\[ \int \frac {e \left (-30 x^4-5 x^5\right )+\left (x^3+30 x^5+5 x^6\right ) \log ^2(x)+\left (e \left (60 x^2+10 x^3\right )+\left (-x-60 x^3-10 x^4\right ) \log ^2(x)\right ) \log (2 x)+\left (e (-30-5 x)+\left (30 x+5 x^2\right ) \log ^2(x)\right ) \log ^2(2 x)+\left (6+x-12 x^2-2 x^3\right ) \log ^2(x) \log (6+x)}{\left (30 x^5+5 x^6\right ) \log ^2(x)+\left (-60 x^3-10 x^4\right ) \log ^2(x) \log (2 x)+\left (30 x+5 x^2\right ) \log ^2(x) \log ^2(2 x)} \, dx \]
Optimal antiderivative \[ \frac {{\mathrm e}}{\ln \! \left (x \right )}+\frac {\ln \! \left (6+x \right )}{5 x^{2}-5 \ln \! \left (2 x \right )}+x \]
command
integrate((((5*x**2+30*x)*ln(x)**2+(-5*x-30)*exp(1))*ln(2*x)**2+((-10*x**4-60*x**3-x)*ln(x)**2+(10*x**3+60*x**2)*exp(1))*ln(2*x)+(-2*x**3-12*x**2+x+6)*ln(x)**2*ln(6+x)+(5*x**6+30*x**5+x**3)*ln(x)**2+(-5*x**5-30*x**4)*exp(1))/((5*x**2+30*x)*ln(x)**2*ln(2*x)**2+(-10*x**4-60*x**3)*ln(x)**2*ln(2*x)+(5*x**6+30*x**5)*ln(x)**2),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \text {Exception raised: TypeError} \]
Sympy 1.8 under Python 3.8.8 output
\[ x + \frac {e}{\log {\left (x \right )}} + \frac {\log {\left (x + 6 \right )}}{5 x^{2} - 5 \log {\left (x \right )} - 5 \log {\left (2 \right )}} \]