\[ \int \frac {15 x-50 e^x x+10 e^{2 x} x-5 x^2+\left (15 x-10 x^2\right ) \log (x)+\left (-125+50 e^x-5 e^{2 x}+\left (-15 x+5 x^2\right ) \log (x)\right ) \log \left (25-10 e^x+e^{2 x}+\left (3 x-x^2\right ) \log (x)\right ) \log \left (\log \left (25-10 e^x+e^{2 x}+\left (3 x-x^2\right ) \log (x)\right )\right )}{\left (-25 x+10 e^x x-e^{2 x} x+\left (-3 x^2+x^3\right ) \log (x)\right ) \log \left (25-10 e^x+e^{2 x}+\left (3 x-x^2\right ) \log (x)\right ) \log \left (\log \left (25-10 e^x+e^{2 x}+\left (3 x-x^2\right ) \log (x)\right )\right ) \log ^2\left (\frac {\log \left (\log \left (25-10 e^x+e^{2 x}+\left (3 x-x^2\right ) \log (x)\right )\right )}{x}\right )} \, dx \]
Optimal antiderivative \[ \frac {5}{\ln \! \left (\frac {\ln \left (\ln \left (\left (5-{\mathrm e}^{x}\right )^{2}+\left (3-x \right ) x \ln \left (x \right )\right )\right )}{x}\right )} \]
command
integrate((((5*x^2-15*x)*log(x)-5*exp(x)^2+50*exp(x)-125)*log((-x^2+3*x)*log(x)+exp(x)^2-10*exp(x)+25)*log(log((-x^2+3*x)*log(x)+exp(x)^2-10*exp(x)+25))+(-10*x^2+15*x)*log(x)+10*x*exp(x)^2-50*exp(x)*x-5*x^2+15*x)/((x^3-3*x^2)*log(x)-x*exp(x)^2+10*exp(x)*x-25*x)/log((-x^2+3*x)*log(x)+exp(x)^2-10*exp(x)+25)/log(log((-x^2+3*x)*log(x)+exp(x)^2-10*exp(x)+25))/log(log(log((-x^2+3*x)*log(x)+exp(x)^2-10*exp(x)+25))/x)^2,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
\[ -\frac {5}{\log \left (x\right ) - \log \left (\log \left (\log \left (-x^{2} \log \left (x\right ) + 3 \, x \log \left (x\right ) + e^{\left (2 \, x\right )} - 10 \, e^{x} + 25\right )\right )\right )} \]