\[ \int \frac {12 x-24 x^2+8 x^3+3 x^4+e^6 \left (7-12 x+3 x^2+2 x^3\right )+\left (26 x-22 x^2-6 x^3+e^6 \left (14-10 x-4 x^2\right )\right ) \log (3)+\left (14 x+3 x^2+e^6 (7+2 x)\right ) \log ^2(3)}{-2+4 x+4 x^2-12 x^3+5 x^4+x^5+e^6 \left (7 x-13 x^2+5 x^3+x^4\right )+\left (-4+4 x+13 x^2-12 x^3-2 x^4+e^6 \left (14 x-12 x^2-2 x^3\right )\right ) \log (3)+\left (-2+7 x^2+x^3+e^6 \left (7 x+x^2\right )\right ) \log ^2(3)} \, dx \]
Optimal antiderivative \[ \ln \left (x \left (\left ({\mathrm e}^{6}+x \right ) \left (7+x \right )+\frac {x}{x -\ln \left (3\right )-1}\right )-2\right ) \]
command
integrate((((7+2*x)*exp(3)**2+3*x**2+14*x)*ln(3)**2+((-4*x**2-10*x+14)*exp(3)**2-6*x**3-22*x**2+26*x)*ln(3)+(2*x**3+3*x**2-12*x+7)*exp(3)**2+3*x**4+8*x**3-24*x**2+12*x)/(((x**2+7*x)*exp(3)**2+x**3+7*x**2-2)*ln(3)**2+((-2*x**3-12*x**2+14*x)*exp(3)**2-2*x**4-12*x**3+13*x**2+4*x-4)*ln(3)+(x**4+5*x**3-13*x**2+7*x)*exp(3)**2+x**5+5*x**4-12*x**3+4*x**2+4*x-2),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ - \log {\left (x - \log {\left (3 \right )} - 1 \right )} + \log {\left (x^{4} + x^{3} \left (- \log {\left (3 \right )} + 6 + e^{6}\right ) + x^{2} \left (- e^{6} \log {\left (3 \right )} - 7 \log {\left (3 \right )} - 6 + 6 e^{6}\right ) + x \left (- 7 e^{6} \log {\left (3 \right )} - 7 e^{6} - 2\right ) + 2 + 2 \log {\left (3 \right )} \right )} \]
Sympy 1.8 under Python 3.8.8 output
\[ \text {Timed out} \]________________________________________________________________________________________