\[ \int \frac {12 x^2 \log (2)+3 e^{2/x} x^2 \log (2)+3 e^{\frac {2 \left (x^3+x^3 \log (2)\right )}{\log (2)}} x^2 \log (2)+e^{\frac {1}{x}} \left (5+12 x^2\right ) \log (2)+e^{\frac {x^3+x^3 \log (2)}{\log (2)}} \left (15 x^4-6 e^{\frac {1}{x}} x^2 \log (2)+\left (-12 x^2+15 x^4\right ) \log (2)\right )}{12 x^2 \log (2)+12 e^{\frac {1}{x}} x^2 \log (2)+3 e^{2/x} x^2 \log (2)+3 e^{\frac {2 \left (x^3+x^3 \log (2)\right )}{\log (2)}} x^2 \log (2)+e^{\frac {x^3+x^3 \log (2)}{\log (2)}} \left (-12 x^2 \log (2)-6 e^{\frac {1}{x}} x^2 \log (2)\right )} \, dx \]
Optimal antiderivative \[ \frac {5}{3 \left ({\mathrm e}^{\frac {1}{x}}-{\mathrm e}^{\frac {x^{2} \left (x \ln \left (2\right )+x \right )}{\ln \left (2\right )}}+2\right )}+x \]
command
Integrate[(12*x^2*Log[2] + 3*E^(2/x)*x^2*Log[2] + 3*E^((2*(x^3 + x^3*Log[2]))/Log[2])*x^2*Log[2] + E^x^(-1)*(5 + 12*x^2)*Log[2] + E^((x^3 + x^3*Log[2])/Log[2])*(15*x^4 - 6*E^x^(-1)*x^2*Log[2] + (-12*x^2 + 15*x^4)*Log[2]))/(12*x^2*Log[2] + 12*E^x^(-1)*x^2*Log[2] + 3*E^(2/x)*x^2*Log[2] + 3*E^((2*(x^3 + x^3*Log[2]))/Log[2])*x^2*Log[2] + E^((x^3 + x^3*Log[2])/Log[2])*(-12*x^2*Log[2] - 6*E^x^(-1)*x^2*Log[2])),x]
Mathematica 13.1 output
\[ \int \frac {12 x^2 \log (2)+3 e^{2/x} x^2 \log (2)+3 e^{\frac {2 \left (x^3+x^3 \log (2)\right )}{\log (2)}} x^2 \log (2)+e^{\frac {1}{x}} \left (5+12 x^2\right ) \log (2)+e^{\frac {x^3+x^3 \log (2)}{\log (2)}} \left (15 x^4-6 e^{\frac {1}{x}} x^2 \log (2)+\left (-12 x^2+15 x^4\right ) \log (2)\right )}{12 x^2 \log (2)+12 e^{\frac {1}{x}} x^2 \log (2)+3 e^{2/x} x^2 \log (2)+3 e^{\frac {2 \left (x^3+x^3 \log (2)\right )}{\log (2)}} x^2 \log (2)+e^{\frac {x^3+x^3 \log (2)}{\log (2)}} \left (-12 x^2 \log (2)-6 e^{\frac {1}{x}} x^2 \log (2)\right )} \, dx \]
Mathematica 12.3 output
\[ \frac {1}{3} \left (3 x+\frac {15 \left (2+e^{\frac {1}{x}}\right ) x^4 (1+\log (2))+e^{\frac {1}{x}} \log (32)}{\left (2+e^{\frac {1}{x}}-e^{x^3 \left (1+\frac {1}{\log (2)}\right )}\right ) \left (e^{\frac {1}{x}} \log (2)+x^4 \left (6+e^{\frac {1}{x}} (3+\log (8))+\log (64)\right )\right )}\right ) \]