\[ \int \frac {12 x+16 x^2+\left (-14 x-8 x^2\right ) \log (x)+\left (3 x+10 x^2+8 x^3\right ) \log ^3(x)+(12+16 x) \log (3+4 x)}{\left (3 x+4 x^2\right ) \log ^3(x)} \, dx \]
Optimal antiderivative \[ x +x^{2}-\frac {2 \ln \! \left (3+4 x \right )+2 x}{\ln \! \left (x \right )^{2}}-2 \]
command
integrate(((16*x+12)*ln(3+4*x)+(8*x**3+10*x**2+3*x)*ln(x)**3+(-8*x**2-14*x)*ln(x)+16*x**2+12*x)/(4*x**2+3*x)/ln(x)**3,x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \text {Exception raised: TypeError} \]
Sympy 1.8 under Python 3.8.8 output
\[ x^{2} + x - \frac {2 x}{\log {\left (x \right )}^{2}} - \frac {2 \log {\left (4 x + 3 \right )}}{\log {\left (x \right )}^{2}} \]