\[ \int \frac {c+d x+e x^2+f x^3+g x^4+h x^5}{\left (a-b x^4\right )^2} \, dx \]
Optimal antiderivative \[ \frac {x \left (b c +a g +\left (a h +b d \right ) x +b e \,x^{2}+b f \,x^{3}\right )}{4 a b \left (-b \,x^{4}+a \right )}+\frac {\left (-a h +b d \right ) \arctanh \left (\frac {x^{2} \sqrt {b}}{\sqrt {a}}\right )}{4 a^{\frac {3}{2}} b^{\frac {3}{2}}}+\frac {\arctan \left (\frac {b^{\frac {1}{4}} x}{a^{\frac {1}{4}}}\right ) \left (3 b c -a g -e \sqrt {a}\, \sqrt {b}\right )}{8 a^{\frac {7}{4}} b^{\frac {5}{4}}}+\frac {\arctanh \left (\frac {b^{\frac {1}{4}} x}{a^{\frac {1}{4}}}\right ) \left (3 b c -a g +e \sqrt {a}\, \sqrt {b}\right )}{8 a^{\frac {7}{4}} b^{\frac {5}{4}}} \]
command
integrate((h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(-b*x^4+a)^2,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 \[ \text {Timed out} \]