\[ \int \frac {96+96 x-36 x^2+12 x^2 \log (5)+e^x \left (-96-96 x+30 x^2-6 x^3-3 x^4-12 x^2 \log (5)\right )+e^{2 x} \left (24+24 x-6 x^2+3 x^2 \log (5)\right )}{64+48 x^2+9 x^4+\left (32 x+12 x^3\right ) \log (5)+4 x^2 \log ^2(5)+e^x \left (-64-40 x^2-6 x^4+\left (-32 x-10 x^3\right ) \log (5)-4 x^2 \log ^2(5)\right )+e^{2 x} \left (16+8 x^2+x^4+\left (8 x+2 x^3\right ) \log (5)+x^2 \log ^2(5)\right )} \, dx \]
Optimal antiderivative \[ \frac {3 \left (2+x \right ) x}{x^{2}+x \left (\frac {x}{-{\mathrm e}^{x}+2}+\ln \! \left (5\right )\right )+4}+9 \]
command
Integrate[(96 + 96*x - 36*x^2 + 12*x^2*Log[5] + E^x*(-96 - 96*x + 30*x^2 - 6*x^3 - 3*x^4 - 12*x^2*Log[5]) + E^(2*x)*(24 + 24*x - 6*x^2 + 3*x^2*Log[5]))/(64 + 48*x^2 + 9*x^4 + (32*x + 12*x^3)*Log[5] + 4*x^2*Log[5]^2 + E^x*(-64 - 40*x^2 - 6*x^4 + (-32*x - 10*x^3)*Log[5] - 4*x^2*Log[5]^2) + E^(2*x)*(16 + 8*x^2 + x^4 + (8*x + 2*x^3)*Log[5] + x^2*Log[5]^2)),x]
Mathematica 13.1 output
\[ \int \frac {96+96 x-36 x^2+12 x^2 \log (5)+e^x \left (-96-96 x+30 x^2-6 x^3-3 x^4-12 x^2 \log (5)\right )+e^{2 x} \left (24+24 x-6 x^2+3 x^2 \log (5)\right )}{64+48 x^2+9 x^4+\left (32 x+12 x^3\right ) \log (5)+4 x^2 \log ^2(5)+e^x \left (-64-40 x^2-6 x^4+\left (-32 x-10 x^3\right ) \log (5)-4 x^2 \log ^2(5)\right )+e^{2 x} \left (16+8 x^2+x^4+\left (8 x+2 x^3\right ) \log (5)+x^2 \log ^2(5)\right )} \, dx \]
Mathematica 12.3 output
\[ \frac {3 \left (256+3 x^6+96 x (-2+\log (25))+x^5 (-12+9 \log (5)+\log (25))+4 x^2 \left (56+4 \log (5) (-3+\log (25))-5 \log (25)+\log ^2(25)\right )+x^4 (44-4 \log (25)+\log (5) (-13+6 \log (25)))+x^3 \left (-88-4 \log ^2(5)+20 \log (25)+\log (5) \left (60-3 \log (25)+\log ^2(25)\right )\right )-e^x (4+x (-2+\log (5))) \left (32+3 x^4+x^2 (20+\log (5) (-1+\log (25)))+x^3 \log (3125)+2 x (-4+\log (390625))\right )\right )}{\left (-8-3 x^2+e^x \left (4+x^2+x \log (5)\right )-x \log (25)\right ) \left (32+3 x^4+x^2 (20+\log (5) (-1+\log (25)))+x^3 \log (3125)+2 x (-4+\log (390625))\right )} \]