\[ \int \frac {5+x+3 x^2+2 x^3}{x^2 \left (2+x+5 x^2+x^3+2 x^4\right )} \, dx \]
Optimal antiderivative \[ \frac {-35+9 i \sqrt {7}}{28 x}+\frac {-35-9 i \sqrt {7}}{28 x}-\frac {3 \ln \left (x \right ) \left (7-11 i \sqrt {7}\right )}{56}+\frac {3 \ln \left (4 i+4 i x^{2}+x \left (i+\sqrt {7}\right )\right ) \left (7-11 i \sqrt {7}\right )}{112}-\frac {3 \ln \left (x \right ) \left (7+11 i \sqrt {7}\right )}{56}+\frac {3 \ln \left (4 i+4 i x^{2}+x \left (i-\sqrt {7}\right )\right ) \left (7+11 i \sqrt {7}\right )}{112}+\frac {11 \arctanh \left (\frac {i+8 i x -\sqrt {7}}{\sqrt {70-2 i \sqrt {7}}}\right ) \left (9+5 i \sqrt {7}\right )}{4 \sqrt {490-14 i \sqrt {7}}}-\frac {11 \arctanh \left (\frac {i+8 i x +\sqrt {7}}{\sqrt {70+2 i \sqrt {7}}}\right ) \left (9-5 i \sqrt {7}\right )}{4 \sqrt {490+14 i \sqrt {7}}} \]
command
integrate((2*x**3+3*x**2+x+5)/x**2/(2*x**4+x**3+5*x**2+x+2),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 \[ \text {Timed out} \]_____________________________________________________