\[ \int \frac {e^{50} (-8-4 x)-18 x-16 x^2-4 x^3+e^{25} \left (-16-24 x-8 x^2\right )+\left (e^{50} (-4-2 x)-8 x-8 x^2-2 x^3+e^{25} \left (-8-12 x-4 x^2\right )\right ) \log \left (\frac {20+10 e^{25}+10 x}{e^{25}+x}\right )+\left (2 e^{50}+4 x+2 x^2+e^{25} (4+4 x)+\left (e^{50}+2 x+x^2+e^{25} (2+2 x)\right ) \log \left (\frac {20+10 e^{25}+10 x}{e^{25}+x}\right )\right ) \log \left (4 x+2 x \log \left (\frac {20+10 e^{25}+10 x}{e^{25}+x}\right )\right )}{2 e^{50}+4 x+2 x^2+e^{25} (4+4 x)+\left (e^{50}+2 x+x^2+e^{25} (2+2 x)\right ) \log \left (\frac {20+10 e^{25}+10 x}{e^{25}+x}\right )} \, dx \]
Optimal antiderivative \[ \left (\ln \left (x \left (4+2 \ln \left (10+\frac {20}{{\mathrm e}^{25}+x}\right )\right )\right )-5-x \right ) x \]
command
integrate((((exp(25)**2+(2+2*x)*exp(25)+x**2+2*x)*ln((10*exp(25)+10*x+20)/(exp(25)+x))+2*exp(25)**2+(4*x+4)*exp(25)+2*x**2+4*x)*ln(2*x*ln((10*exp(25)+10*x+20)/(exp(25)+x))+4*x)+((-2*x-4)*exp(25)**2+(-4*x**2-12*x-8)*exp(25)-2*x**3-8*x**2-8*x)*ln((10*exp(25)+10*x+20)/(exp(25)+x))+(-4*x-8)*exp(25)**2+(-8*x**2-24*x-16)*exp(25)-4*x**3-16*x**2-18*x)/((exp(25)**2+(2+2*x)*exp(25)+x**2+2*x)*ln((10*exp(25)+10*x+20)/(exp(25)+x))+2*exp(25)**2+(4*x+4)*exp(25)+2*x**2+4*x),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ - x^{2} - 5 x + \left (x + \frac {1}{6} + \frac {e^{25}}{6}\right ) \log {\left (2 x \log {\left (\frac {10 x + 20 + 10 e^{25}}{x + e^{25}} \right )} + 4 x \right )} - \frac {\left (1 + e\right ) \left (- e^{3} - e + 1 + e^{2} + e^{4}\right ) \left (- e^{15} - e^{5} + 1 + e^{10} + e^{20}\right ) \log {\left (x \right )}}{6} - \frac {\left (1 + e\right ) \left (- e^{3} - e + 1 + e^{2} + e^{4}\right ) \left (- e^{15} - e^{5} + 1 + e^{10} + e^{20}\right ) \log {\left (\log {\left (\frac {10 x + 20 + 10 e^{25}}{x + e^{25}} \right )} + 2 \right )}}{6} \]
Sympy 1.8 under Python 3.8.8 output
\[ \text {Exception raised: CoercionFailed} \]________________________________________________________________________________________