\[ \int \frac {c+d x+e x^2}{\left (a-b x^4\right )^4} \, dx \]
Optimal antiderivative \[ \frac {x \left (e \,x^{2}+d x +c \right )}{12 a \left (-b \,x^{4}+a \right )^{3}}+\frac {x \left (9 e \,x^{2}+10 d x +11 c \right )}{96 a^{2} \left (-b \,x^{4}+a \right )^{2}}+\frac {x \left (45 e \,x^{2}+60 d x +77 c \right )}{384 a^{3} \left (-b \,x^{4}+a \right )}+\frac {5 d \arctanh \left (\frac {x^{2} \sqrt {b}}{\sqrt {a}}\right )}{32 a^{\frac {7}{2}} \sqrt {b}}+\frac {\arctan \left (\frac {b^{\frac {1}{4}} x}{a^{\frac {1}{4}}}\right ) \left (-15 e \sqrt {a}+77 c \sqrt {b}\right )}{256 a^{\frac {15}{4}} b^{\frac {3}{4}}}+\frac {\arctanh \left (\frac {b^{\frac {1}{4}} x}{a^{\frac {1}{4}}}\right ) \left (15 e \sqrt {a}+77 c \sqrt {b}\right )}{256 a^{\frac {15}{4}} b^{\frac {3}{4}}} \]
command
integrate((e*x^2+d*x+c)/(-b*x^4+a)^4,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 \[ \text {Timed out} \]