<s>[INST] What's the integral of $\int_0^\infty \frac{dx}{(x^4+1)^5}$ $$\int_0^\infty \frac{dx}{(x^4+1)^5}$$
My answer would be : $\dfrac{\Gamma(\tfrac{1}{4})\Gamma(\tfrac{19}{4})}{4\Gamma(5)}$
Solution: You can use this technique. –  Mhenni Benghorbal
 [/INST] \begin{align}
x^4+1 & = (x^4 +2x^2 + 1)-2x^2 \\[8pt]
& = (x^2+1)^2 - (\sqrt{2}\, x)^2 \\[8pt]
& = (x^2 - \sqrt{2}\, x +1)(x^2 + \sqrt{2}\, x + 1)
\end{align}
Then go to partial fractions.
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