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Does anybody know how to determine a primitive of the function

$f(u)=\frac{u^2}{(au^4+bu^2+c)^{3/2}}$?

Here $a,b,c$ are positive real numbers and one assume that $u>0$.

Thank you in advance.

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Wolfram alpha gives a result in terms of elliptic integrals. – Eckhard Jan 10 '13 at 16:22

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