\[ \int \frac {-507 x^2+481 x^3-152 x^4+16 x^5+\left (-234 x^2+150 x^3-24 x^4\right ) \log \left (81-108 x+54 x^2-12 x^3+x^4\right )+\left (-27 x^2+9 x^3\right ) \log ^2\left (81-108 x+54 x^2-12 x^3+x^4\right )+e^{\frac {1}{13 x-4 x^2+3 x \log \left (81-108 x+54 x^2-12 x^3+x^4\right )}} \left (39-49 x+8 x^2+(9-3 x) \log \left (81-108 x+54 x^2-12 x^3+x^4\right )\right )}{-507 x^2+481 x^3-152 x^4+16 x^5+\left (-234 x^2+150 x^3-24 x^4\right ) \log \left (81-108 x+54 x^2-12 x^3+x^4\right )+\left (-27 x^2+9 x^3\right ) \log ^2\left (81-108 x+54 x^2-12 x^3+x^4\right )} \, dx \]
Optimal antiderivative \[ x +{\mathrm e}^{\frac {1}{x \left (-4 x +13+3 \ln \left (\left (-3+x \right )^{4}\right )\right )}} \]
command
integrate((((-3*x+9)*ln(x**4-12*x**3+54*x**2-108*x+81)+8*x**2-49*x+39)*exp(1/(3*x*ln(x**4-12*x**3+54*x**2-108*x+81)-4*x**2+13*x))+(9*x**3-27*x**2)*ln(x**4-12*x**3+54*x**2-108*x+81)**2+(-24*x**4+150*x**3-234*x**2)*ln(x**4-12*x**3+54*x**2-108*x+81)+16*x**5-152*x**4+481*x**3-507*x**2)/((9*x**3-27*x**2)*ln(x**4-12*x**3+54*x**2-108*x+81)**2+(-24*x**4+150*x**3-234*x**2)*ln(x**4-12*x**3+54*x**2-108*x+81)+16*x**5-152*x**4+481*x**3-507*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
\[ x + e^{\frac {1}{- 4 x^{2} + 3 x \log {\left (x^{4} - 12 x^{3} + 54 x^{2} - 108 x + 81 \right )} + 13 x}} \]