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