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Could I have some help for this question?

$\int \frac {x^4}{x^4 +5x^2 +4} \, dx$

I've reduced the equation to...

$\int \frac {1}{1 + 5x^{-2} + 4x^{-4}} \, dx$

But I'm stuck after this step. Could I have some help for this question?

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    @melyong: good. +12012-11-15

2 Answers 2

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Hint:

Using partial fraction, you can write the integrand as

$\frac {x^4}{x^4 +5x^2 +4}= 1+\frac{1}{3(x^2+1)} - \frac{16}{3(x^2+4)}.$

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Using the fact that $x^4+5x^2+4=(x^2+1)(x^2+4)$, change the initial integrand to a form only involving $\frac{1}{x^2+a}$.