22.55 Problem number 10272

$$\int \frac{6x^3-4x^2\log (2)+e^x(-16x^5+(-16x^3+32x^4)\log (2)+(20x^2-24x^3){\log }^2(2)+(-8x+8x^2){\log }^3(2)+(1-x){\log }^4(2))+e^{2x}(-32x^5+64x^4\log (2)-48x^3{\log }^2(2)+16x^2{\log }^3(2)-2x{\log }^4(2))}{x^2+e^x(8x^3-8x^2\log (2)+2x{\log }^2(2))+e^{2x}(16x^4-32x^3\log (2)+24x^2{\log }^2(2)-8x{\log }^3(2)+{\log }^4(2))}dx$$

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

command

Integrate[(6*x^3 - 4*x^2*Log[2] + E^x*(-16*x^5 + (-16*x^3 + 32*x^4)*Log[2] + (20*x^2 - 24*x^3)*Log[2]^2 + (-8*x + 8*x^2)*Log[2]^3 + (1 - x)*Log[2]^4) + E^(2*x)*(-32*x^5 + 64*x^4*Log[2] - 48*x^3*Log[2]^2 + 16*x^2*Log[2]^3 - 2*x*Log[2]^4))/(x^2 + E^x*(8*x^3 - 8*x^2*Log[2] + 2*x*Log[2]^2) + E^(2*x)*(16*x^4 - 32*x^3*Log[2] + 24*x^2*Log[2]^2 - 8*x*Log[2]^3 + Log[2]^4)),x]

Mathematica 13.1 output

$$\int \frac{6x^3-4x^2\log (2)+e^x(-16x^5+(-16x^3+32x^4)\log (2)+(20x^2-24x^3){\log }^2(2)+(-8x+8x^2){\log }^3(2)+(1-x){\log }^4(2))+e^{2x}(-32x^5+64x^4\log (2)-48x^3{\log }^2(2)+16x^2{\log }^3(2)-2x{\log }^4(2))}{x^2+e^x(8x^3-8x^2\log (2)+2x{\log }^2(2))+e^{2x}(16x^4-32x^3\log (2)+24x^2{\log }^2(2)-8x{\log }^3(2)+{\log }^4(2))}dx$$

Mathematica 12.3 output

$$x(-x+\frac{64x^7-{\log }^6(2)+x{\log }^5(2)(8+\log (2))-64x^6(-1+\log (8))-x^2{\log }^3(2)(4{\log }^2(2)+\log (4)+2\log (2)(9+\log (16)))-16x^4{\log }^2(2)(-5+\log (1024))+16x^5\log (2)(-8+\log (32768))+4x^3{\log }^3(2)\log (32768)}{(2x-\log (2){)}^3(2x^2-x(-2+\log (2))+\log (2))(x+4e^x{x}^2-4e^{x}x\log (2)+e^x{\log }^2(2))})$$