\[ \int \frac {x+x^{\frac {3 e^{e^3+4 x^2}}{x}} \left (3 e^{e^3+4 x^2}+e^{e^3+4 x^2} \left (-3+24 x^2\right ) \log (x)\right )}{x^2} \, dx \]
Optimal antiderivative \[ \ln \left (x \right )+{\mathrm e}^{\frac {3 \,{\mathrm e}^{{\mathrm e}^{3}+4 x^{2}} \ln \left (x \right )}{x}} \]
command
integrate((((24*x^2-3)*exp(exp(3)+4*x^2)*log(x)+3*exp(exp(3)+4*x^2))*exp(3*exp(exp(3)+4*x^2)*log(x)/x)+x)/x^2,x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ x^{\frac {3 \, e^{\left (4 \, x^{2} + e^{3}\right )}}{x}} + \log \left (x\right ) \]
Giac 1.7.0 via sagemath 9.3 output
\[ \int \frac {3 \, {\left ({\left (8 \, x^{2} - 1\right )} e^{\left (4 \, x^{2} + e^{3}\right )} \log \left (x\right ) + e^{\left (4 \, x^{2} + e^{3}\right )}\right )} x^{\frac {3 \, e^{\left (4 \, x^{2} + e^{3}\right )}}{x}} + x}{x^{2}}\,{d x} \]________________________________________________________________________________________