\[ \int \frac {-2-25 x+e^{x^2} \left (-27+4 x^2\right )+27 \log (x)+\left (-e^{x^2}-x+\log (x)\right ) \log \left (\frac {e^{2 x^2}+2 e^{x^2} x+x^2+\left (-2 e^{x^2}-2 x\right ) \log (x)+\log ^2(x)}{x^2}\right )}{-e^{x^2} x^2-x^3+x^2 \log (x)} \, dx \]
Optimal antiderivative \[ 5-\frac {25+\ln \left (\frac {\left ({\mathrm e}^{x^{2}}-\ln \left (x \right )+x \right )^{2}}{x^{2}}\right )}{x} \]
command
integrate(((log(x)-exp(x^2)-x)*log((log(x)^2+(-2*exp(x^2)-2*x)*log(x)+exp(x^2)^2+2*exp(x^2)*x+x^2)/x^2)+27*log(x)+(4*x^2-27)*exp(x^2)-25*x-2)/(x^2*log(x)-x^2*exp(x^2)-x^3),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ -\frac {\log \left (x^{2} + 2 \, x e^{\left (x^{2}\right )} - 2 \, x \log \left (x\right ) - 2 \, e^{\left (x^{2}\right )} \log \left (x\right ) + \log \left (x\right )^{2} + e^{\left (2 \, x^{2}\right )}\right ) - 2 \, \log \left (x\right ) + 25}{x} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Timed out} \]________________________________________________________________________________________