Integrand size = 590, antiderivative size = 30 \[ \int \frac {-1000 x^2-600 x^3-620 x^4-308 x^5-60 x^6-4 x^7+\left (40 x-1192 x^2-660 x^3-1124 x^4-608 x^5-120 x^6-8 x^7+\left (20 x-96 x^2-30 x^3-2 x^4\right ) \log (2)\right ) \log (5)+\left (8 x-200 x^2-60 x^3-504 x^4-300 x^5-60 x^6-4 x^7+\left (8 x-100 x^2-30 x^3-2 x^4\right ) \log (2)+2 x \log ^2(2)\right ) \log ^2(5)+\left (\left (-80-16 x-40 x^2-8 x^3+\left (-40-8 x-20 x^2-4 x^3\right ) \log (2)\right ) \log (5)+\left (-16-40 x^2-8 x^3+\left (-16-20 x^2-4 x^3\right ) \log (2)-4 \log ^2(2)\right ) \log ^2(5)\right ) \log (x)+\left (600 x^2+240 x^3+324 x^4+120 x^5+12 x^6+\left (-8 x+680 x^2+252 x^3+624 x^4+240 x^5+24 x^6+\left (-4 x+40 x^2+6 x^3\right ) \log (2)\right ) \log (5)+\left (80 x^2+12 x^3+300 x^4+120 x^5+12 x^6+\left (40 x^2+6 x^3\right ) \log (2)\right ) \log ^2(5)\right ) \log ^2(x)+\left (\left (16+8 x^2+\left (8+4 x^2\right ) \log (2)\right ) \log (5)+\left (8 x^2+4 x^2 \log (2)\right ) \log ^2(5)\right ) \log ^3(x)+\left (-120 x^2-24 x^3-60 x^4-12 x^5+\left (-128 x^2-24 x^3-120 x^4-24 x^5-4 x^2 \log (2)\right ) \log (5)+\left (-8 x^2-60 x^4-12 x^5-4 x^2 \log (2)\right ) \log ^2(5)\right ) \log ^4(x)+\left (8 x^2+4 x^4+\left (8 x^2+8 x^4\right ) \log (5)+4 x^4 \log ^2(5)\right ) \log ^6(x)}{-125 x-75 x^2-15 x^3-x^4+\left (75 x+30 x^2+3 x^3\right ) \log ^2(x)+\left (-15 x-3 x^2\right ) \log ^4(x)+x \log ^6(x)} \, dx=\left (2+x^2+\log (5) \left (x^2+\frac {2+\log (2)}{5+x-\log ^2(x)}\right )\right )^2 \]
\[ \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=\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 \]
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)*L og[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]
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)*L og[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]
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {-4 x^7-60 x^6-308 x^5-620 x^4-600 x^3-1000 x^2+\left (\log ^2(5) \left (8 x^2+4 x^2 \log (2)\right )+\log (5) \left (8 x^2+\left (4 x^2+8\right ) \log (2)+16\right )\right ) \log ^3(x)+\left (4 x^4+4 x^4 \log ^2(5)+8 x^2+\left (8 x^4+8 x^2\right ) \log (5)\right ) \log ^6(x)+\left (\log ^2(5) \left (-8 x^3-40 x^2+\left (-4 x^3-20 x^2-16\right ) \log (2)-16-4 \log ^2(2)\right )+\log (5) \left (-8 x^3-40 x^2+\left (-4 x^3-20 x^2-8 x-40\right ) \log (2)-16 x-80\right )\right ) \log (x)+\left (-12 x^5-60 x^4-24 x^3-120 x^2+\log ^2(5) \left (-12 x^5-60 x^4-8 x^2-4 x^2 \log (2)\right )+\log (5) \left (-24 x^5-120 x^4-24 x^3-128 x^2-4 x^2 \log (2)\right )\right ) \log ^4(x)+\left (12 x^6+120 x^5+324 x^4+240 x^3+600 x^2+\log ^2(5) \left (12 x^6+120 x^5+300 x^4+12 x^3+80 x^2+\left (6 x^3+40 x^2\right ) \log (2)\right )+\log (5) \left (24 x^6+240 x^5+624 x^4+252 x^3+680 x^2+\left (6 x^3+40 x^2-4 x\right ) \log (2)-8 x\right )\right ) \log ^2(x)+\log ^2(5) \left (-4 x^7-60 x^6-300 x^5-504 x^4-60 x^3-200 x^2+\left (-2 x^4-30 x^3-100 x^2+8 x\right ) \log (2)+8 x+2 x \log ^2(2)\right )+\log (5) \left (-8 x^7-120 x^6-608 x^5-1124 x^4-660 x^3-1192 x^2+\left (-2 x^4-30 x^3-96 x^2+20 x\right ) \log (2)+40 x\right )}{-x^4-15 x^3-75 x^2+\left (-3 x^2-15 x\right ) \log ^4(x)+\left (3 x^3+30 x^2+75 x\right ) \log ^2(x)-125 x+x \log ^6(x)} \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {4 x^7+60 x^6+308 x^5+620 x^4+600 x^3+1000 x^2-\left (\log ^2(5) \left (8 x^2+4 x^2 \log (2)\right )+\log (5) \left (8 x^2+\left (4 x^2+8\right ) \log (2)+16\right )\right ) \log ^3(x)-\left (4 x^4+4 x^4 \log ^2(5)+8 x^2+\left (8 x^4+8 x^2\right ) \log (5)\right ) \log ^6(x)-\left (\log ^2(5) \left (-8 x^3-40 x^2+\left (-4 x^3-20 x^2-16\right ) \log (2)-16-4 \log ^2(2)\right )+\log (5) \left (-8 x^3-40 x^2+\left (-4 x^3-20 x^2-8 x-40\right ) \log (2)-16 x-80\right )\right ) \log (x)-\left (-12 x^5-60 x^4-24 x^3-120 x^2+\log ^2(5) \left (-12 x^5-60 x^4-8 x^2-4 x^2 \log (2)\right )+\log (5) \left (-24 x^5-120 x^4-24 x^3-128 x^2-4 x^2 \log (2)\right )\right ) \log ^4(x)-\left (12 x^6+120 x^5+324 x^4+240 x^3+600 x^2+\log ^2(5) \left (12 x^6+120 x^5+300 x^4+12 x^3+80 x^2+\left (6 x^3+40 x^2\right ) \log (2)\right )+\log (5) \left (24 x^6+240 x^5+624 x^4+252 x^3+680 x^2+\left (6 x^3+40 x^2-4 x\right ) \log (2)-8 x\right )\right ) \log ^2(x)-\log ^2(5) \left (-4 x^7-60 x^6-300 x^5-504 x^4-60 x^3-200 x^2+\left (-2 x^4-30 x^3-100 x^2+8 x\right ) \log (2)+8 x+2 x \log ^2(2)\right )-\log (5) \left (-8 x^7-120 x^6-608 x^5-1124 x^4-660 x^3-1192 x^2+\left (-2 x^4-30 x^3-96 x^2+20 x\right ) \log (2)+40 x\right )}{x \left (x-\log ^2(x)+5\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {2 (2+\log (2)) \log (5) \left (x^2 (1+\log (5))+2\right ) (2 \log (x)-x)}{x \left (x-\log ^2(x)+5\right )^2}+4 x (1+\log (5)) \left (x^2 (1+\log (5))+2\right )+\frac {4 x (2+\log (2)) \log (5) (1+\log (5))}{x-\log ^2(x)+5}-\frac {2 (2+\log (2))^2 \log ^2(5) (x-2 \log (x))}{x \left (x-\log ^2(x)+5\right )^3}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -2 (2+\log (2)) \log (5) (1+\log (5)) \int \frac {x^2}{\left (-\log ^2(x)+x+5\right )^2}dx+4 (2+\log (2)) \log (5) (1+\log (5)) \int \frac {x \log (x)}{\left (-\log ^2(x)+x+5\right )^2}dx+4 (2+\log (2)) \log (5) (1+\log (5)) \int \frac {x}{-\log ^2(x)+x+5}dx+x^4 (1+\log (5))^2+4 x^2 (1+\log (5))+\frac {4 (2+\log (2)) \log (5)}{x-\log ^2(x)+5}+\frac {(2+\log (2))^2 \log ^2(5)}{\left (x-\log ^2(x)+5\right )^2}\) |
Int[(-1000*x^2 - 600*x^3 - 620*x^4 - 308*x^5 - 60*x^6 - 4*x^7 + (40*x - 11 92*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)*L og[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]
3.23.64.3.1 Defintions of rubi rules used
Leaf count of result is larger than twice the leaf count of optimal. \(173\) vs. \(2(30)=60\).
