22.31 Problem number 5410

$$\int \frac{-5x^6+e{x}^6+e^{-\frac{3x}{-5+e}}(320-240x+60x^2-5x^3+e(-64+48x-12x^2+x^3))+e^{-\frac{2x}{-5+e}}(-240x^2+120x^3-15x^4+e(48x^2-24x^3+3x^4))+e^{-\frac{x}{-5+e}}(-320x^3+132x^4-23x^5+e(64x^3-20x^4+3x^5))}{-5x^6+e{x}^6+e^{-\frac{3x}{-5+e}}(320-240x+60x^2-5x^3+e(-64+48x-12x^2+x^3))+e^{-\frac{2x}{-5+e}}(-240x^2+120x^3-15x^4+e(48x^2-24x^3+3x^4))+e^{-\frac{x}{-5+e}}(60x^4-15x^5+e(-12x^4+3x^5))}dx$$

Optimal antiderivative $$x-\frac{4x^2}{{(\frac{(-4+x){\mathrm{e}}^{\frac{x}{5-\mathrm{e}}}}{x}+x)}^2}$$

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

$$\frac{e^{-\frac{20}{-5+e}}(-4+x)x(2e^{\frac{4e}{-5+e}}(-8+x{)}^3(-4+x)+4e^{\frac{4e+x}{-5+e}}(-8+x{)}^3{x}^2+2e^{\frac{2(2e+x)}{-5+e}}(-8+x{)}^3{x}^3+4e^{\frac{15+e+x}{-5+e}}{x}^2(160-24x+x^2){(40-9x+x^2)}^2+2e^{\frac{15+e+2x}{-5+e}}{x}^3(160-24x+x^2){(40-9x+x^2)}^2-10e^{\frac{20}{-5+e}}(-4+x){(40-9x+x^2)}^3-20e^{\frac{20+x}{-5+e}}{x}^2{(40-9x+x^2)}^3-10e^{\frac{2(10+x)}{-5+e}}{x}^3{(40-9x+x^2)}^3+4e^{\frac{5+3e+x}{-5+e}}(-8+x{)}^2{x}^2(160-32x+3x^2)+2e^{\frac{5+3e+2x}{-5+e}}(-8+x{)}^2{x}^3(160-32x+3x^2)+2e^{\frac{15+e}{-5+e}}{(40-9x+x^2)}^2(-640+256x-28x^2+x^3)-8e^{\frac{5+3e}{-5+e}}(4416-3104x+864x^2-111x^3+5x^4)+12e^{\frac{10+2e+x}{-5+e}}{x}^2(-25600+13440x-3248x^2+430x^3-31x^4+x^5)+6e^{\frac{2(5+e+x)}{-5+e}}{x}^3(-25600+13440x-3248x^2+430x^3-31x^4+x^5)+2e^{3+\frac{20}{-5+e}}(-23296+16256x-4608x^2+740x^3-72x^4+3x^5)+6e^{\frac{2(5+e)}{-5+e}}(102400-79360x+26432x^2-4968x^3+554x^4-35x^5+x^6))}{2(-5+e){(40+e(-8+x)-9x+x^2)}^3{(-4+x+e^{\frac{x}{-5+e}}{x}^2)}^2}$$