\[ \int \frac {e^{\frac {1}{15} \left (12+5 e^{\frac {2-16 x+4 x^2+4 x \log \left (25+10 x+x^2\right )}{-4 x+x^2+x \log \left (25+10 x+x^2\right )}} x\right )+\frac {2-16 x+4 x^2+4 x \log \left (25+10 x+x^2\right )}{-4 x+x^2+x \log \left (25+10 x+x^2\right )}} \left (40+64 x-28 x^2-3 x^3+x^4+\left (-10-42 x+2 x^2+2 x^3\right ) \log \left (25+10 x+x^2\right )+\left (5 x+x^2\right ) \log ^2\left (25+10 x+x^2\right )\right )}{240 x-72 x^2-9 x^3+3 x^4+\left (-120 x+6 x^2+6 x^3\right ) \log \left (25+10 x+x^2\right )+\left (15 x+3 x^2\right ) \log ^2\left (25+10 x+x^2\right )} \, dx \]
Optimal antiderivative \[ {\mathrm e}^{\frac {x \,{\mathrm e}^{4-\frac {2}{x \left (5-\ln \left (\left (5+x \right )^{2}\right )-x \right )-x}}}{3}+\frac {4}{5}} \]
command
integrate(((x**2+5*x)*ln(x**2+10*x+25)**2+(2*x**3+2*x**2-42*x-10)*ln(x**2+10*x+25)+x**4-3*x**3-28*x**2+64*x+40)*exp((4*x*ln(x**2+10*x+25)+4*x**2-16*x+2)/(x*ln(x**2+10*x+25)+x**2-4*x))*exp(1/3*x*exp((4*x*ln(x**2+10*x+25)+4*x**2-16*x+2)/(x*ln(x**2+10*x+25)+x**2-4*x))+4/5)/((3*x**2+15*x)*ln(x**2+10*x+25)**2+(6*x**3+6*x**2-120*x)*ln(x**2+10*x+25)+3*x**4-9*x**3-72*x**2+240*x),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \text {Exception raised: TypeError} \]
Sympy 1.8 under Python 3.8.8 output
\[ e^{\frac {x e^{\frac {4 x^{2} + 4 x \log {\left (x^{2} + 10 x + 25 \right )} - 16 x + 2}{x^{2} + x \log {\left (x^{2} + 10 x + 25 \right )} - 4 x}}}{3} + \frac {4}{5}} \]