Time = 1.09 (sec) , antiderivative size = 174, normalized size of antiderivative = 5.80
| method | result | size |
| risch | \(\left (x^{2} \ln \left (5\right )+x^{2}+2\right )^{2}+\frac {\ln \left (5\right ) \left (-2 x^{2} \ln \left (5\right ) \ln \left (x \right )^{2} \ln \left (2\right )+2 \ln \left (5\right ) \ln \left (2\right ) x^{3}-4 \ln \left (5\right ) \ln \left (x \right )^{2} x^{2}-2 x^{2} \ln \left (2\right ) \ln \left (x \right )^{2}+10 x^{2} \ln \left (2\right ) \ln \left (5\right )+4 x^{3} \ln \left (5\right )+2 x^{3} \ln \left (2\right )-4 x^{2} \ln \left (x \right )^{2}+\ln \left (2\right )^{2} \ln \left (5\right )+20 x^{2} \ln \left (5\right )+10 x^{2} \ln \left (2\right )-4 \ln \left (2\right ) \ln \left (x \right )^{2}+4 x^{3}+4 \ln \left (2\right ) \ln \left (5\right )+4 x \ln \left (2\right )+20 x^{2}-8 \ln \left (x \right )^{2}+4 \ln \left (5\right )+20 \ln \left (2\right )+8 x +40\right )}{\left (5+x -\ln \left (x \right )^{2}\right )^{2}}\) | \(174\) |
| default | \(2 \ln \left (2\right ) \left (-\frac {\ln \left (5\right ) \left (x^{2}+2\right )}{\ln \left (x \right )^{2}-5-x}-\ln \left (5\right )^{2} \left (-\ln \left (x \right )^{2}-x +\frac {\ln \left (x \right )^{6}-x \ln \left (x \right )^{4}-15 \ln \left (x \right )^{4}+10 x \ln \left (x \right )^{2}+75 \ln \left (x \right )^{2}-25 x -127}{\left (\ln \left (x \right )^{2}-5-x \right )^{2}}\right )\right )+\left (x^{2}+2\right )^{2}+4 \ln \left (5\right ) \left (\ln \left (x \right )^{2}+\frac {x^{4}}{2}+x^{2}+x -\frac {\ln \left (x \right )^{4}-10 \ln \left (x \right )^{2}+27}{\ln \left (x \right )^{2}-5-x}\right )+4 \ln \left (5\right )^{2} \left (\ln \left (x \right )^{2}+\frac {x^{4}}{4}+x -\frac {\ln \left (x \right )^{6}-x \ln \left (x \right )^{4}-15 \ln \left (x \right )^{4}+10 x \ln \left (x \right )^{2}+75 \ln \left (x \right )^{2}-25 x -126}{\left (\ln \left (x \right )^{2}-5-x \right )^{2}}\right )+\frac {\ln \left (2\right )^{2} \ln \left (5\right )^{2}}{\left (\ln \left (x \right )^{2}-5-x \right )^{2}}\) | \(225\) |
| parallelrisch | \(\frac {\ln \left (5\right )^{2} \ln \left (x \right )^{4} x^{4}-2 \ln \left (5\right )^{2} \ln \left (x \right )^{2} x^{5}+2 \ln \left (5\right ) \ln \left (x \right )^{4} x^{4}-4 \ln \left (5\right ) \ln \left (x \right )^{2} x^{5}+4 \ln \left (5\right ) \ln \left (x \right )^{4} x^{2}-20 \ln \left (5\right ) \ln \left (x \right )^{2} x^{4}-10 \ln \left (5\right )^{2} x^{4} \ln \left (x \right )^{2}+2 \ln \left (5\right )^{2} \ln \left (2\right ) x^{3}-8 \ln \left (5\right ) \ln \left (x \right )^{2} x^{3}-44 \ln \left (5\right ) \ln \left (x \right )^{2} x^{2}-4 \ln \left (5\right ) \ln \left (x \right )^{2} \ln \left (2\right )-4 x^{2} \ln \left (5\right )^{2} \ln \left (x \right )^{2}+x^{6} \ln \left (5\right )^{2}+10 x^{5} \ln \left (5\right )^{2}+4 x^{3} \ln \left (5\right )^{2}+4 x \ln \left (2\right ) \ln \left (5\right )-10 x^{4} \ln \left (x \right )^{2}+20 x^{5} \ln \left (5\right )+2 x^{6} \ln \left (5\right )+20 \ln \left (2\right ) \ln \left (5\right )+8 x \ln \left (5\right )+20 x^{2} \ln \left (5\right )^{2}+44 x^{3} \ln \left (5\right )+\ln \left (2\right )^{2} \ln \left (5\right )^{2}-2 \ln \left (5\right )^{2} \ln \left (x \right )^{2} \ln \left (2\right ) x^{2}+25 x^{4} \ln \left (5\right )^{2}+x^{4} \ln \left (x \right )^{4}-2 x^{2} \ln \left (5\right ) \ln \left (x \right )^{2} \ln \left (2\right )-2 x^{5} \ln \left (x \right )^{2}+54 x^{4} \ln \left (5\right )-8 x^{3} \ln \left (x \right )^{2}+120 x^{2} \ln \left (5\right )-40 x^{2} \ln \left (x \right )^{2}+4 x^{2} \ln \left (x \right )^{4}+40 \ln \left (5\right )+4 \ln \left (5\right )^{2}+10 x^{2} \ln \left (2\right ) \ln \left (5\right )+x^{6}+10 x^{5}+29 x^{4}+40 x^{3}+100 x^{2}-8 \ln \left (5\right ) \ln \left (x \right )^{2}+2 \ln \left (5\right ) \ln \left (2\right ) x^{3}+4 \ln \left (5\right )^{2} \ln \left (2\right )+10 \ln \left (5\right )^{2} \ln \left (2\right ) x^{2}}{\ln \left (x \right )^{4}-2 x \ln \left (x \right )^{2}-10 \ln \left (x \right )^{2}+x^{2}+10 x +25}\) | \(433\) |
int(((4*x^4*ln(5)^2+(8*x^4+8*x^2)*ln(5)+4*x^4+8*x^2)*ln(x)^6+((-4*x^2*ln(2 )-12*x^5-60*x^4-8*x^2)*ln(5)^2+(-4*x^2*ln(2)-24*x^5-120*x^4-24*x^3-128*x^2 )*ln(5)-12*x^5-60*x^4-24*x^3-120*x^2)*ln(x)^4+((4*x^2*ln(2)+8*x^2)*ln(5)^2 +((4*x^2+8)*ln(2)+8*x^2+16)*ln(5))*ln(x)^3+(((6*x^3+40*x^2)*ln(2)+12*x^6+1 20*x^5+300*x^4+12*x^3+80*x^2)*ln(5)^2+((6*x^3+40*x^2-4*x)*ln(2)+24*x^6+240 *x^5+624*x^4+252*x^3+680*x^2-8*x)*ln(5)+12*x^6+120*x^5+324*x^4+240*x^3+600 *x^2)*ln(x)^2+((-4*ln(2)^2+(-4*x^3-20*x^2-16)*ln(2)-8*x^3-40*x^2-16)*ln(5) ^2+((-4*x^3-20*x^2-8*x-40)*ln(2)-8*x^3-40*x^2-16*x-80)*ln(5))*ln(x)+(2*x*l n(2)^2+(-2*x^4-30*x^3-100*x^2+8*x)*ln(2)-4*x^7-60*x^6-300*x^5-504*x^4-60*x ^3-200*x^2+8*x)*ln(5)^2+((-2*x^4-30*x^3-96*x^2+20*x)*ln(2)-8*x^7-120*x^6-6 08*x^5-1124*x^4-660*x^3-1192*x^2+40*x)*ln(5)-4*x^7-60*x^6-308*x^5-620*x^4- 600*x^3-1000*x^2)/(x*ln(x)^6+(-3*x^2-15*x)*ln(x)^4+(3*x^3+30*x^2+75*x)*ln( x)^2-x^4-15*x^3-75*x^2-125*x),x,method=_RETURNVERBOSE)
(x^2*ln(5)+x^2+2)^2+ln(5)*(-2*x^2*ln(5)*ln(x)^2*ln(2)+2*ln(5)*ln(2)*x^3-4* ln(5)*ln(x)^2*x^2-2*x^2*ln(2)*ln(x)^2+10*x^2*ln(2)*ln(5)+4*x^3*ln(5)+2*x^3 *ln(2)-4*x^2*ln(x)^2+ln(2)^2*ln(5)+20*x^2*ln(5)+10*x^2*ln(2)-4*ln(2)*ln(x) ^2+4*x^3+4*ln(2)*ln(5)+4*x*ln(2)+20*x^2-8*ln(x)^2+4*ln(5)+20*ln(2)+8*x+40) /(5+x-ln(x)^2)^2
Leaf count of result is larger than twice the leaf count of optimal. 262 vs. \(2 (31) = 62\).
