Integrate $ \int \frac{x^4 +1}{x^6 - 1}dx $ Integrate
$$ \int \frac{x^4 +1}{x^6 - 1}\, \mathrm dx$$
I have tried using partial fractions but to no use. Thanks for help.

Hint: Use that $$\frac{x^4+1}{x^6-1}=\frac16\,{\frac {-2\,x-1}{{x}^{2}+x+1}}-\frac13\, \left( x+1 \right) ^{-1}+\frac16
\,{\frac {2\,x-1}{{x}^{2}-x+1}}+\frac13\, \left( x-1 \right) ^{-1}.
$$
