\[ \int \frac {e^{\frac {9 x}{\log \left (\frac {e^{10}+2 e^5 x+x^2}{e^8}\right )}} \left (36 x+\left (-18 e^5-18 x\right ) \log \left (\frac {e^{10}+2 e^5 x+x^2}{e^8}\right )\right )}{e^{\frac {18 x}{\log \left (\frac {e^{10}+2 e^5 x+x^2}{e^8}\right )}} \left (e^5+x\right ) \log ^2\left (\frac {e^{10}+2 e^5 x+x^2}{e^8}\right )+e^{\frac {9 x}{\log \left (\frac {e^{10}+2 e^5 x+x^2}{e^8}\right )}} \left (2 e^7+2 e^2 x\right ) \log ^2\left (\frac {e^{10}+2 e^5 x+x^2}{e^8}\right )+\left (e^9+e^4 x\right ) \log ^2\left (\frac {e^{10}+2 e^5 x+x^2}{e^8}\right )} \, dx \]
Optimal antiderivative \[ \frac {2}{{\mathrm e}^{\frac {9 x}{\ln \left (\left ({\mathrm e}^{5}+x \right )^{2} {\mathrm e}^{-8}\right )}}+{\mathrm e}^{2}} \]
command
integrate(((-18*exp(5)-18*x)*log((exp(5)^2+2*x*exp(5)+x^2)/exp(4)^2)+36*x)*exp(9*x/log((exp(5)^2+2*x*exp(5)+x^2)/exp(4)^2))/((exp(5)+x)*log((exp(5)^2+2*x*exp(5)+x^2)/exp(4)^2)^2*exp(9*x/log((exp(5)^2+2*x*exp(5)+x^2)/exp(4)^2))^2+(2*exp(2)*exp(5)+2*exp(2)*x)*log((exp(5)^2+2*x*exp(5)+x^2)/exp(4)^2)^2*exp(9*x/log((exp(5)^2+2*x*exp(5)+x^2)/exp(4)^2))+(exp(2)^2*exp(5)+x*exp(2)^2)*log((exp(5)^2+2*x*exp(5)+x^2)/exp(4)^2)^2),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \text {could not integrate} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \frac {2 \, {\left (x^{2} \log \left (x^{2} + 2 \, x e^{5} + e^{10}\right )^{3} + 2 \, x e^{5} \log \left (x^{2} + 2 \, x e^{5} + e^{10}\right )^{3} - 26 \, x^{2} \log \left (x^{2} + 2 \, x e^{5} + e^{10}\right )^{2} - 50 \, x e^{5} \log \left (x^{2} + 2 \, x e^{5} + e^{10}\right )^{2} + e^{10} \log \left (x^{2} + 2 \, x e^{5} + e^{10}\right )^{3} + 224 \, x^{2} \log \left (x^{2} + 2 \, x e^{5} + e^{10}\right ) + 416 \, x e^{5} \log \left (x^{2} + 2 \, x e^{5} + e^{10}\right ) - 24 \, e^{10} \log \left (x^{2} + 2 \, x e^{5} + e^{10}\right )^{2} - 640 \, x^{2} - 1152 \, x e^{5} + 192 \, e^{10} \log \left (x^{2} + 2 \, x e^{5} + e^{10}\right ) - 512 \, e^{10}\right )}}{x^{2} e^{2} \log \left (x^{2} + 2 \, x e^{5} + e^{10}\right )^{3} + x^{2} e^{\left (\frac {9 \, x}{\log \left (x^{2} + 2 \, x e^{5} + e^{10}\right ) - 8}\right )} \log \left (x^{2} + 2 \, x e^{5} + e^{10}\right )^{3} - 26 \, x^{2} e^{2} \log \left (x^{2} + 2 \, x e^{5} + e^{10}\right )^{2} - 26 \, x^{2} e^{\left (\frac {9 \, x}{\log \left (x^{2} + 2 \, x e^{5} + e^{10}\right ) - 8}\right )} \log \left (x^{2} + 2 \, x e^{5} + e^{10}\right )^{2} + 2 \, x e^{7} \log \left (x^{2} + 2 \, x e^{5} + e^{10}\right )^{3} + 2 \, x e^{\left (\frac {9 \, x}{\log \left (x^{2} + 2 \, x e^{5} + e^{10}\right ) - 8} + 5\right )} \log \left (x^{2} + 2 \, x e^{5} + e^{10}\right )^{3} + 224 \, x^{2} e^{2} \log \left (x^{2} + 2 \, x e^{5} + e^{10}\right ) + 224 \, x^{2} e^{\left (\frac {9 \, x}{\log \left (x^{2} + 2 \, x e^{5} + e^{10}\right ) - 8}\right )} \log \left (x^{2} + 2 \, x e^{5} + e^{10}\right ) - 50 \, x e^{7} \log \left (x^{2} + 2 \, x e^{5} + e^{10}\right )^{2} - 50 \, x e^{\left (\frac {9 \, x}{\log \left (x^{2} + 2 \, x e^{5} + e^{10}\right ) - 8} + 5\right )} \log \left (x^{2} + 2 \, x e^{5} + e^{10}\right )^{2} + e^{12} \log \left (x^{2} + 2 \, x e^{5} + e^{10}\right )^{3} + e^{\left (\frac {9 \, x}{\log \left (x^{2} + 2 \, x e^{5} + e^{10}\right ) - 8} + 10\right )} \log \left (x^{2} + 2 \, x e^{5} + e^{10}\right )^{3} - 640 \, x^{2} e^{2} - 640 \, x^{2} e^{\left (\frac {9 \, x}{\log \left (x^{2} + 2 \, x e^{5} + e^{10}\right ) - 8}\right )} + 416 \, x e^{7} \log \left (x^{2} + 2 \, x e^{5} + e^{10}\right ) + 416 \, x e^{\left (\frac {9 \, x}{\log \left (x^{2} + 2 \, x e^{5} + e^{10}\right ) - 8} + 5\right )} \log \left (x^{2} + 2 \, x e^{5} + e^{10}\right ) - 24 \, e^{12} \log \left (x^{2} + 2 \, x e^{5} + e^{10}\right )^{2} - 24 \, e^{\left (\frac {9 \, x}{\log \left (x^{2} + 2 \, x e^{5} + e^{10}\right ) - 8} + 10\right )} \log \left (x^{2} + 2 \, x e^{5} + e^{10}\right )^{2} - 1152 \, x e^{7} - 1152 \, x e^{\left (\frac {9 \, x}{\log \left (x^{2} + 2 \, x e^{5} + e^{10}\right ) - 8} + 5\right )} + 192 \, e^{12} \log \left (x^{2} + 2 \, x e^{5} + e^{10}\right ) + 192 \, e^{\left (\frac {9 \, x}{\log \left (x^{2} + 2 \, x e^{5} + e^{10}\right ) - 8} + 10\right )} \log \left (x^{2} + 2 \, x e^{5} + e^{10}\right ) - 512 \, e^{12} - 512 \, e^{\left (\frac {9 \, x}{\log \left (x^{2} + 2 \, x e^{5} + e^{10}\right ) - 8} + 10\right )}} \]