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