\[ \int \frac {e^{\frac {16 x-81 x^2-24 e^{\frac {1}{5} (5 x+\log (5))} x^2+9 e^{\frac {2}{5} (5 x+\log (5))} x^3}{16-24 e^{\frac {1}{5} (5 x+\log (5))} x+9 e^{\frac {2}{5} (5 x+\log (5))} x^2}} \left (-64+648 x-108 e^{\frac {2}{5} (5 x+\log (5))} x^2+27 e^{\frac {3}{5} (5 x+\log (5))} x^3+e^{\frac {1}{5} (5 x+\log (5))} \left (144 x+486 x^3\right )\right )}{-64+144 e^{\frac {1}{5} (5 x+\log (5))} x-108 e^{\frac {2}{5} (5 x+\log (5))} x^2+27 e^{\frac {3}{5} (5 x+\log (5))} x^3} \, dx \]
Optimal antiderivative \[ {\mathrm e}^{x -\frac {9}{\left (\frac {4}{3 x}-{\mathrm e}^{\frac {\ln \left (5\right )}{5}+x}\right )^{2}}} \]
command
integrate((27*x^3*exp(1/5*log(5)+x)^3-108*x^2*exp(1/5*log(5)+x)^2+(486*x^3+144*x)*exp(1/5*log(5)+x)+648*x-64)*exp((9*x^3*exp(1/5*log(5)+x)^2-24*x^2*exp(1/5*log(5)+x)-81*x^2+16*x)/(9*x^2*exp(1/5*log(5)+x)^2-24*x*exp(1/5*log(5)+x)+16))/(27*x^3*exp(1/5*log(5)+x)^3-108*x^2*exp(1/5*log(5)+x)^2+144*x*exp(1/5*log(5)+x)-64),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \text {Exception raised: TypeError} \]
Giac 1.7.0 via sagemath 9.3 output
\[ e^{\left (\frac {9 \, x^{3} e^{\left (2 \, x + \frac {2}{5} \, \log \left (5\right )\right )}}{9 \, x^{2} e^{\left (2 \, x + \frac {2}{5} \, \log \left (5\right )\right )} - 24 \, x e^{\left (x + \frac {1}{5} \, \log \left (5\right )\right )} + 16} - \frac {24 \, x^{2} e^{\left (x + \frac {1}{5} \, \log \left (5\right )\right )}}{9 \, x^{2} e^{\left (2 \, x + \frac {2}{5} \, \log \left (5\right )\right )} - 24 \, x e^{\left (x + \frac {1}{5} \, \log \left (5\right )\right )} + 16} - \frac {81 \, x^{2}}{9 \, x^{2} e^{\left (2 \, x + \frac {2}{5} \, \log \left (5\right )\right )} - 24 \, x e^{\left (x + \frac {1}{5} \, \log \left (5\right )\right )} + 16} + \frac {16 \, x}{9 \, x^{2} e^{\left (2 \, x + \frac {2}{5} \, \log \left (5\right )\right )} - 24 \, x e^{\left (x + \frac {1}{5} \, \log \left (5\right )\right )} + 16}\right )} \]