\[ \int \frac {1}{x^4 \left (a+b x^2\right ) \left (c+d x^2\right )} \, dx \]
Optimal antiderivative \[ -\frac {1}{3 a c \,x^{3}}+\frac {a d +b c}{a^{2} c^{2} x}+\frac {b^{\frac {5}{2}} \arctan \! \left (\frac {x \sqrt {b}}{\sqrt {a}}\right )}{a^{\frac {5}{2}} \left (-a d +b c \right )}-\frac {d^{\frac {5}{2}} \arctan \! \left (\frac {x \sqrt {d}}{\sqrt {c}}\right )}{c^{\frac {5}{2}} \left (-a d +b c \right )} \]
command
integrate(1/x**4/(b*x**2+a)/(d*x**2+c),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \text {Timed out} \]
Sympy 1.8 under Python 3.8.8 output
\[ \text {output too large to display} \]