\[ \int \frac {e^{\frac {2 x}{\log (x)}} \left (-2 x^2+2 x^2 \log (x)+2 x \log ^2(x)+e^{-30+2 x-2 x \log (2 x)} \left (-2+2 \log (x)-2 \log ^2(x) \log (2 x)\right )+e^{-15+x-x \log (2 x)} \left (4 x-4 x \log (x)-2 \log ^2(x)+2 x \log ^2(x) \log (2 x)\right )\right )}{5 \log ^2(x)} \, dx \]
Optimal antiderivative \[ \frac {{\mathrm e}^{\frac {2 x}{\ln \left (x \right )}} \left (x -{\mathrm e}^{-x \ln \left (2 x \right )+x -15}\right )^{2}}{5} \]
command
integrate(1/5*((-2*ln(x)**2*ln(2*x)+2*ln(x)-2)*exp(-x*ln(2*x)+x-15)**2+(2*x*ln(x)**2*ln(2*x)-2*ln(x)**2-4*x*ln(x)+4*x)*exp(-x*ln(2*x)+x-15)+2*x*ln(x)**2+2*x**2*ln(x)-2*x**2)*exp(x/ln(x))**2/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
\[ \frac {x^{2} e^{\frac {2 x}{\log {\left (x \right )}}}}{5} - \frac {2 x e^{\frac {2 x}{\log {\left (x \right )}}} e^{- x \left (\log {\left (x \right )} + \log {\left (2 \right )}\right ) + x - 15}}{5} + \frac {e^{\frac {2 x}{\log {\left (x \right )}}} e^{- 2 x \left (\log {\left (x \right )} + \log {\left (2 \right )}\right ) + 2 x - 30}}{5} \]