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