44.31 Problem number 2240

$$\int \frac{e^{\frac{135x}{-5x^2+\log (x)}}(-270x+1350x^3+50x^4+(270x-20x^2)\log (x)+2{\log }^2(x))}{375x^4-150x^2\log (x)+15{\log }^2(x)}dx$$

Optimal antiderivative $$\frac{2x{\mathrm{e}}^{\frac{27}{\frac{\ln \left(x\right)}{5x}-x}}}{15}$$

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

$$\frac{2x{e}^{\frac{135x}{-5x^2+\log \left(x\right)}}}{15}$$