\[ \int \frac {e^{\frac {1}{3} (-4-15 x)} \left (-75 \log ^2(x)+e^{\frac {2}{3} \left (-1+e^{\frac {x}{\log (x)}}\right )} \left (-75 \log ^2(x)+e^{\frac {x}{\log (x)}} (-10+10 \log (x))\right )\right )}{\log ^2(x)} \, dx \]
Optimal antiderivative \[ 15 \left ({\mathrm e}^{\frac {2 \,{\mathrm e}^{\frac {x}{\ln \left (x \right )}}}{3}-\frac {2}{3}}+1\right ) {\mathrm e}^{-5 x -\frac {4}{3}} \]
command
integrate((((10*ln(x)-10)*exp(x/ln(x))-75*ln(x)**2)*exp(1/3*exp(x/ln(x))-1/3)**2-75*ln(x)**2)/exp(5*x+4/3)/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
\[ 15 e^{- 5 x - \frac {4}{3}} e^{\frac {2 e^{\frac {x}{\log {\left (x \right )}}}}{3} - \frac {2}{3}} + 15 e^{- 5 x - \frac {4}{3}} \]