<s>[INST] Integral $\int\frac{dx}{x^5+1}$ Calculate $\displaystyle\int\dfrac{dx}{x^5+1}$
 [/INST] Hint:
$$
\begin{split}
x^5+1&=(1 + x)(x^4 - x^3 + x^2 - x + 1) \\
&=(1 + x)(x^2 + ((-1 + \sqrt 5) / 2)x + 1)(x^2 + ((-1 - \sqrt 5) / 2)x + 1) 
\end{split}
$$
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