\[ \int \frac {a+b \log (c x)}{\left (d+\frac {e}{x}\right ) x^4} \, dx \]
Optimal antiderivative \[ -\frac {b}{4 e \,x^{2}}+\frac {b d}{e^{2} x}+\frac {-a -b \ln \! \left (c x \right )}{2 e \,x^{2}}+\frac {d \left (a +b \ln \! \left (c x \right )\right )}{e^{2} x}+\frac {d^{2} \left (a +b \ln \! \left (c x \right )\right )^{2}}{2 b \,e^{3}}-\frac {d^{2} \left (a +b \ln \! \left (c x \right )\right ) \ln \! \left (1+\frac {d x}{e}\right )}{e^{3}}-\frac {b \,d^{2} \polylog \! \left (2, -\frac {d x}{e}\right )}{e^{3}} \]
command
integrate((a+b*ln(c*x))/(d+e/x)/x**4,x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \text {Timed out} \]
Sympy 1.8 under Python 3.8.8 output
\[ - \frac {a d^{3} \left (\begin {cases} \frac {x}{e} & \text {for}\: d = 0 \\\frac {\log {\left (d x + e \right )}}{d} & \text {otherwise} \end {cases}\right )}{e^{3}} + \frac {a d^{2} \log {\left (x \right )}}{e^{3}} + \frac {a d}{e^{2} x} - \frac {a}{2 e x^{2}} + \frac {b d^{3} \left (\begin {cases} \frac {x}{e} & \text {for}\: d = 0 \\\frac {\begin {cases} \log {\left (e \right )} \log {\left (x \right )} - \operatorname {Li}_{2}\left (\frac {d x e^{i \pi }}{e}\right ) & \text {for}\: \left |{x}\right | < 1 \\- \log {\left (e \right )} \log {\left (\frac {1}{x} \right )} - \operatorname {Li}_{2}\left (\frac {d x e^{i \pi }}{e}\right ) & \text {for}\: \frac {1}{\left |{x}\right |} < 1 \\- {G_{2, 2}^{2, 0}\left (\begin {matrix} & 1, 1 \\0, 0 & \end {matrix} \middle | {x} \right )} \log {\left (e \right )} + {G_{2, 2}^{0, 2}\left (\begin {matrix} 1, 1 & \\ & 0, 0 \end {matrix} \middle | {x} \right )} \log {\left (e \right )} - \operatorname {Li}_{2}\left (\frac {d x e^{i \pi }}{e}\right ) & \text {otherwise} \end {cases}}{d} & \text {otherwise} \end {cases}\right )}{e^{3}} - \frac {b d^{3} \left (\begin {cases} \frac {x}{e} & \text {for}\: d = 0 \\\frac {\log {\left (d x + e \right )}}{d} & \text {otherwise} \end {cases}\right ) \log {\left (c x \right )}}{e^{3}} - \frac {b d^{2} \log {\left (x \right )}^{2}}{2 e^{3}} + \frac {b d^{2} \log {\left (x \right )} \log {\left (c x \right )}}{e^{3}} + \frac {b d \log {\left (c x \right )}}{e^{2} x} + \frac {b d}{e^{2} x} - \frac {b \log {\left (c x \right )}}{2 e x^{2}} - \frac {b}{4 e x^{2}} \]