\[ \int \frac {1}{x^2 \left (a^5+x^5\right )} \, dx \]
Optimal antiderivative \[ -\frac {1}{a^{5} x}+\frac {\ln \left (a +x \right )}{5 a^{6}}-\frac {\ln \left (a^{2}+x^{2}-\frac {a x \left (-\sqrt {5}+1\right )}{2}\right ) \left (-\sqrt {5}+1\right )}{20 a^{6}}-\frac {\ln \left (a^{2}+x^{2}-\frac {a x \left (\sqrt {5}+1\right )}{2}\right ) \left (\sqrt {5}+1\right )}{20 a^{6}}+\frac {\arctan \left (\frac {\left (-4 x +a \left (\sqrt {5}+1\right )\right ) \sqrt {50+10 \sqrt {5}}}{20 a}\right ) \sqrt {10-2 \sqrt {5}}}{10 a^{6}}+\frac {\arctan \left (\frac {-4 x +a \left (-\sqrt {5}+1\right )}{a \sqrt {10+2 \sqrt {5}}}\right ) \sqrt {10+2 \sqrt {5}}}{10 a^{6}} \]
command
integrate(1/x^2/(a^5+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 \[ \text {Timed out} \]