\[ \int \frac {10 x-20 x^2+30 x^3-20 x^4-2 x^5+10 x^6-20 x^7+20 x^8-10 x^9+2 x^{10}+\left (5 x-16 x^3+52 x^4-60 x^5+28 x^6-4 x^7\right ) \log (3)+\left (-32 x+48 x^2-18 x^3+2 x^4\right ) \log ^2(3)+\left (-10+10 x-20 x^2+8 x^4-32 x^5+48 x^6-32 x^7+8 x^8+\left (32 x^2-72 x^3+48 x^4-8 x^5\right ) \log (3)\right ) \log (x)+\left (-12 x^3+36 x^4-36 x^5+12 x^6+\left (-16 x+20 x^2-4 x^3\right ) \log (3)\right ) \log ^2(x)+\left (8 x^2-16 x^3+8 x^4\right ) \log ^3(x)+\left (-2 x+2 x^2\right ) \log ^4(x)}{x^5-4 x^6+6 x^7-4 x^8+x^9+\left (8 x^3-18 x^4+12 x^5-2 x^6\right ) \log (3)+\left (16 x-8 x^2+x^3\right ) \log ^2(3)+\left (-4 x^4+12 x^5-12 x^6+4 x^7+\left (-16 x^2+20 x^3-4 x^4\right ) \log (3)\right ) \log (x)+\left (6 x^3-12 x^4+6 x^5+\left (8 x-2 x^2\right ) \log (3)\right ) \log ^2(x)+\left (-4 x^2+4 x^3\right ) \log ^3(x)+x \log ^4(x)} \, dx \]
Optimal antiderivative \[ x^{2}-2 x +\frac {5}{\left (4-x \right ) \ln \! \left (3\right )+\left (x -\ln \! \left (x \right )-x^{2}\right )^{2}} \]
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
\[ \int \frac {10 x-20 x^2+30 x^3-20 x^4-2 x^5+10 x^6-20 x^7+20 x^8-10 x^9+2 x^{10}+\left (5 x-16 x^3+52 x^4-60 x^5+28 x^6-4 x^7\right ) \log (3)+\left (-32 x+48 x^2-18 x^3+2 x^4\right ) \log ^2(3)+\left (-10+10 x-20 x^2+8 x^4-32 x^5+48 x^6-32 x^7+8 x^8+\left (32 x^2-72 x^3+48 x^4-8 x^5\right ) \log (3)\right ) \log (x)+\left (-12 x^3+36 x^4-36 x^5+12 x^6+\left (-16 x+20 x^2-4 x^3\right ) \log (3)\right ) \log ^2(x)+\left (8 x^2-16 x^3+8 x^4\right ) \log ^3(x)+\left (-2 x+2 x^2\right ) \log ^4(x)}{x^5-4 x^6+6 x^7-4 x^8+x^9+\left (8 x^3-18 x^4+12 x^5-2 x^6\right ) \log (3)+\left (16 x-8 x^2+x^3\right ) \log ^2(3)+\left (-4 x^4+12 x^5-12 x^6+4 x^7+\left (-16 x^2+20 x^3-4 x^4\right ) \log (3)\right ) \log (x)+\left (6 x^3-12 x^4+6 x^5+\left (8 x-2 x^2\right ) \log (3)\right ) \log ^2(x)+\left (-4 x^2+4 x^3\right ) \log ^3(x)+x \log ^4(x)} \, dx \]
Mathematica 12.3 output
\[ \frac {16 x^{11} \log (3)-20 \log (81)+x^3 \left (-48 \log ^3(3)+88 \log (81)+(84+\log (9)) \log ^2(81)+6 \log ^2(3) (28+\log (81))-24 \log (3) (-5+6 \log (81))-4 \log (243)\right )+4 x \left (10 \log (81)+2 \log ^2(81)+\log (243)\right )-x^8 \left (136 \log (3)+17 \log ^2(3)+300 \log (81)-80 \log (729)\right )+4 x^9 (89 \log (3)+38 \log (81)-20 \log (729))+4 x^7 \left (41 \log ^2(3)+\log (3) (-30+\log (81))+86 \log (81)-12 \log (729)\right )+x^4 \left (14 \log ^3(3)-112 \log ^2(81)-\log ^2(3) (228+5 \log (81))+2 \log (3) (-43+50 \log (81))+6 \log (243)+4 \log (81) (-31+4 \log (729))\right )+x^5 \left (258 \log ^2(3)+\log ^3(3)+108 \log ^2(81)-4 \log (243)+4 \log (81) (34-4 \log (729))-4 \log (3) (6+17 \log (81)+4 \log (729))\right )+x^6 \left (-73 \log ^2(3)-8 \left (5 \log ^2(81)+\log (81) (33-4 \log (729))-2 \log (729)\right )-4 \log (3) (53 \log (81)-4 (12+\log (729)))\right )-16 x^{10} \log (19683)+x^2 \left (-64 \log ^2(3)+32 \log ^3(3)-100 \log (81)-(32+\log (9)) \log ^2(81)+\log (3) (-50+48 \log (81)-\log (243))+\log (59049)\right )+2 x^2 \left (2-3 x+x^2\right ) \left (16 x^5 \log (3)-4 \log (81)+9 x \log (81)-x^2 \left (8 \log (3)+\log ^2(3)+20 \log (81)\right )-16 x^4 \log (243)+4 x^3 (4 \log (81)+\log (243))\right ) \log (x)+(-2+x) x \left (16 x^5 \log (3)-4 \log (81)+9 x \log (81)-x^2 \left (8 \log (3)+\log ^2(3)+20 \log (81)\right )-16 x^4 \log (243)+4 x^3 (4 \log (81)+\log (243))\right ) \log ^2(x)}{\left (16 x^5 \log (3)-4 \log (81)+9 x \log (81)-x^2 \left (8 \log (3)+\log ^2(3)+20 \log (81)\right )-16 x^4 \log (243)+4 x^3 (4 \log (81)+\log (243))\right ) \left (x^2-2 x^3+x^4-x \log (3)+\log (81)+2 (-1+x) x \log (x)+\log ^2(x)\right )} \]