adding 0' in the numerator .
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