22.34 Problem number 6066

$$\int \frac{10x-20x^2+30x^3-20x^4-2x^5+10x^6-20x^7+20x^8-10x^9+2x^{10}+(5x-16x^3+52x^4-60x^5+28x^6-4x^7)\log (3)+(-32x+48x^2-18x^3+2x^4){\log }^2(3)+(-10+10x-20x^2+8x^4-32x^5+48x^6-32x^7+8x^8+(32x^2-72x^3+48x^4-8x^5)\log (3))\log (x)+(-12x^3+36x^4-36x^5+12x^6+(-16x+20x^2-4x^3)\log (3)){\log }^2(x)+(8x^2-16x^3+8x^4){\log }^3(x)+(-2x+2x^2){\log }^4(x)}{x^5-4x^6+6x^7-4x^8+x^9+(8x^3-18x^4+12x^5-2x^6)\log (3)+(16x-8x^2+x^3){\log }^2(3)+(-4x^4+12x^5-12x^6+4x^7+(-16x^2+20x^3-4x^4)\log (3))\log (x)+(6x^3-12x^4+6x^5+(8x-2x^2)\log (3)){\log }^2(x)+(-4x^2+4x^3){\log }^3(x)+x{\log }^4(x)}dx$$

Optimal antiderivative $$x^2-2x+\frac{5}{(4-x)\ln \left(3\right)+{(x-\ln \left(x\right)-x^2)}^2}$$

command

Integrate[(10*x - 20*x^2 + 30*x^3 - 20*x^4 - 2*x^5 + 10*x^6 - 20*x^7 + 20*x^8 - 10*x^9 + 2*x^10 + (5*x - 16*x^3 + 52*x^4 - 60*x^5 + 28*x^6 - 4*x^7)*Log[3] + (-32*x + 48*x^2 - 18*x^3 + 2*x^4)*Log[3]^2 + (-10 + 10*x - 20*x^2 + 8*x^4 - 32*x^5 + 48*x^6 - 32*x^7 + 8*x^8 + (32*x^2 - 72*x^3 + 48*x^4 - 8*x^5)*Log[3])*Log[x] + (-12*x^3 + 36*x^4 - 36*x^5 + 12*x^6 + (-16*x + 20*x^2 - 4*x^3)*Log[3])*Log[x]^2 + (8*x^2 - 16*x^3 + 8*x^4)*Log[x]^3 + (-2*x + 2*x^2)*Log[x]^4)/(x^5 - 4*x^6 + 6*x^7 - 4*x^8 + x^9 + (8*x^3 - 18*x^4 + 12*x^5 - 2*x^6)*Log[3] + (16*x - 8*x^2 + x^3)*Log[3]^2 + (-4*x^4 + 12*x^5 - 12*x^6 + 4*x^7 + (-16*x^2 + 20*x^3 - 4*x^4)*Log[3])*Log[x] + (6*x^3 - 12*x^4 + 6*x^5 + (8*x - 2*x^2)*Log[3])*Log[x]^2 + (-4*x^2 + 4*x^3)*Log[x]^3 + x*Log[x]^4),x]

Mathematica 13.1 output

$$\int \frac{10x-20x^2+30x^3-20x^4-2x^5+10x^6-20x^7+20x^8-10x^9+2x^{10}+(5x-16x^3+52x^4-60x^5+28x^6-4x^7)\log (3)+(-32x+48x^2-18x^3+2x^4){\log }^2(3)+(-10+10x-20x^2+8x^4-32x^5+48x^6-32x^7+8x^8+(32x^2-72x^3+48x^4-8x^5)\log (3))\log (x)+(-12x^3+36x^4-36x^5+12x^6+(-16x+20x^2-4x^3)\log (3)){\log }^2(x)+(8x^2-16x^3+8x^4){\log }^3(x)+(-2x+2x^2){\log }^4(x)}{x^5-4x^6+6x^7-4x^8+x^9+(8x^3-18x^4+12x^5-2x^6)\log (3)+(16x-8x^2+x^3){\log }^2(3)+(-4x^4+12x^5-12x^6+4x^7+(-16x^2+20x^3-4x^4)\log (3))\log (x)+(6x^3-12x^4+6x^5+(8x-2x^2)\log (3)){\log }^2(x)+(-4x^2+4x^3){\log }^3(x)+x{\log }^4(x)}dx$$

Mathematica 12.3 output

$$\frac{16x^{11}\log (3)-20\log (81)+x^3(-48{\log }^3(3)+88\log (81)+(84+\log (9)){\log }^2(81)+6{\log }^2(3)(28+\log (81))-24\log (3)(-5+6\log (81))-4\log (243))+4x(10\log (81)+2{\log }^2(81)+\log (243))-x^8(136\log (3)+17{\log }^2(3)+300\log (81)-80\log (729))+4x^9(89\log (3)+38\log (81)-20\log (729))+4x^7(41{\log }^2(3)+\log (3)(-30+\log (81))+86\log (81)-12\log (729))+x^4(14{\log }^3(3)-112{\log }^2(81)-{\log }^2(3)(228+5\log (81))+2\log (3)(-43+50\log (81))+6\log (243)+4\log (81)(-31+4\log (729)))+x^5(258{\log }^2(3)+{\log }^3(3)+108{\log }^2(81)-4\log (243)+4\log (81)(34-4\log (729))-4\log (3)(6+17\log (81)+4\log (729)))+x^6(-73{\log }^2(3)-8(5{\log }^2(81)+\log (81)(33-4\log (729))-2\log (729))-4\log (3)(53\log (81)-4(12+\log (729))))-16x^{10}\log (19683)+x^2(-64{\log }^2(3)+32{\log }^3(3)-100\log (81)-(32+\log (9)){\log }^2(81)+\log (3)(-50+48\log (81)-\log (243))+\log (59049))+2x^2(2-3x+x^2)(16x^5\log (3)-4\log (81)+9x\log (81)-x^2(8\log (3)+{\log }^2(3)+20\log (81))-16x^4\log (243)+4x^3(4\log (81)+\log (243)))\log (x)+(-2+x)x(16x^5\log (3)-4\log (81)+9x\log (81)-x^2(8\log (3)+{\log }^2(3)+20\log (81))-16x^4\log (243)+4x^3(4\log (81)+\log (243))){\log }^2(x)}{(16x^5\log (3)-4\log (81)+9x\log (81)-x^2(8\log (3)+{\log }^2(3)+20\log (81))-16x^4\log (243)+4x^3(4\log (81)+\log (243)))(x^2-2x^3+x^4-x\log (3)+\log (81)+2(-1+x)x\log (x)+{\log }^2(x))}$$