\[ \int \frac {-1+2 x^6}{\sqrt {1+x^6} \left (1-x^2+x^6\right )} \, dx \]
Optimal antiderivative \[ -\arctanh \left (\frac {x}{\sqrt {x^{6}+1}}\right ) \]
command
Integrate[(-1 + 2*x^6)/(Sqrt[1 + x^6]*(1 - x^2 + x^6)),x]
Mathematica 13.1 output
\[ -\tanh ^{-1}\left (\frac {x}{\sqrt {1+x^6}}\right ) \]
Mathematica 12.3 output
\[ \int \frac {-1+2 x^6}{\sqrt {1+x^6} \left (1-x^2+x^6\right )} \, dx \]________________________________________________________________________________________