\[ \int \frac {e^{3 x} \left (12-80 x+72 x^2-16 x^3+(12-8 x) \log (4)\right )+e^{2 x} \left (24-328 x+440 x^2-160 x^3+16 x^4+\left (52-80 x+16 x^2\right ) \log (4)+4 \log ^2(4)\right )+e^x \left (-288 x+576 x^2-256 x^3+32 x^4+\left (48-128 x+32 x^2\right ) \log (4)+8 \log ^2(4)\right )}{-1728 x^3+1728 x^4-576 x^5+64 x^6+\left (864 x^2-576 x^3+96 x^4\right ) \log (4)+\left (-144 x+48 x^2\right ) \log ^2(4)+8 \log ^3(4)+e^{3 x} \left (-216 x^3+216 x^4-72 x^5+8 x^6+\left (108 x^2-72 x^3+12 x^4\right ) \log (4)+\left (-18 x+6 x^2\right ) \log ^2(4)+\log ^3(4)\right )+e^{2 x} \left (-1296 x^3+1296 x^4-432 x^5+48 x^6+\left (648 x^2-432 x^3+72 x^4\right ) \log (4)+\left (-108 x+36 x^2\right ) \log ^2(4)+6 \log ^3(4)\right )+e^x \left (-2592 x^3+2592 x^4-864 x^5+96 x^6+\left (1296 x^2-864 x^3+144 x^4\right ) \log (4)+\left (-216 x+72 x^2\right ) \log ^2(4)+12 \log ^3(4)\right )} \, dx \]
Optimal antiderivative \[ \left (\frac {{\mathrm e}^{x}}{\left (2 \ln \! \left (2\right )-x \left (6-2 x \right )\right ) \left (2+{\mathrm e}^{x}\right )}+1\right )^{2} \]
command
Integrate[(E^(3*x)*(12 - 80*x + 72*x^2 - 16*x^3 + (12 - 8*x)*Log[4]) + E^(2*x)*(24 - 328*x + 440*x^2 - 160*x^3 + 16*x^4 + (52 - 80*x + 16*x^2)*Log[4] + 4*Log[4]^2) + E^x*(-288*x + 576*x^2 - 256*x^3 + 32*x^4 + (48 - 128*x + 32*x^2)*Log[4] + 8*Log[4]^2))/(-1728*x^3 + 1728*x^4 - 576*x^5 + 64*x^6 + (864*x^2 - 576*x^3 + 96*x^4)*Log[4] + (-144*x + 48*x^2)*Log[4]^2 + 8*Log[4]^3 + E^(3*x)*(-216*x^3 + 216*x^4 - 72*x^5 + 8*x^6 + (108*x^2 - 72*x^3 + 12*x^4)*Log[4] + (-18*x + 6*x^2)*Log[4]^2 + Log[4]^3) + E^(2*x)*(-1296*x^3 + 1296*x^4 - 432*x^5 + 48*x^6 + (648*x^2 - 432*x^3 + 72*x^4)*Log[4] + (-108*x + 36*x^2)*Log[4]^2 + 6*Log[4]^3) + E^x*(-2592*x^3 + 2592*x^4 - 864*x^5 + 96*x^6 + (1296*x^2 - 864*x^3 + 144*x^4)*Log[4] + (-216*x + 72*x^2)*Log[4]^2 + 12*Log[4]^3)),x]
Mathematica 13.1 output
\[ \int \frac {e^{3 x} \left (12-80 x+72 x^2-16 x^3+(12-8 x) \log (4)\right )+e^{2 x} \left (24-328 x+440 x^2-160 x^3+16 x^4+\left (52-80 x+16 x^2\right ) \log (4)+4 \log ^2(4)\right )+e^x \left (-288 x+576 x^2-256 x^3+32 x^4+\left (48-128 x+32 x^2\right ) \log (4)+8 \log ^2(4)\right )}{-1728 x^3+1728 x^4-576 x^5+64 x^6+\left (864 x^2-576 x^3+96 x^4\right ) \log (4)+\left (-144 x+48 x^2\right ) \log ^2(4)+8 \log ^3(4)+e^{3 x} \left (-216 x^3+216 x^4-72 x^5+8 x^6+\left (108 x^2-72 x^3+12 x^4\right ) \log (4)+\left (-18 x+6 x^2\right ) \log ^2(4)+\log ^3(4)\right )+e^{2 x} \left (-1296 x^3+1296 x^4-432 x^5+48 x^6+\left (648 x^2-432 x^3+72 x^4\right ) \log (4)+\left (-108 x+36 x^2\right ) \log ^2(4)+6 \log ^3(4)\right )+e^x \left (-2592 x^3+2592 x^4-864 x^5+96 x^6+\left (1296 x^2-864 x^3+144 x^4\right ) \log (4)+\left (-216 x+72 x^2\right ) \log ^2(4)+12 \log ^3(4)\right )} \, dx \]
Mathematica 12.3 output
\[ -\frac {e^x \left (-e^x \left (-6 x+2 x^2+\log (4)\right )^2 \left (1-12 x+4 x^2+\log (16)\right )-4 \left (-72 x^5+8 x^6+\log ^3(4)-4 x^3 (54+28 \log (4)-5 \log (16))+4 x^4 (54+\log (64))+2 x^2 \left (5 \log ^2(4)-\log (4) (-20+\log (16))-3 \log (16)+10 \log (256)\right )-2 x \log (4) \log (262144)\right )\right )}{\left (2+e^x\right )^2 \left (-6 x+2 x^2+\log (4)\right )^4} \]