Time = 0.28 (sec) , antiderivative size = 262, normalized size of antiderivative = 8.73 \[ \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=\frac {x^{6} + 10 \, x^{5} + {\left (x^{4} \log \left (5\right )^{2} + x^{4} + 4 \, x^{2} + 2 \, {\left (x^{4} + 2 \, x^{2}\right )} \log \left (5\right )\right )} \log \left (x\right )^{4} + 29 \, x^{4} + 40 \, x^{3} + {\left (x^{6} + 10 \, x^{5} + 25 \, x^{4} + 4 \, x^{3} + 20 \, x^{2} + 2 \, {\left (x^{3} + 5 \, x^{2} + 2\right )} \log \left (2\right ) + \log \left (2\right )^{2} + 4\right )} \log \left (5\right )^{2} - 2 \, {\left (x^{5} + 5 \, x^{4} + 4 \, x^{3} + {\left (x^{5} + 5 \, x^{4} + x^{2} \log \left (2\right ) + 2 \, x^{2}\right )} \log \left (5\right )^{2} + 20 \, x^{2} + {\left (2 \, x^{5} + 10 \, x^{4} + 4 \, x^{3} + 22 \, x^{2} + {\left (x^{2} + 2\right )} \log \left (2\right ) + 4\right )} \log \left (5\right )\right )} \log \left (x\right )^{2} + 100 \, x^{2} + 2 \, {\left (x^{6} + 10 \, x^{5} + 27 \, x^{4} + 22 \, x^{3} + 60 \, x^{2} + {\left (x^{3} + 5 \, x^{2} + 2 \, x + 10\right )} \log \left (2\right ) + 4 \, x + 20\right )} \log \left (5\right )}{\log \left (x\right )^{4} - 2 \, {\left (x + 5\right )} \log \left (x\right )^{2} + x^{2} + 10 \, x + 25} \]
integrate(((4*x^4*log(5)^2+(8*x^4+8*x^2)*log(5)+4*x^4+8*x^2)*log(x)^6+((-4 *x^2*log(2)-12*x^5-60*x^4-8*x^2)*log(5)^2+(-4*x^2*log(2)-24*x^5-120*x^4-24 *x^3-128*x^2)*log(5)-12*x^5-60*x^4-24*x^3-120*x^2)*log(x)^4+((4*x^2*log(2) +8*x^2)*log(5)^2+((4*x^2+8)*log(2)+8*x^2+16)*log(5))*log(x)^3+(((6*x^3+40* x^2)*log(2)+12*x^6+120*x^5+300*x^4+12*x^3+80*x^2)*log(5)^2+((6*x^3+40*x^2- 4*x)*log(2)+24*x^6+240*x^5+624*x^4+252*x^3+680*x^2-8*x)*log(5)+12*x^6+120* x^5+324*x^4+240*x^3+600*x^2)*log(x)^2+((-4*log(2)^2+(-4*x^3-20*x^2-16)*log (2)-8*x^3-40*x^2-16)*log(5)^2+((-4*x^3-20*x^2-8*x-40)*log(2)-8*x^3-40*x^2- 16*x-80)*log(5))*log(x)+(2*x*log(2)^2+(-2*x^4-30*x^3-100*x^2+8*x)*log(2)-4 *x^7-60*x^6-300*x^5-504*x^4-60*x^3-200*x^2+8*x)*log(5)^2+((-2*x^4-30*x^3-9 6*x^2+20*x)*log(2)-8*x^7-120*x^6-608*x^5-1124*x^4-660*x^3-1192*x^2+40*x)*l og(5)-4*x^7-60*x^6-308*x^5-620*x^4-600*x^3-1000*x^2)/(x*log(x)^6+(-3*x^2-1 5*x)*log(x)^4+(3*x^3+30*x^2+75*x)*log(x)^2-x^4-15*x^3-75*x^2-125*x),x, alg orithm=\
(x^6 + 10*x^5 + (x^4*log(5)^2 + x^4 + 4*x^2 + 2*(x^4 + 2*x^2)*log(5))*log( x)^4 + 29*x^4 + 40*x^3 + (x^6 + 10*x^5 + 25*x^4 + 4*x^3 + 20*x^2 + 2*(x^3 + 5*x^2 + 2)*log(2) + log(2)^2 + 4)*log(5)^2 - 2*(x^5 + 5*x^4 + 4*x^3 + (x ^5 + 5*x^4 + x^2*log(2) + 2*x^2)*log(5)^2 + 20*x^2 + (2*x^5 + 10*x^4 + 4*x ^3 + 22*x^2 + (x^2 + 2)*log(2) + 4)*log(5))*log(x)^2 + 100*x^2 + 2*(x^6 + 10*x^5 + 27*x^4 + 22*x^3 + 60*x^2 + (x^3 + 5*x^2 + 2*x + 10)*log(2) + 4*x + 20)*log(5))/(log(x)^4 - 2*(x + 5)*log(x)^2 + x^2 + 10*x + 25)
Leaf count of result is larger than twice the leaf count of optimal. 260 vs. \(2 (26) = 52\).
