\[ \int \frac {e^{\frac {135 x}{-5 x^2+\log (x)}} \left (-270 x+1350 x^3+50 x^4+\left (270 x-20 x^2\right ) \log (x)+2 \log ^2(x)\right )}{375 x^4-150 x^2 \log (x)+15 \log ^2(x)} \, dx \]
Optimal antiderivative \[ \frac {2 x \,{\mathrm e}^{\frac {27}{\frac {\ln \left (x \right )}{5 x}-x}}}{15} \]
command
integrate((2*ln(x)**2+(-20*x**2+270*x)*ln(x)+50*x**4+1350*x**3-270*x)*exp(135*x/(ln(x)-5*x**2))/(15*ln(x)**2-150*x**2*ln(x)+375*x**4),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \text {Exception raised: TypeError} \]
Sympy 1.8 under Python 3.8.8 output
\[ \frac {2 x e^{\frac {135 x}{- 5 x^{2} + \log {\left (x \right )}}}}{15} \]