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