\[ \int \frac {\tanh ^{-1}\left (\frac {\sqrt {e} x}{\sqrt {d+e x^2}}\right )}{x^3} \, dx \]
Optimal antiderivative \[ -\frac {\arctanh \! \left (\frac {x \sqrt {e}}{\sqrt {e \,x^{2}+d}}\right )}{2 x^{2}}-\frac {\sqrt {e}\, \sqrt {e \,x^{2}+d}}{2 d x} \]
command
integrate(arctanh(x*e^(1/2)/(e*x^2+d)^(1/2))/x^3,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
\[ \frac {e}{{\left (x e^{\frac {1}{2}} - \sqrt {x^{2} e + d}\right )}^{2} - d} - \frac {\log \left (-\frac {\frac {x e^{\frac {1}{2}}}{\sqrt {x^{2} e + d}} + 1}{\frac {x e^{\frac {1}{2}}}{\sqrt {x^{2} e + d}} - 1}\right )}{4 \, x^{2}} \]