\[ \int \frac {e^{\frac {25+10 x^3 \log (x)+\left (-5 x^4+x^6\right ) \log ^2(x)}{x^4 \log ^2(x)}} \left (-50+\left (-100-10 x^3\right ) \log (x)-10 x^3 \log ^2(x)+2 x^6 \log ^3(x)\right )}{\left (-100 x^5 \log ^3(x)+20 e^{\frac {25+10 x^3 \log (x)+\left (-5 x^4+x^6\right ) \log ^2(x)}{x^4 \log ^2(x)}} x^5 \log ^3(x)+\log \left (5-e^{\frac {25+10 x^3 \log (x)+\left (-5 x^4+x^6\right ) \log ^2(x)}{x^4 \log ^2(x)}}\right ) \left (-5 x^5 \log ^3(x)+e^{\frac {25+10 x^3 \log (x)+\left (-5 x^4+x^6\right ) \log ^2(x)}{x^4 \log ^2(x)}} x^5 \log ^3(x)\right )\right ) \log \left (20+\log \left (5-e^{\frac {25+10 x^3 \log (x)+\left (-5 x^4+x^6\right ) \log ^2(x)}{x^4 \log ^2(x)}}\right )\right )} \, dx \]
Optimal antiderivative \[ \ln \left (\ln \left (\ln \left (5-{\mathrm e}^{\left (\frac {5}{x^{2} \ln \left (x \right )}+x \right )^{2}-5}\right )+20\right )\right ) \]
command
integrate((2*x^6*log(x)^3-10*x^3*log(x)^2+(-10*x^3-100)*log(x)-50)*exp(((x^6-5*x^4)*log(x)^2+10*x^3*log(x)+25)/x^4/log(x)^2)/((x^5*log(x)^3*exp(((x^6-5*x^4)*log(x)^2+10*x^3*log(x)+25)/x^4/log(x)^2)-5*x^5*log(x)^3)*log(-exp(((x^6-5*x^4)*log(x)^2+10*x^3*log(x)+25)/x^4/log(x)^2)+5)+20*x^5*log(x)^3*exp(((x^6-5*x^4)*log(x)^2+10*x^3*log(x)+25)/x^4/log(x)^2)-100*x^5*log(x)^3)/log(log(-exp(((x^6-5*x^4)*log(x)^2+10*x^3*log(x)+25)/x^4/log(x)^2)+5)+20),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \log \left (\log \left (\log \left (-e^{\left (\frac {x^{6} \log \left (x\right )^{2} - 5 \, x^{4} \log \left (x\right )^{2} + 10 \, x^{3} \log \left (x\right ) + 25}{x^{4} \log \left (x\right )^{2}}\right )} + 5\right ) + 20\right )\right ) \]
Giac 1.7.0 via sagemath 9.3 output
\[ \mathit {sage}_{0} x \]________________________________________________________________________________________