\[ \int \frac {d+e x+f x^2}{\left (4-5 x^2+x^4\right )^3} \, dx \]
Optimal antiderivative \[ \frac {e \left (-2 x^{2}+5\right )}{36 \left (x^{4}-5 x^{2}+4\right )^{2}}+\frac {x \left (17 d +20 f -\left (5 d +8 f \right ) x^{2}\right )}{144 \left (x^{4}-5 x^{2}+4\right )^{2}}-\frac {e \left (-2 x^{2}+5\right )}{54 \left (x^{4}-5 x^{2}+4\right )}-\frac {x \left (59 d +380 f -35 \left (d +4 f \right ) x^{2}\right )}{3456 \left (x^{4}-5 x^{2}+4\right )}-\frac {\left (313 d +820 f \right ) \arctanh \! \left (\frac {x}{2}\right )}{20736}+\frac {\left (13 d +25 f \right ) \arctanh \! \left (x \right )}{648}-\frac {e \ln \! \left (-x^{2}+1\right )}{81}+\frac {e \ln \! \left (-x^{2}+4\right )}{81} \]
command
integrate((f*x**2+e*x+d)/(x**4-5*x**2+4)**3,x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \text {Timed out} \]
Sympy 1.8 under Python 3.8.8 output
\[ \text {output too large to display} \]