\[ \int \frac {1}{x^2 \left (d+e x^2\right ) \left (a+b x^2+c x^4\right )} \, dx \]
Optimal antiderivative \[ -\frac {1}{a d x}-\frac {e^{\frac {5}{2}} \arctan \left (\frac {x \sqrt {e}}{\sqrt {d}}\right )}{d^{\frac {3}{2}} \left (a \,e^{2}-b d e +c \,d^{2}\right )}-\frac {\arctan \left (\frac {x \sqrt {2}\, \sqrt {c}}{\sqrt {b -\sqrt {-4 a c +b^{2}}}}\right ) \sqrt {c}\, \left (c d -b e +\frac {2 a c e -b^{2} e +b c d}{\sqrt {-4 a c +b^{2}}}\right ) \sqrt {2}}{2 a \left (a \,e^{2}-b d e +c \,d^{2}\right ) \sqrt {b -\sqrt {-4 a c +b^{2}}}}-\frac {\arctan \left (\frac {x \sqrt {2}\, \sqrt {c}}{\sqrt {b +\sqrt {-4 a c +b^{2}}}}\right ) \sqrt {c}\, \left (c d -b e +\frac {-2 a c e +b^{2} e -b c d}{\sqrt {-4 a c +b^{2}}}\right ) \sqrt {2}}{2 a \left (a \,e^{2}-b d e +c \,d^{2}\right ) \sqrt {b +\sqrt {-4 a c +b^{2}}}} \]
command
integrate(1/x^2/(e*x^2+d)/(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 \[ \text {Timed out} \]