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Math Help - How to find this integral?

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    How to find this integral?

    Integrate: (x^4)/(x^2 + 4)
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    Quote Originally Posted by AlphaRock View Post
    Integrate: (x^4)/(x^2 + 4)
    Since the numerator has higher degree than the denominator, start by dividing: \frac{x^4}{x^2+ 1}= x^2- 1- \frac{1}{x^2+ 1}. The first two should be easy and \int \frac{1}{x^2+ 1} dx= arctan(x)+ C
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    Quote Originally Posted by HallsofIvy View Post
    Since the numerator has higher degree than the denominator, start by dividing: \frac{x^4}{x^2+ 1}= x^2- 1- \frac{1}{x^2+ 1}. The first two should be easy and \int \frac{1}{x^2+ 1} dx= arctan(x)+ C
    Thanks. Now if the numerator has the same degree as the denominator, would we just leave and do the integration by partial fractions?
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    Quote Originally Posted by AlphaRock View Post
    Thanks. Now if the numerator has the same degree as the denominator, would we just leave and do the integration by partial fractions?
    If the numerator and denominator have the same degree, it's technically still an improper fraction so cancelling it will often make in easier to integrate.
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