Evaluate the integral $\int \frac{dx}{1+x^5}$ 
$$\int \frac{dx}{1+x^5}$$

I have tried to add a $x^5$ and subtract $x^5$, but got nothing.

Hint. One may start with
$$
x^5+1=(x+1)\left(x^2-\frac{\sqrt{5}+1}{2} x+1\right)\left(x^2+\frac{\sqrt{5}-1}{2} x+1\right)
$$ then one may obtain a partial fraction decomposition,
$$
\frac1{x^5+1}=\frac{a_0}{x+1}+\frac{a_1x+b_1}{x^2-\frac{\sqrt{5}+1}{2} x+1}+\frac{a_2x+b_2}{x^2+\frac{\sqrt{5}-1}{2} x+1}
$$ and integrate classically each term.
