\[ \int \frac {-5 x^6+e x^6+e^{-\frac {3 x}{-5+e}} \left (320-240 x+60 x^2-5 x^3+e \left (-64+48 x-12 x^2+x^3\right )\right )+e^{-\frac {2 x}{-5+e}} \left (-240 x^2+120 x^3-15 x^4+e \left (48 x^2-24 x^3+3 x^4\right )\right )+e^{-\frac {x}{-5+e}} \left (-320 x^3+132 x^4-23 x^5+e \left (64 x^3-20 x^4+3 x^5\right )\right )}{-5 x^6+e x^6+e^{-\frac {3 x}{-5+e}} \left (320-240 x+60 x^2-5 x^3+e \left (-64+48 x-12 x^2+x^3\right )\right )+e^{-\frac {2 x}{-5+e}} \left (-240 x^2+120 x^3-15 x^4+e \left (48 x^2-24 x^3+3 x^4\right )\right )+e^{-\frac {x}{-5+e}} \left (60 x^4-15 x^5+e \left (-12 x^4+3 x^5\right )\right )} \, dx \]
Optimal antiderivative \[ x -\frac {4 x^{2}}{\left (\frac {\left (-4+x \right ) {\mathrm e}^{\frac {x}{5-{\mathrm e}}}}{x}+x \right )^{2}} \]
command
Integrate[(-5*x^6 + E*x^6 + (320 - 240*x + 60*x^2 - 5*x^3 + E*(-64 + 48*x - 12*x^2 + x^3))/E^((3*x)/(-5 + E)) + (-240*x^2 + 120*x^3 - 15*x^4 + E*(48*x^2 - 24*x^3 + 3*x^4))/E^((2*x)/(-5 + E)) + (-320*x^3 + 132*x^4 - 23*x^5 + E*(64*x^3 - 20*x^4 + 3*x^5))/E^(x/(-5 + E)))/(-5*x^6 + E*x^6 + (320 - 240*x + 60*x^2 - 5*x^3 + E*(-64 + 48*x - 12*x^2 + x^3))/E^((3*x)/(-5 + E)) + (-240*x^2 + 120*x^3 - 15*x^4 + E*(48*x^2 - 24*x^3 + 3*x^4))/E^((2*x)/(-5 + E)) + (60*x^4 - 15*x^5 + E*(-12*x^4 + 3*x^5))/E^(x/(-5 + E))),x]
Mathematica 13.1 output
\[ \text {\$Aborted} \]
Mathematica 12.3 output
\[ \frac {e^{-\frac {20}{-5+e}} (-4+x) x \left (2 e^{\frac {4 e}{-5+e}} (-8+x)^3 (-4+x)+4 e^{\frac {4 e+x}{-5+e}} (-8+x)^3 x^2+2 e^{\frac {2 (2 e+x)}{-5+e}} (-8+x)^3 x^3+4 e^{\frac {15+e+x}{-5+e}} x^2 \left (160-24 x+x^2\right ) \left (40-9 x+x^2\right )^2+2 e^{\frac {15+e+2 x}{-5+e}} x^3 \left (160-24 x+x^2\right ) \left (40-9 x+x^2\right )^2-10 e^{\frac {20}{-5+e}} (-4+x) \left (40-9 x+x^2\right )^3-20 e^{\frac {20+x}{-5+e}} x^2 \left (40-9 x+x^2\right )^3-10 e^{\frac {2 (10+x)}{-5+e}} x^3 \left (40-9 x+x^2\right )^3+4 e^{\frac {5+3 e+x}{-5+e}} (-8+x)^2 x^2 \left (160-32 x+3 x^2\right )+2 e^{\frac {5+3 e+2 x}{-5+e}} (-8+x)^2 x^3 \left (160-32 x+3 x^2\right )+2 e^{\frac {15+e}{-5+e}} \left (40-9 x+x^2\right )^2 \left (-640+256 x-28 x^2+x^3\right )-8 e^{\frac {5+3 e}{-5+e}} \left (4416-3104 x+864 x^2-111 x^3+5 x^4\right )+12 e^{\frac {10+2 e+x}{-5+e}} x^2 \left (-25600+13440 x-3248 x^2+430 x^3-31 x^4+x^5\right )+6 e^{\frac {2 (5+e+x)}{-5+e}} x^3 \left (-25600+13440 x-3248 x^2+430 x^3-31 x^4+x^5\right )+2 e^{3+\frac {20}{-5+e}} \left (-23296+16256 x-4608 x^2+740 x^3-72 x^4+3 x^5\right )+6 e^{\frac {2 (5+e)}{-5+e}} \left (102400-79360 x+26432 x^2-4968 x^3+554 x^4-35 x^5+x^6\right )\right )}{2 (-5+e) \left (40+e (-8+x)-9 x+x^2\right )^3 \left (-4+x+e^{\frac {x}{-5+e}} x^2\right )^2} \]