\[ \int \frac {\tanh ^{-1}\left (\frac {\sqrt {e} x}{\sqrt {d+e x^2}}\right )}{x^7} \, dx \]
Optimal antiderivative \[ -\frac {\arctanh \! \left (\frac {x \sqrt {e}}{\sqrt {e \,x^{2}+d}}\right )}{6 x^{6}}+\frac {2 e^{\frac {3}{2}} \sqrt {e \,x^{2}+d}}{45 d^{2} x^{3}}-\frac {4 e^{\frac {5}{2}} \sqrt {e \,x^{2}+d}}{45 d^{3} x}-\frac {\sqrt {e}\, \sqrt {e \,x^{2}+d}}{30 d \,x^{5}} \]
command
integrate(arctanh(x*e^(1/2)/(e*x^2+d)^(1/2))/x^7,x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \text {Timed out} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \frac {8 \, {\left (10 \, {\left (x e^{\frac {1}{2}} - \sqrt {x^{2} e + d}\right )}^{4} d^{2} e^{2} - 5 \, {\left (x e^{\frac {1}{2}} - \sqrt {x^{2} e + d}\right )}^{2} d^{3} e^{2} + d^{4} e^{2}\right )} e}{45 \, {\left ({\left (x e^{\frac {1}{2}} - \sqrt {x^{2} e + d}\right )}^{2} - d\right )}^{5} d^{2}} - \frac {\log \left (-\frac {\frac {x e^{\frac {1}{2}}}{\sqrt {x^{2} e + d}} + 1}{\frac {x e^{\frac {1}{2}}}{\sqrt {x^{2} e + d}} - 1}\right )}{12 \, x^{6}} \]