44.3 Problem number 152

\[ \int \frac {e^{\frac {4 x^3}{11 x-2 e^2 x-2 x^2+2 \log (x)}} \left (-8 x^2+88 x^3-16 e^2 x^3-8 x^4+24 x^2 \log (x)\right )}{121 x^2+4 e^4 x^2-44 x^3+4 x^4+e^2 \left (-44 x^2+8 x^3\right )+\left (44 x-8 e^2 x-8 x^2\right ) \log (x)+4 \log ^2(x)} \, dx \]

Optimal antiderivative \[ {\mathrm e}^{\frac {2 x^{2}}{\frac {\ln \left (x \right )}{x}+\frac {11}{2}-x -{\mathrm e}^{2}}}-4 \,{\mathrm e}^{-2} \]

command

integrate((24*x**2*ln(x)-16*x**3*exp(2)-8*x**4+88*x**3-8*x**2)*exp(2*x**3/(2*ln(x)-2*exp(2)*x-2*x**2+11*x))**2/(4*ln(x)**2+(-8*exp(2)*x-8*x**2+44*x)*ln(x)+4*x**2*exp(2)**2+(8*x**3-44*x**2)*exp(2)+4*x**4-44*x**3+121*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

\[ e^{\frac {4 x^{3}}{- 2 x^{2} - 2 x e^{2} + 11 x + 2 \log {\left (x \right )}}} \]