Time = 1.11 (sec) , antiderivative size = 260, normalized size of antiderivative = 8.67 \[ \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=x^{4} \cdot \left (1 + \log {\left (5 \right )}^{2} + 2 \log {\left (5 \right )}\right ) + x^{2} \cdot \left (4 + 4 \log {\left (5 \right )}\right ) + \frac {2 x^{3} \log {\left (2 \right )} \log {\left (5 \right )} + 2 x^{3} \log {\left (2 \right )} \log {\left (5 \right )}^{2} + 4 x^{3} \log {\left (5 \right )} + 4 x^{3} \log {\left (5 \right )}^{2} + 10 x^{2} \log {\left (2 \right )} \log {\left (5 \right )} + 10 x^{2} \log {\left (2 \right )} \log {\left (5 \right )}^{2} + 20 x^{2} \log {\left (5 \right )} + 20 x^{2} \log {\left (5 \right )}^{2} + 4 x \log {\left (2 \right )} \log {\left (5 \right )} + 8 x \log {\left (5 \right )} + \left (- 4 x^{2} \log {\left (5 \right )}^{2} - 4 x^{2} \log {\left (5 \right )} - 2 x^{2} \log {\left (2 \right )} \log {\left (5 \right )}^{2} - 2 x^{2} \log {\left (2 \right )} \log {\left (5 \right )} - 8 \log {\left (5 \right )} - 4 \log {\left (2 \right )} \log {\left (5 \right )}\right ) \log {\left (x \right )}^{2} + \log {\left (2 \right )}^{2} \log {\left (5 \right )}^{2} + 4 \log {\left (2 \right )} \log {\left (5 \right )}^{2} + 4 \log {\left (5 \right )}^{2} + 20 \log {\left (2 \right )} \log {\left (5 \right )} + 40 \log {\left (5 \right )}}{x^{2} + 10 x + \left (- 2 x - 10\right ) \log {\left (x \right )}^{2} + \log {\left (x \right )}^{4} + 25} \]
integrate(((4*x**4*ln(5)**2+(8*x**4+8*x**2)*ln(5)+4*x**4+8*x**2)*ln(x)**6+ ((-4*x**2*ln(2)-12*x**5-60*x**4-8*x**2)*ln(5)**2+(-4*x**2*ln(2)-24*x**5-12 0*x**4-24*x**3-128*x**2)*ln(5)-12*x**5-60*x**4-24*x**3-120*x**2)*ln(x)**4+ ((4*x**2*ln(2)+8*x**2)*ln(5)**2+((4*x**2+8)*ln(2)+8*x**2+16)*ln(5))*ln(x)* *3+(((6*x**3+40*x**2)*ln(2)+12*x**6+120*x**5+300*x**4+12*x**3+80*x**2)*ln( 5)**2+((6*x**3+40*x**2-4*x)*ln(2)+24*x**6+240*x**5+624*x**4+252*x**3+680*x **2-8*x)*ln(5)+12*x**6+120*x**5+324*x**4+240*x**3+600*x**2)*ln(x)**2+((-4* ln(2)**2+(-4*x**3-20*x**2-16)*ln(2)-8*x**3-40*x**2-16)*ln(5)**2+((-4*x**3- 20*x**2-8*x-40)*ln(2)-8*x**3-40*x**2-16*x-80)*ln(5))*ln(x)+(2*x*ln(2)**2+( -2*x**4-30*x**3-100*x**2+8*x)*ln(2)-4*x**7-60*x**6-300*x**5-504*x**4-60*x* *3-200*x**2+8*x)*ln(5)**2+((-2*x**4-30*x**3-96*x**2+20*x)*ln(2)-8*x**7-120 *x**6-608*x**5-1124*x**4-660*x**3-1192*x**2+40*x)*ln(5)-4*x**7-60*x**6-308 *x**5-620*x**4-600*x**3-1000*x**2)/(x*ln(x)**6+(-3*x**2-15*x)*ln(x)**4+(3* x**3+30*x**2+75*x)*ln(x)**2-x**4-15*x**3-75*x**2-125*x),x)
x**4*(1 + log(5)**2 + 2*log(5)) + x**2*(4 + 4*log(5)) + (2*x**3*log(2)*log (5) + 2*x**3*log(2)*log(5)**2 + 4*x**3*log(5) + 4*x**3*log(5)**2 + 10*x**2 *log(2)*log(5) + 10*x**2*log(2)*log(5)**2 + 20*x**2*log(5) + 20*x**2*log(5 )**2 + 4*x*log(2)*log(5) + 8*x*log(5) + (-4*x**2*log(5)**2 - 4*x**2*log(5) - 2*x**2*log(2)*log(5)**2 - 2*x**2*log(2)*log(5) - 8*log(5) - 4*log(2)*lo g(5))*log(x)**2 + log(2)**2*log(5)**2 + 4*log(2)*log(5)**2 + 4*log(5)**2 + 20*log(2)*log(5) + 40*log(5))/(x**2 + 10*x + (-2*x - 10)*log(x)**2 + log( x)**4 + 25)
Leaf count of result is larger than twice the leaf count of optimal. 279 vs. \(2 (31) = 62\).
