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Math Help - partial fraction decomposition

  1. #1
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    partial fraction decomposition

    x^2 / (x^2 + 5^2)

    what do i do since the power of the numerator is the same as the power of the denominator ... ??
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  2. #2
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    If the power in the numerator is not smaller than the denominator, use long divison to fix the problem. You should get: \frac{x^2}{x^2 + 25} = 1 - {\color{blue}\frac{25}{x^2 + 25}}

    But for this example, partial fraction decomposition is not needed. You should recognize the blue as it is in the form of: \frac{1}{a^2 + x^2}

    Why? Because: \int \frac{1}{a^2 + x^2} \ dx = \frac{1}{a}\! \tan^{-1} \left(\frac{x}{a}\right) + C
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    yeah i know i can use trig substitution ... but the question specifically asked for partial fraction decomposition ... maybe thats why i wasnt thinking straight ...
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    But you can't. x^2 + 25 is irreducible over the reals (i.e. can't be factored without getting into complex numbers).
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  5. #5
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    Quote Originally Posted by razorfever View Post
    yeah i know i can use trig substitution ... but the question specifically asked for partial fraction decomposition ... maybe thats why i wasnt thinking straight ...
    Are you sure it wasn't asking for

    \int{\frac{x^2}{x^2 - 5^2}\,dx}?
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