\[ \int \frac {24-4 x+100 x^2-117 x^3+12 x^4+12 x^5+e^{2 x} \left (12 x^2+3 x^3\right )+e^x \left (8+4 x+72 x^2-30 x^3-12 x^4\right )+\left (-36+31 x+10 x^2+e^x \left (-12-11 x-2 x^2\right )\right ) \log \left (4 x+x^2\right )}{\left (108 x^3-117 x^4+12 x^5+12 x^6+e^{2 x} \left (12 x^3+3 x^4\right )+e^x \left (72 x^3-30 x^4-12 x^5\right )+\left (12 x-5 x^2-2 x^3+e^x \left (4 x+x^2\right )\right ) \log \left (4 x+x^2\right )\right ) \log \left (\frac {81 x^4+9 e^{2 x} x^4-108 x^5+36 x^6+e^x \left (54 x^4-36 x^5\right )+\left (18 x^2+6 e^x x^2-12 x^3\right ) \log \left (4 x+x^2\right )+\log ^2\left (4 x+x^2\right )}{9 x^3+e^{2 x} x^3-12 x^4+4 x^5+e^x \left (6 x^3-4 x^4\right )}\right )} \, dx \]
Optimal antiderivative \[ \ln \left (\ln \left (\left (3-\frac {\ln \left (\left (4+x \right ) x \right )}{x^{2} \left (2 x -3-{\mathrm e}^{x}\right )}\right )^{2} x \right )\right ) \]
command
integrate((((-2*x**2-11*x-12)*exp(x)+10*x**2+31*x-36)*ln(x**2+4*x)+(3*x**3+12*x**2)*exp(x)**2+(-12*x**4-30*x**3+72*x**2+4*x+8)*exp(x)+12*x**5+12*x**4-117*x**3+100*x**2-4*x+24)/(((x**2+4*x)*exp(x)-2*x**3-5*x**2+12*x)*ln(x**2+4*x)+(3*x**4+12*x**3)*exp(x)**2+(-12*x**5-30*x**4+72*x**3)*exp(x)+12*x**6+12*x**5-117*x**4+108*x**3)/ln((ln(x**2+4*x)**2+(6*exp(x)*x**2-12*x**3+18*x**2)*ln(x**2+4*x)+9*exp(x)**2*x**4+(-36*x**5+54*x**4)*exp(x)+36*x**6-108*x**5+81*x**4)/(exp(x)**2*x**3+(-4*x**4+6*x**3)*exp(x)+4*x**5-12*x**4+9*x**3)),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \log {\left (\log {\left (\frac {36 x^{6} - 108 x^{5} + 9 x^{4} e^{2 x} + 81 x^{4} + \left (- 36 x^{5} + 54 x^{4}\right ) e^{x} + \left (- 12 x^{3} + 6 x^{2} e^{x} + 18 x^{2}\right ) \log {\left (x^{2} + 4 x \right )} + \log {\left (x^{2} + 4 x \right )}^{2}}{4 x^{5} - 12 x^{4} + x^{3} e^{2 x} + 9 x^{3} + \left (- 4 x^{4} + 6 x^{3}\right ) e^{x}} \right )} \right )} \]
Sympy 1.8 under Python 3.8.8 output
\[ \text {Timed out} \]________________________________________________________________________________________