\[ \int \frac {e^{5+x} \left (-80 x+\left (-960 x+384 x^2+48 x^3\right ) \log (2)\right )+e^{5+x} \left (1280-1200 x-80 x^2+\left (-1024+1984 x-1152 x^2+176 x^3+16 x^4\right ) \log (2)\right ) \log \left (-80-5 x+\left (64-60 x+12 x^2+x^3\right ) \log (2)\right )}{-80 x^2-5 x^3+\left (64 x^2-60 x^3+12 x^4+x^5\right ) \log (2)} \, dx \]
Optimal antiderivative \[ \frac {16 \ln \! \left (\left (\left (2-x \right )^{2} \ln \! \left (2\right )-5\right ) \left (x +16\right )\right ) {\mathrm e}^{5+x}}{x} \]
command
Int[(E^(5 + x)*(-80*x + (-960*x + 384*x^2 + 48*x^3)*Log[2]) + E^(5 + x)*(1280 - 1200*x - 80*x^2 + (-1024 + 1984*x - 1152*x^2 + 176*x^3 + 16*x^4)*Log[2])*Log[-80 - 5*x + (64 - 60*x + 12*x^2 + x^3)*Log[2]])/(-80*x^2 - 5*x^3 + (64*x^2 - 60*x^3 + 12*x^4 + x^5)*Log[2]),x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ \int \frac {e^{5+x} \left (-80 x+\left (-960 x+384 x^2+48 x^3\right ) \log (2)\right )+e^{5+x} \left (1280-1200 x-80 x^2+\left (-1024+1984 x-1152 x^2+176 x^3+16 x^4\right ) \log (2)\right ) \log \left (-80-5 x+\left (64-60 x+12 x^2+x^3\right ) \log (2)\right )}{-80 x^2-5 x^3+\left (64 x^2-60 x^3+12 x^4+x^5\right ) \log (2)} \, dx \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ -\frac {8 e^{7+\frac {\sqrt {\log (32)}}{\log (2)}} \left (2400 \log ^3(2)+20 \log ^2(2) \left (155-27 \log (16)-60 \sqrt {\log (32)}\right )-\log (8) (5-\log (16))^2+4 \sqrt {\log (32)} (\log (32)-\log (16) \log (64))+\log (2) (25+8 \log (32)-\log (16) (5+8 \log (64)))\right ) \operatorname {ExpIntegralEi}\left (\frac {\log (2) x-\sqrt {\log (32)}-\log (4)}{\log (2)}\right )}{(5-\log (16)) (5-320 \log (2)-\log (16)) \sqrt {\log (32)}}+\frac {8 e^{7-\frac {\sqrt {\log (32)}}{\log (2)}} \left (2400 \log ^3(2)+20 \log ^2(2) \left (155-27 \log (16)+60 \sqrt {\log (32)}\right )-\log (8) (5-\log (16))^2-4 \sqrt {\log (32)} (\log (32)-\log (16) \log (64))+\log (2) (25+8 \log (32)-\log (16) (5+8 \log (64)))\right ) \operatorname {ExpIntegralEi}\left (\frac {2 \log (2) x+2 \sqrt {\log (32)}-\log (16)}{2 \log (2)}\right )}{(5-\log (16)) (5-320 \log (2)-\log (16)) \sqrt {\log (32)}}-\frac {8 e^{7-\frac {\sqrt {\log (32)}}{\log (2)}} \left (2560 \log ^3(2)+\log (2) \left (25+\log ^2(16)\right )+8 \log ^2(2) \left (390-79 \log (16)+160 \sqrt {\log (32)}\right )+\left (\log ^2(16)-4 \log (32)\right ) \sqrt {\log (32)}-\log (8) (5-\log (16))^2\right ) \operatorname {ExpIntegralEi}\left (\frac {2 \log (2) x+2 \sqrt {\log (32)}-\log (16)}{2 \log (2)}\right )}{(5-\log (16)) (5-320 \log (2)-\log (16)) \sqrt {\log (32)}}+\frac {8 e^{7+\frac {\sqrt {\log (32)}}{\log (2)}} \left (4 \log ^{\frac {3}{2}}(32)+2560 \log ^3(2)+8 \log ^2(2) \left (390-79 \log (16)-160 \sqrt {\log (32)}\right )+\log (2) \left (25+\log ^2(16)-4 \log (16) \sqrt {\log (32)}\right )-\log (8) (5-\log (16))^2\right ) \operatorname {ExpIntegralEi}\left (\frac {\log (2) x-\sqrt {\log (32)}-\log (4)}{\log (2)}\right )}{(5-\log (16)) (5-320 \log (2)-\log (16)) \sqrt {\log (32)}}+\frac {5 e^5 (1+\log (4096)) \operatorname {ExpIntegralEi}(x)}{5-\log (16)}-\frac {e^5 (5+64 \log (2)-\log (16)) \operatorname {ExpIntegralEi}(x)}{5-\log (16)}+\frac {16 e^{x+5} \log \left (-\left ((x+16) \left (x^2 (-\log (2))+4 x \log (2)+5-\log (16)\right )\right )\right )}{x} \]