\[ \int \frac {-1+x}{(-3+x) (1+x) \sqrt [4]{-2-2 x+x^2}} \, dx \]
Optimal antiderivative \[ \arctan \left (\left (x^{2}-2 x -2\right )^{\frac {1}{4}}\right )-\arctanh \left (\left (x^{2}-2 x -2\right )^{\frac {1}{4}}\right ) \]
command
Integrate[(-1 + x)/((-3 + x)*(1 + x)*(-2 - 2*x + x^2)^(1/4)),x]
Mathematica 13.1 output
\[ \text {ArcTan}\left (\sqrt [4]{-2-2 x+x^2}\right )-\tanh ^{-1}\left (\sqrt [4]{-2-2 x+x^2}\right ) \]
Mathematica 12.3 output
\[ \int \frac {-1+x}{(-3+x) (1+x) \sqrt [4]{-2-2 x+x^2}} \, dx \]________________________________________________________________________________________