\[ \int \frac {x^7}{\left (a+b x^4\right ) \left (c+d x^4\right )} \, dx \]
Optimal antiderivative \[ -\frac {a \ln \! \left (b \,x^{4}+a \right )}{4 b \left (-a d +b c \right )}+\frac {c \ln \! \left (d \,x^{4}+c \right )}{4 d \left (-a d +b c \right )} \]
command
integrate(x**7/(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
\[ \frac {a \log {\left (x^{4} + \frac {\frac {a^{3} d^{2}}{b \left (a d - b c\right )} - \frac {2 a^{2} c d}{a d - b c} + \frac {a b c^{2}}{a d - b c} + 2 a c}{a d + b c} \right )}}{4 b \left (a d - b c\right )} - \frac {c \log {\left (x^{4} + \frac {- \frac {a^{2} c d}{a d - b c} + \frac {2 a b c^{2}}{a d - b c} + 2 a c - \frac {b^{2} c^{3}}{d \left (a d - b c\right )}}{a d + b c} \right )}}{4 d \left (a d - b c\right )} \]