\[ \int \frac {1}{a+\frac {b}{x^5}} \, dx \]
Optimal antiderivative \[ \frac {x}{a}-\frac {b^{\frac {1}{5}} \ln \left (b^{\frac {1}{5}}+a^{\frac {1}{5}} x \right )}{5 a^{\frac {6}{5}}}+\frac {b^{\frac {1}{5}} \ln \left (b^{\frac {2}{5}}+a^{\frac {2}{5}} x^{2}-\frac {a^{\frac {1}{5}} b^{\frac {1}{5}} x \left (-\sqrt {5}+1\right )}{2}\right ) \left (-\sqrt {5}+1\right )}{20 a^{\frac {6}{5}}}+\frac {b^{\frac {1}{5}} \ln \left (b^{\frac {2}{5}}+a^{\frac {2}{5}} x^{2}-\frac {a^{\frac {1}{5}} b^{\frac {1}{5}} x \left (\sqrt {5}+1\right )}{2}\right ) \left (\sqrt {5}+1\right )}{20 a^{\frac {6}{5}}}-\frac {b^{\frac {1}{5}} \arctan \left (\frac {a^{\frac {1}{5}} x \sqrt {50+10 \sqrt {5}}}{5 b^{\frac {1}{5}}}-\frac {\sqrt {25+10 \sqrt {5}}}{5}\right ) \sqrt {10-2 \sqrt {5}}}{10 a^{\frac {6}{5}}}-\frac {b^{\frac {1}{5}} \arctan \left (\frac {\sqrt {25-10 \sqrt {5}}}{5}+\frac {2 a^{\frac {1}{5}} x \sqrt {2}}{\sqrt {5+\sqrt {5}}\, b^{\frac {1}{5}}}\right ) \sqrt {10+2 \sqrt {5}}}{10 a^{\frac {6}{5}}} \]
command
integrate(1/(a+b/x^5),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 \[ \text {Timed out} \]