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