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