22.8 Problem number 379

$$\int \frac{-4x^6+2x^6\log (2)+e^{4x^2}(-4x^2+2x^2\log (2))+e^{3x^2}(-16x^3+8x^3\log (2))+(-4x^3-3x^2\log (2))\log (4)+e^{2x^2}(-24x^4+12x^4\log (2)+(-2x-4x^3+(-1-4x^2)\log (2))\log (4))+e^{x^2}(-16x^5+8x^5\log (2)+(-6x^2-4x^4+(-4x-4x^3)\log (2))\log (4))}{16x^6+16x^7+4x^8+e^{4x^2}(16x^2+16x^3+4x^4)+e^{3x^2}(64x^3+64x^4+16x^5)+(8x^3+4x^4)\log (4)+{\log }^2(4)+e^{2x^2}(96x^4+96x^5+24x^6+(8x+4x^2)\log (4))+e^{x^2}(64x^5+64x^6+16x^7+(16x^2+8x^3)\log (4))}dx$$

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

command

Integrate[(-4*x^6 + 2*x^6*Log[2] + E^(4*x^2)*(-4*x^2 + 2*x^2*Log[2]) + E^(3*x^2)*(-16*x^3 + 8*x^3*Log[2]) + (-4*x^3 - 3*x^2*Log[2])*Log[4] + E^(2*x^2)*(-24*x^4 + 12*x^4*Log[2] + (-2*x - 4*x^3 + (-1 - 4*x^2)*Log[2])*Log[4]) + E^x^2*(-16*x^5 + 8*x^5*Log[2] + (-6*x^2 - 4*x^4 + (-4*x - 4*x^3)*Log[2])*Log[4]))/(16*x^6 + 16*x^7 + 4*x^8 + E^(4*x^2)*(16*x^2 + 16*x^3 + 4*x^4) + E^(3*x^2)*(64*x^3 + 64*x^4 + 16*x^5) + (8*x^3 + 4*x^4)*Log[4] + Log[4]^2 + E^(2*x^2)*(96*x^4 + 96*x^5 + 24*x^6 + (8*x + 4*x^2)*Log[4]) + E^x^2*(64*x^5 + 64*x^6 + 16*x^7 + (16*x^2 + 8*x^3)*Log[4])),x]

Mathematica 13.1 output

$$\int \frac{-4x^6+2x^6\log (2)+e^{4x^2}(-4x^2+2x^2\log (2))+e^{3x^2}(-16x^3+8x^3\log (2))+(-4x^3-3x^2\log (2))\log (4)+e^{2x^2}(-24x^4+12x^4\log (2)+(-2x-4x^3+(-1-4x^2)\log (2))\log (4))+e^{x^2}(-16x^5+8x^5\log (2)+(-6x^2-4x^4+(-4x-4x^3)\log (2))\log (4))}{16x^6+16x^7+4x^8+e^{4x^2}(16x^2+16x^3+4x^4)+e^{3x^2}(64x^3+64x^4+16x^5)+(8x^3+4x^4)\log (4)+{\log }^2(4)+e^{2x^2}(96x^4+96x^5+24x^6+(8x+4x^2)\log (4))+e^{x^2}(64x^5+64x^6+16x^7+(16x^2+8x^3)\log (4))}dx$$

Mathematica 12.3 output

$$\frac{2{\log }^3(4)+4x{\log }^3(4)+18x^2{\log }^3(4)-2e^{2x^2}x\log (4)(16x^7(-4+\log (4))+88x^8(-4+\log (4))+48x^9(-4+\log (4))+8x^{10}(-4+\log (4))+(-4+\log (4))\log (4)+2x(-4+\log (4))\log (4)+9x^2(-4+\log (4))\log (4)+2x^6(188-55\log (4)+2{\log }^2(4))+4x^3(-16-8\log (4)+3{\log }^2(4))+4x^5(52-29\log (4)+4{\log }^2(4))+4x^4(-24-14\log (4)+5{\log }^2(4)))-4e^{x^2}{x}^2\log (4)(16x^7(-4+\log (4))+88x^8(-4+\log (4))+48x^9(-4+\log (4))+8x^{10}(-4+\log (4))+(-4+\log (4))\log (4)+2x(-4+\log (4))\log (4)+9x^2(-4+\log (4))\log (4)+2x^6(188-55\log (4)+2{\log }^2(4))+4x^3(-16-8\log (4)+3{\log }^2(4))+4x^5(52-29\log (4)+4{\log }^2(4))+4x^4(-24-14\log (4)+5{\log }^2(4)))+4x^4{\log }^2(4)(16-2{\log }^2(4)+\log (4)(9+\log (16)))-4x^8\log (4)(104-(105+16\log (2))\log (4)+16{\log }^2(4)+\log (64))-4x^{11}(-4+\log (4))(35\log (4)+3\log (64))-8x^{12}(-63\log (4)+12{\log }^2(4)+5\log (64))-4x^{13}(-85\log (4)+4{\log }^2(4)+23\log (64))-2x^9\log (4)(376+8{\log }^2(4)+25\log (64)-\log (4)(233+\log (256)))+x^7(192\log (4)-54{\log }^3(4)-{\log }^2(16)\log (64)+4{\log }^2(4)(36+\log (8192)))+16x^{10}(8{\log }^2(4)-{\log }^2(64)+\log (65536))+x^3{\log }^2(4)(40-3{\log }^2(4)+\log (4)(14+\log (64))+\log (65536))+4x^6\log (4)(32+9{\log }^2(4)-\log (4)(31+\log (67108864)))+x^5{\log }^2(4)(-32-4{\log }^2(4)+\log (4)\log (256)+\log (268435456))}{4\log (4)(4x^3+2x^4+2e^{2x^2}x(2+x)+4e^{x^2}{x}^2(2+x)+\log (4))(16x^7+88x^8+48x^9+8x^{10}+\log (4)+9x^2\log (4)+4x^4(6+5\log (4))+x\log (16)+4x^3(4+\log (64))+x^6(-94+\log (256))+4x^5(-13+\log (256)))}$$