\[ \int \frac {\left (-e^5+x\right )^{\frac {20 x}{-x^2+\log ^4(7)}} \left (20 x^3-20 x \log ^4(7)+\left (20 e^5 x^2-20 x^3+\left (20 e^5-20 x\right ) \log ^4(7)\right ) \log \left (-e^5+x\right )\right )}{e^5 x^4-x^5+\left (-2 e^5 x^2+2 x^3\right ) \log ^4(7)+\left (e^5-x\right ) \log ^8(7)} \, dx \]
Optimal antiderivative \[ {\mathrm e}^{\frac {20 \ln \left (-{\mathrm e}^{5}+x \right )}{\frac {\ln \left (7\right )^{4}}{x}-x}} \]
command
integrate((((20*exp(5)-20*x)*log(7)^4+20*x^2*exp(5)-20*x^3)*log(-exp(5)+x)-20*x*log(7)^4+20*x^3)*exp(5*x*log(-exp(5)+x)/(log(7)^4-x^2))^4/((exp(5)-x)*log(7)^8+(-2*x^2*exp(5)+2*x^3)*log(7)^4+x^4*exp(5)-x^5),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
\[ {\left (x - e^{5}\right )}^{\frac {20 \, {\left (x - e^{5}\right )}}{\log \left (7\right )^{4} - {\left (x - e^{5}\right )}^{2} - 2 \, {\left (x - e^{5}\right )} e^{5} - e^{10}}} {\left (x - e^{5}\right )}^{\frac {20 \, e^{5}}{\log \left (7\right )^{4} - {\left (x - e^{5}\right )}^{2} - 2 \, {\left (x - e^{5}\right )} e^{5} - e^{10}}} \]