\[ \int \frac {e^{x-\frac {2 \log ^2(4)}{-3 \log ^2(4)+e^x \left (x^2-2 x \log (3) \log (4)+\log ^2(3) \log ^2(4)\right )}} \left (\left (-8 x-4 x^2\right ) \log ^2(4)+(8+8 x) \log (3) \log ^3(4)-4 \log ^2(3) \log ^4(4)\right )}{9 \log ^4(4)+e^x \left (-6 x^2 \log ^2(4)+12 x \log (3) \log ^3(4)-6 \log ^2(3) \log ^4(4)\right )+e^{2 x} \left (x^4-4 x^3 \log (3) \log (4)+6 x^2 \log ^2(3) \log ^2(4)-4 x \log ^3(3) \log ^3(4)+\log ^4(3) \log ^4(4)\right )} \, dx \]
Optimal antiderivative \[ 2 \ln \left (2\right )-2 \,{\mathrm e}^{\frac {2}{3-{\mathrm e}^{x} \left (\ln \left (3\right )-\frac {x}{2 \ln \left (2\right )}\right )^{2}}} \]
command
integrate((-64*log(3)^2*log(2)^4+8*(8*x+8)*log(3)*log(2)^3+4*(-4*x^2-8*x)*log(2)^2)*exp(x)*exp(-8*log(2)^2/((4*log(3)^2*log(2)^2-4*x*log(2)*log(3)+x^2)*exp(x)-12*log(2)^2))/((16*log(3)^4*log(2)^4-32*x*log(3)^3*log(2)^3+24*x^2*log(3)^2*log(2)^2-8*x^3*log(3)*log(2)+x^4)*exp(x)^2+(-96*log(3)^2*log(2)^4+96*x*log(3)*log(2)^3-24*x^2*log(2)^2)*exp(x)+144*log(2)^4),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ -2 \, e^{\left (-\frac {8 \, \log \left (2\right )^{2}}{4 \, e^{x} \log \left (3\right )^{2} \log \left (2\right )^{2} - 4 \, x e^{x} \log \left (3\right ) \log \left (2\right ) + x^{2} e^{x} - 12 \, \log \left (2\right )^{2}}\right )} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \int -\frac {16 \, {\left (4 \, \log \left (3\right )^{2} \log \left (2\right )^{4} - 4 \, {\left (x + 1\right )} \log \left (3\right ) \log \left (2\right )^{3} + {\left (x^{2} + 2 \, x\right )} \log \left (2\right )^{2}\right )} e^{\left (x - \frac {8 \, \log \left (2\right )^{2}}{{\left (4 \, \log \left (3\right )^{2} \log \left (2\right )^{2} - 4 \, x \log \left (3\right ) \log \left (2\right ) + x^{2}\right )} e^{x} - 12 \, \log \left (2\right )^{2}}\right )}}{144 \, \log \left (2\right )^{4} + {\left (16 \, \log \left (3\right )^{4} \log \left (2\right )^{4} - 32 \, x \log \left (3\right )^{3} \log \left (2\right )^{3} + 24 \, x^{2} \log \left (3\right )^{2} \log \left (2\right )^{2} - 8 \, x^{3} \log \left (3\right ) \log \left (2\right ) + x^{4}\right )} e^{\left (2 \, x\right )} - 24 \, {\left (4 \, \log \left (3\right )^{2} \log \left (2\right )^{4} - 4 \, x \log \left (3\right ) \log \left (2\right )^{3} + x^{2} \log \left (2\right )^{2}\right )} e^{x}}\,{d x} \]________________________________________________________________________________________