Time = 0.38 (sec) , antiderivative size = 279, normalized size of antiderivative = 9.30 \[ \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=\frac {{\left (\log \left (5\right )^{2} + 2 \, \log \left (5\right ) + 1\right )} x^{6} + 10 \, {\left (\log \left (5\right )^{2} + 2 \, \log \left (5\right ) + 1\right )} x^{5} + {\left (25 \, \log \left (5\right )^{2} + 54 \, \log \left (5\right ) + 29\right )} x^{4} + {\left ({\left (\log \left (5\right )^{2} + 2 \, \log \left (5\right ) + 1\right )} x^{4} + 4 \, x^{2} {\left (\log \left (5\right ) + 1\right )}\right )} \log \left (x\right )^{4} + 2 \, {\left (2 \, \log \left (5\right )^{2} + {\left (\log \left (5\right )^{2} + \log \left (5\right )\right )} \log \left (2\right ) + 22 \, \log \left (5\right ) + 20\right )} x^{3} + \log \left (5\right )^{2} \log \left (2\right )^{2} + 10 \, {\left (2 \, \log \left (5\right )^{2} + {\left (\log \left (5\right )^{2} + \log \left (5\right )\right )} \log \left (2\right ) + 12 \, \log \left (5\right ) + 10\right )} x^{2} - 2 \, {\left ({\left (\log \left (5\right )^{2} + 2 \, \log \left (5\right ) + 1\right )} x^{5} + 5 \, {\left (\log \left (5\right )^{2} + 2 \, \log \left (5\right ) + 1\right )} x^{4} + 4 \, x^{3} {\left (\log \left (5\right ) + 1\right )} + {\left (2 \, \log \left (5\right )^{2} + {\left (\log \left (5\right )^{2} + \log \left (5\right )\right )} \log \left (2\right ) + 22 \, \log \left (5\right ) + 20\right )} x^{2} + 2 \, \log \left (5\right ) \log \left (2\right ) + 4 \, \log \left (5\right )\right )} \log \left (x\right )^{2} + 4 \, {\left (\log \left (5\right ) \log \left (2\right ) + 2 \, \log \left (5\right )\right )} x + 4 \, \log \left (5\right )^{2} + 4 \, {\left (\log \left (5\right )^{2} + 5 \, \log \left (5\right )\right )} \log \left (2\right ) + 40 \, \log \left (5\right )}{\log \left (x\right )^{4} - 2 \, {\left (x + 5\right )} \log \left (x\right )^{2} + x^{2} + 10 \, x + 25} \]
integrate(((4*x^4*log(5)^2+(8*x^4+8*x^2)*log(5)+4*x^4+8*x^2)*log(x)^6+((-4 *x^2*log(2)-12*x^5-60*x^4-8*x^2)*log(5)^2+(-4*x^2*log(2)-24*x^5-120*x^4-24 *x^3-128*x^2)*log(5)-12*x^5-60*x^4-24*x^3-120*x^2)*log(x)^4+((4*x^2*log(2) +8*x^2)*log(5)^2+((4*x^2+8)*log(2)+8*x^2+16)*log(5))*log(x)^3+(((6*x^3+40* x^2)*log(2)+12*x^6+120*x^5+300*x^4+12*x^3+80*x^2)*log(5)^2+((6*x^3+40*x^2- 4*x)*log(2)+24*x^6+240*x^5+624*x^4+252*x^3+680*x^2-8*x)*log(5)+12*x^6+120* x^5+324*x^4+240*x^3+600*x^2)*log(x)^2+((-4*log(2)^2+(-4*x^3-20*x^2-16)*log (2)-8*x^3-40*x^2-16)*log(5)^2+((-4*x^3-20*x^2-8*x-40)*log(2)-8*x^3-40*x^2- 16*x-80)*log(5))*log(x)+(2*x*log(2)^2+(-2*x^4-30*x^3-100*x^2+8*x)*log(2)-4 *x^7-60*x^6-300*x^5-504*x^4-60*x^3-200*x^2+8*x)*log(5)^2+((-2*x^4-30*x^3-9 6*x^2+20*x)*log(2)-8*x^7-120*x^6-608*x^5-1124*x^4-660*x^3-1192*x^2+40*x)*l og(5)-4*x^7-60*x^6-308*x^5-620*x^4-600*x^3-1000*x^2)/(x*log(x)^6+(-3*x^2-1 5*x)*log(x)^4+(3*x^3+30*x^2+75*x)*log(x)^2-x^4-15*x^3-75*x^2-125*x),x, alg orithm=\
((log(5)^2 + 2*log(5) + 1)*x^6 + 10*(log(5)^2 + 2*log(5) + 1)*x^5 + (25*lo g(5)^2 + 54*log(5) + 29)*x^4 + ((log(5)^2 + 2*log(5) + 1)*x^4 + 4*x^2*(log (5) + 1))*log(x)^4 + 2*(2*log(5)^2 + (log(5)^2 + log(5))*log(2) + 22*log(5 ) + 20)*x^3 + log(5)^2*log(2)^2 + 10*(2*log(5)^2 + (log(5)^2 + log(5))*log (2) + 12*log(5) + 10)*x^2 - 2*((log(5)^2 + 2*log(5) + 1)*x^5 + 5*(log(5)^2 + 2*log(5) + 1)*x^4 + 4*x^3*(log(5) + 1) + (2*log(5)^2 + (log(5)^2 + log( 5))*log(2) + 22*log(5) + 20)*x^2 + 2*log(5)*log(2) + 4*log(5))*log(x)^2 + 4*(log(5)*log(2) + 2*log(5))*x + 4*log(5)^2 + 4*(log(5)^2 + 5*log(5))*log( 2) + 40*log(5))/(log(x)^4 - 2*(x + 5)*log(x)^2 + x^2 + 10*x + 25)
Leaf count of result is larger than twice the leaf count of optimal. 242 vs. \(2 (31) = 62\).
