\[ \int \frac {\left (f+g x^2\right ) \log \left (c \left (d+e x^2\right )^p\right )}{x^6} \, dx \]
Optimal antiderivative \[ -\frac {2 e f p}{15 d \,x^{3}}+\frac {2 e^{2} f p}{5 d^{2} x}-\frac {2 e g p}{3 d x}+\frac {2 e^{\frac {5}{2}} f p \arctan \left (\frac {x \sqrt {e}}{\sqrt {d}}\right )}{5 d^{\frac {5}{2}}}-\frac {2 e^{\frac {3}{2}} g p \arctan \left (\frac {x \sqrt {e}}{\sqrt {d}}\right )}{3 d^{\frac {3}{2}}}-\frac {f \ln \left (c \left (e \,x^{2}+d \right )^{p}\right )}{5 x^{5}}-\frac {g \ln \left (c \left (e \,x^{2}+d \right )^{p}\right )}{3 x^{3}} \]
command
integrate((g*x**2+f)*ln(c*(e*x**2+d)**p)/x**6,x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \text {output too large to display} \]
Sympy 1.8 under Python 3.8.8 output \[ \text {Timed out} \]_____________________________________________________