\[ \int \frac {-1000 x^2-600 x^3-620 x^4-308 x^5-60 x^6-4 x^7+\left (40 x-1192 x^2-660 x^3-1124 x^4-608 x^5-120 x^6-8 x^7+\left (20 x-96 x^2-30 x^3-2 x^4\right ) \log (2)\right ) \log (5)+\left (8 x-200 x^2-60 x^3-504 x^4-300 x^5-60 x^6-4 x^7+\left (8 x-100 x^2-30 x^3-2 x^4\right ) \log (2)+2 x \log ^2(2)\right ) \log ^2(5)+\left (\left (-80-16 x-40 x^2-8 x^3+\left (-40-8 x-20 x^2-4 x^3\right ) \log (2)\right ) \log (5)+\left (-16-40 x^2-8 x^3+\left (-16-20 x^2-4 x^3\right ) \log (2)-4 \log ^2(2)\right ) \log ^2(5)\right ) \log (x)+\left (600 x^2+240 x^3+324 x^4+120 x^5+12 x^6+\left (-8 x+680 x^2+252 x^3+624 x^4+240 x^5+24 x^6+\left (-4 x+40 x^2+6 x^3\right ) \log (2)\right ) \log (5)+\left (80 x^2+12 x^3+300 x^4+120 x^5+12 x^6+\left (40 x^2+6 x^3\right ) \log (2)\right ) \log ^2(5)\right ) \log ^2(x)+\left (\left (16+8 x^2+\left (8+4 x^2\right ) \log (2)\right ) \log (5)+\left (8 x^2+4 x^2 \log (2)\right ) \log ^2(5)\right ) \log ^3(x)+\left (-120 x^2-24 x^3-60 x^4-12 x^5+\left (-128 x^2-24 x^3-120 x^4-24 x^5-4 x^2 \log (2)\right ) \log (5)+\left (-8 x^2-60 x^4-12 x^5-4 x^2 \log (2)\right ) \log ^2(5)\right ) \log ^4(x)+\left (8 x^2+4 x^4+\left (8 x^2+8 x^4\right ) \log (5)+4 x^4 \log ^2(5)\right ) \log ^6(x)}{-125 x-75 x^2-15 x^3-x^4+\left (75 x+30 x^2+3 x^3\right ) \log ^2(x)+\left (-15 x-3 x^2\right ) \log ^4(x)+x \log ^6(x)} \, dx \]
Optimal antiderivative \[ \left (\ln \! \left (5\right ) \left (x^{2}+\frac {\ln \! \left (2\right )+2}{5+x -\ln \! \left (x \right )^{2}}\right )+x^{2}+2\right )^{2} \]
command
Integrate[(-1000*x^2 - 600*x^3 - 620*x^4 - 308*x^5 - 60*x^6 - 4*x^7 + (40*x - 1192*x^2 - 660*x^3 - 1124*x^4 - 608*x^5 - 120*x^6 - 8*x^7 + (20*x - 96*x^2 - 30*x^3 - 2*x^4)*Log[2])*Log[5] + (8*x - 200*x^2 - 60*x^3 - 504*x^4 - 300*x^5 - 60*x^6 - 4*x^7 + (8*x - 100*x^2 - 30*x^3 - 2*x^4)*Log[2] + 2*x*Log[2]^2)*Log[5]^2 + ((-80 - 16*x - 40*x^2 - 8*x^3 + (-40 - 8*x - 20*x^2 - 4*x^3)*Log[2])*Log[5] + (-16 - 40*x^2 - 8*x^3 + (-16 - 20*x^2 - 4*x^3)*Log[2] - 4*Log[2]^2)*Log[5]^2)*Log[x] + (600*x^2 + 240*x^3 + 324*x^4 + 120*x^5 + 12*x^6 + (-8*x + 680*x^2 + 252*x^3 + 624*x^4 + 240*x^5 + 24*x^6 + (-4*x + 40*x^2 + 6*x^3)*Log[2])*Log[5] + (80*x^2 + 12*x^3 + 300*x^4 + 120*x^5 + 12*x^6 + (40*x^2 + 6*x^3)*Log[2])*Log[5]^2)*Log[x]^2 + ((16 + 8*x^2 + (8 + 4*x^2)*Log[2])*Log[5] + (8*x^2 + 4*x^2*Log[2])*Log[5]^2)*Log[x]^3 + (-120*x^2 - 24*x^3 - 60*x^4 - 12*x^5 + (-128*x^2 - 24*x^3 - 120*x^4 - 24*x^5 - 4*x^2*Log[2])*Log[5] + (-8*x^2 - 60*x^4 - 12*x^5 - 4*x^2*Log[2])*Log[5]^2)*Log[x]^4 + (8*x^2 + 4*x^4 + (8*x^2 + 8*x^4)*Log[5] + 4*x^4*Log[5]^2)*Log[x]^6)/(-125*x - 75*x^2 - 15*x^3 - x^4 + (75*x + 30*x^2 + 3*x^3)*Log[x]^2 + (-15*x - 3*x^2)*Log[x]^4 + x*Log[x]^6),x]
Mathematica 13.1 output
\[ \text {\$Aborted} \]
Mathematica 12.3 output
\[ 4 x^2 (1+\log (5))+x^4 (1+\log (5))^2+\frac {x^2 \left (\log ^2(2) \log ^2(5)+5 \log (4) \log (5) (9+10 \log (5))+\log ^2(25)+\log (2) \log (5) (-90-98 \log (5)+\log (25))\right )+x^4 (1+\log (5)) (\log (8) \log (3125)-\log (5) \log (32768))-10 \log (5) \left (\log (5) \log (16)+\log ^2(2) \log (25)+\log (4) \log (25)+\log (390625)\right )-2 x \log (5) \left (\log (5) \log (16)+\log ^2(2) \log (25)+\log (4) \log (25)+\log (390625)\right )+x^3 \left (-100 \log ^2(5)+\log (625) \log (298023223876953125)\right )}{\left (-20-4 x+x^2\right ) \left (5+x-\log ^2(x)\right )^2}+\frac {-8000 \log (5) (8+\log (16))-4800 x \log (5) (8+\log (16))-160 x^2 \log (5) (188+200 \log (5)+5 \log (4) (9+10 \log (5))+\log (16))-4 x^3 \log (5) (3968+3000 \log (2)-430 \log (4)-39 \log (16)+4000 \log (25)+300 \log (5) (16+\log (256))-2000 \log (625))+x^6 \left (\log ^2(5) (-524+390 \log (2)-39 \log (4)-112 \log (8))+360 \log (25)+\log (5) (-516+392 \log (2)-38 \log (4)-112 \log (8)+360 \log (25)-61 \log (625))-61 \log (625)\right )+x^8 (1+\log (5)) (\log (4) \log (5)+\log (625))+4 x^5 \left (2 \log ^2(5) (-312+40 \log (2)+167 \log (4)-90 \log (8))-60 \log (25)+290 \log (625)+\log (5) (-648+76 \log (2)+332 \log (4)-180 \log (8)-\log (16)-60 \log (25)+290 \log (625))\right )+x^4 \left (-20 \log ^2(5) (-28+390 \log (2)-267 \log (4)+40 \log (8))+(-12400+\log (16)) \log (25)+6300 \log (625)+\log (5) (464-7920 \log (2)+5372 \log (4)-800 \log (8)-12400 \log (25)+6300 \log (625))\right )-2 x^7 (1+\log (5)) (15 \log (25)+8 \log (625)+\log (5) (-38+\log (4096)))}{\left (-20-4 x+x^2\right )^3 \left (5+x-\log ^2(x)\right )} \]