\[ \int \frac {-1+7 x^8}{\left (1+x^8\right ) \sqrt {3-x+x^2+6 x^8-x^9+3 x^{16}}} \, dx \]
Optimal antiderivative \[ 2 \arctanh \left (\frac {x}{\sqrt {3}+\sqrt {3}\, x^{8}-\sqrt {3 x^{16}-x^{9}+6 x^{8}+x^{2}-x +3}}\right ) \]
command
Integrate[(-1 + 7*x^8)/((1 + x^8)*Sqrt[3 - x + x^2 + 6*x^8 - x^9 + 3*x^16]),x]
Mathematica 13.1 output
\[ 2 \tanh ^{-1}\left (\frac {x}{\sqrt {3}+\sqrt {3} x^8-\sqrt {3-x+x^2+6 x^8-x^9+3 x^{16}}}\right ) \]
Mathematica 12.3 output
\[ \int \frac {-1+7 x^8}{\left (1+x^8\right ) \sqrt {3-x+x^2+6 x^8-x^9+3 x^{16}}} \, dx \]________________________________________________________________________________________