\[ \int \frac {A+B x+C x^2}{a+b x^2+c x^4} \, dx \]
Optimal antiderivative \[ -\frac {B \arctanh \left (\frac {2 c \,x^{2}+b}{\sqrt {-4 a c +b^{2}}}\right )}{\sqrt {-4 a c +b^{2}}}+\frac {\arctan \left (\frac {x \sqrt {2}\, \sqrt {c}}{\sqrt {b -\sqrt {-4 a c +b^{2}}}}\right ) \left (C +\frac {2 A c -b C}{\sqrt {-4 a c +b^{2}}}\right ) \sqrt {2}}{2 \sqrt {c}\, \sqrt {b -\sqrt {-4 a c +b^{2}}}}+\frac {\arctan \left (\frac {x \sqrt {2}\, \sqrt {c}}{\sqrt {b +\sqrt {-4 a c +b^{2}}}}\right ) \left (C +\frac {-2 A c +b C}{\sqrt {-4 a c +b^{2}}}\right ) \sqrt {2}}{2 \sqrt {c}\, \sqrt {b +\sqrt {-4 a c +b^{2}}}} \]
command
integrate((C*x^2+B*x+A)/(c*x^4+b*x^2+a),x, algorithm="fricas")
Fricas 1.3.8 (sbcl 2.2.11.debian) via sagemath 9.6 output
\[ \text {output too large to display} \]
Fricas 1.3.7 via sagemath 9.3 output \[ \text {Timed out} \]