\[ \int \frac {\left (600-160 x-136 x^2-16 x^3\right ) \log ^2(2 x)+e^{\frac {x}{(40+8 x) \log (2 x)}} \left (-5 x-x^2+5 x \log (2 x)+\left (200+80 x+8 x^2\right ) \log ^2(2 x)\right )}{\left (200+80 x+8 x^2\right ) \log ^2(2 x)} \, dx \]
Optimal antiderivative \[ \left (3+{\mathrm e}^{\frac {x}{8 \left (5+x \right ) \ln \left (2 x \right )}}-x \right ) x \]
command
integrate((((8*x**2+80*x+200)*ln(2*x)**2+5*x*ln(2*x)-x**2-5*x)*exp(x/(8*x+40)/ln(2*x))+(-16*x**3-136*x**2-160*x+600)*ln(2*x)**2)/(8*x**2+80*x+200)/ln(2*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
\[ - x^{2} + x e^{\frac {x}{\left (8 x + 40\right ) \log {\left (2 x \right )}}} + 3 x \]