\[ \int \frac {x^6}{\left (d+e x^2\right ) \left (a+b x^2+c x^4\right )} \, dx \]
Optimal antiderivative \[ \frac {x}{c e}-\frac {d^{\frac {5}{2}} \arctan \left (\frac {x \sqrt {e}}{\sqrt {d}}\right )}{e^{\frac {3}{2}} \left (a \,e^{2}-b d e +c \,d^{2}\right )}+\frac {\arctan \left (\frac {x \sqrt {2}\, \sqrt {c}}{\sqrt {b -\sqrt {-4 a c +b^{2}}}}\right ) \left (b^{2} d -a c d -a b e +\frac {-2 a^{2} c e +a \,b^{2} e +3 a b c d -b^{3} d}{\sqrt {-4 a c +b^{2}}}\right ) \sqrt {2}}{2 c^{\frac {3}{2}} \left (a \,e^{2}-b d e +c \,d^{2}\right ) \sqrt {b -\sqrt {-4 a c +b^{2}}}}+\frac {\arctan \left (\frac {x \sqrt {2}\, \sqrt {c}}{\sqrt {b +\sqrt {-4 a c +b^{2}}}}\right ) \left (b^{2} d -a c d -a b e +\frac {2 a^{2} c e -a \,b^{2} e -3 a b c d +b^{3} d}{\sqrt {-4 a c +b^{2}}}\right ) \sqrt {2}}{2 c^{\frac {3}{2}} \left (a \,e^{2}-b d e +c \,d^{2}\right ) \sqrt {b +\sqrt {-4 a c +b^{2}}}} \]
command
integrate(x^6/(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 \[ \text {Timed out} \]