\[ \int \frac {\left (625+1500 x+1350 x^2+540 x^3+81 x^4\right ) \log (2)+\left (625+1500 x+1350 x^2+540 x^3+81 x^4\right ) \log ^2(2)+e^{2 x} \left (4 x^2+4 x^3+\left (4 x^3+x^4\right ) \log (2)+x^4 \log ^2(2)\right )+e^x \left (-10 x^2+22 x^3+18 x^4+\left (-100 x-170 x^2-96 x^3-18 x^4\right ) \log (2)+\left (-50 x^2-60 x^3-18 x^4\right ) \log ^2(2)\right )+\left (\left (50 x^2+60 x^3+18 x^4\right ) \log (2)+\left (50 x^2+60 x^3+18 x^4\right ) \log ^2(2)+e^x \left (-4 x^3+2 x^4+\left (-4 x^3-2 x^4\right ) \log (2)-2 x^4 \log ^2(2)\right )\right ) \log (x)+\left (x^4 \log (2)+x^4 \log ^2(2)\right ) \log ^2(x)}{\left (625+1500 x+1350 x^2+540 x^3+81 x^4\right ) \log ^2(2)+e^{2 x} \left (4 x^2+4 x^3 \log (2)+x^4 \log ^2(2)\right )+e^x \left (\left (-100 x-120 x^2-36 x^3\right ) \log (2)+\left (-50 x^2-60 x^3-18 x^4\right ) \log ^2(2)\right )+\left (\left (50 x^2+60 x^3+18 x^4\right ) \log ^2(2)+e^x \left (-4 x^3 \log (2)-2 x^4 \log ^2(2)\right )\right ) \log (x)+x^4 \log ^2(2) \log ^2(x)} \, dx \]
Optimal antiderivative \[ \frac {x}{\ln \! \left (2\right )-\frac {2 \,{\mathrm e}^{x}}{x \left (\left (3+\frac {5}{x}\right )^{2}-{\mathrm e}^{x}+\ln \left (x \right )\right )}}+x \]
command
Integrate[((625 + 1500*x + 1350*x^2 + 540*x^3 + 81*x^4)*Log[2] + (625 + 1500*x + 1350*x^2 + 540*x^3 + 81*x^4)*Log[2]^2 + E^(2*x)*(4*x^2 + 4*x^3 + (4*x^3 + x^4)*Log[2] + x^4*Log[2]^2) + E^x*(-10*x^2 + 22*x^3 + 18*x^4 + (-100*x - 170*x^2 - 96*x^3 - 18*x^4)*Log[2] + (-50*x^2 - 60*x^3 - 18*x^4)*Log[2]^2) + ((50*x^2 + 60*x^3 + 18*x^4)*Log[2] + (50*x^2 + 60*x^3 + 18*x^4)*Log[2]^2 + E^x*(-4*x^3 + 2*x^4 + (-4*x^3 - 2*x^4)*Log[2] - 2*x^4*Log[2]^2))*Log[x] + (x^4*Log[2] + x^4*Log[2]^2)*Log[x]^2)/((625 + 1500*x + 1350*x^2 + 540*x^3 + 81*x^4)*Log[2]^2 + E^(2*x)*(4*x^2 + 4*x^3*Log[2] + x^4*Log[2]^2) + E^x*((-100*x - 120*x^2 - 36*x^3)*Log[2] + (-50*x^2 - 60*x^3 - 18*x^4)*Log[2]^2) + ((50*x^2 + 60*x^3 + 18*x^4)*Log[2]^2 + E^x*(-4*x^3*Log[2] - 2*x^4*Log[2]^2))*Log[x] + x^4*Log[2]^2*Log[x]^2),x]
Mathematica 13.1 output
\[ \int \frac {\left (625+1500 x+1350 x^2+540 x^3+81 x^4\right ) \log (2)+\left (625+1500 x+1350 x^2+540 x^3+81 x^4\right ) \log ^2(2)+e^{2 x} \left (4 x^2+4 x^3+\left (4 x^3+x^4\right ) \log (2)+x^4 \log ^2(2)\right )+e^x \left (-10 x^2+22 x^3+18 x^4+\left (-100 x-170 x^2-96 x^3-18 x^4\right ) \log (2)+\left (-50 x^2-60 x^3-18 x^4\right ) \log ^2(2)\right )+\left (\left (50 x^2+60 x^3+18 x^4\right ) \log (2)+\left (50 x^2+60 x^3+18 x^4\right ) \log ^2(2)+e^x \left (-4 x^3+2 x^4+\left (-4 x^3-2 x^4\right ) \log (2)-2 x^4 \log ^2(2)\right )\right ) \log (x)+\left (x^4 \log (2)+x^4 \log ^2(2)\right ) \log ^2(x)}{\left (625+1500 x+1350 x^2+540 x^3+81 x^4\right ) \log ^2(2)+e^{2 x} \left (4 x^2+4 x^3 \log (2)+x^4 \log ^2(2)\right )+e^x \left (\left (-100 x-120 x^2-36 x^3\right ) \log (2)+\left (-50 x^2-60 x^3-18 x^4\right ) \log ^2(2)\right )+\left (\left (50 x^2+60 x^3+18 x^4\right ) \log ^2(2)+e^x \left (-4 x^3 \log (2)-2 x^4 \log ^2(2)\right )\right ) \log (x)+x^4 \log ^2(2) \log ^2(x)} \, dx \]
Mathematica 12.3 output
\[ \frac {x \left (1+\log (2)-\frac {e^x x \left (100 \log (2)+60 x \log (2)-x^2 \left (36 \log ^2(2)+\log (4)-18 \log (2) \log (4)\right )+e^x x \left (-4+x^2 \log (4)+x \left (4-\log ^2(4)+\log (2) \log (16)\right )\right )\right )}{\left (\left (50+30 x-x^2\right ) \log (2)+e^x x \left (-2+2 x+x^2 \log (2)\right )\right ) \left (-(5+3 x)^2 \log (2)+e^x x (2+x \log (2))-x^2 \log (2) \log (x)\right )}\right )}{\log (2)} \]