Time = 0.37 (sec) , antiderivative size = 242, normalized size of antiderivative = 8.07 \[ \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={\left (\log \left (5\right )^{2} + 2 \, \log \left (5\right ) + 1\right )} x^{4} + 4 \, x^{2} {\left (\log \left (5\right ) + 1\right )} - \frac {2 \, x^{2} \log \left (5\right )^{2} \log \left (2\right ) \log \left (x\right )^{2} - 2 \, x^{3} \log \left (5\right )^{2} \log \left (2\right ) + 4 \, x^{2} \log \left (5\right )^{2} \log \left (x\right )^{2} + 2 \, x^{2} \log \left (5\right ) \log \left (2\right ) \log \left (x\right )^{2} - 4 \, x^{3} \log \left (5\right )^{2} - 2 \, x^{3} \log \left (5\right ) \log \left (2\right ) - 10 \, x^{2} \log \left (5\right )^{2} \log \left (2\right ) + 4 \, x^{2} \log \left (5\right ) \log \left (x\right )^{2} - 4 \, x^{3} \log \left (5\right ) - 20 \, x^{2} \log \left (5\right )^{2} - 10 \, x^{2} \log \left (5\right ) \log \left (2\right ) - \log \left (5\right )^{2} \log \left (2\right )^{2} + 4 \, \log \left (5\right ) \log \left (2\right ) \log \left (x\right )^{2} - 20 \, x^{2} \log \left (5\right ) - 4 \, x \log \left (5\right ) \log \left (2\right ) - 4 \, \log \left (5\right )^{2} \log \left (2\right ) + 8 \, \log \left (5\right ) \log \left (x\right )^{2} - 8 \, x \log \left (5\right ) - 4 \, \log \left (5\right )^{2} - 20 \, \log \left (5\right ) \log \left (2\right ) - 40 \, \log \left (5\right )}{\log \left (x\right )^{4} - 2 \, x \log \left (x\right )^{2} + x^{2} - 10 \, \log \left (x\right )^{2} + 10 \, x + 25} \]
integrate(((4*x^4*log(5)^2+(8*x^4+8*x^2)*log(5)+4*x^4+8*x^2)*log(x)^6+((-4 *x^2*log(2)-12*x^5-60*x^4-8*x^2)*log(5)^2+(-4*x^2*log(2)-24*x^5-120*x^4-24 *x^3-128*x^2)*log(5)-12*x^5-60*x^4-24*x^3-120*x^2)*log(x)^4+((4*x^2*log(2) +8*x^2)*log(5)^2+((4*x^2+8)*log(2)+8*x^2+16)*log(5))*log(x)^3+(((6*x^3+40* x^2)*log(2)+12*x^6+120*x^5+300*x^4+12*x^3+80*x^2)*log(5)^2+((6*x^3+40*x^2- 4*x)*log(2)+24*x^6+240*x^5+624*x^4+252*x^3+680*x^2-8*x)*log(5)+12*x^6+120* x^5+324*x^4+240*x^3+600*x^2)*log(x)^2+((-4*log(2)^2+(-4*x^3-20*x^2-16)*log (2)-8*x^3-40*x^2-16)*log(5)^2+((-4*x^3-20*x^2-8*x-40)*log(2)-8*x^3-40*x^2- 16*x-80)*log(5))*log(x)+(2*x*log(2)^2+(-2*x^4-30*x^3-100*x^2+8*x)*log(2)-4 *x^7-60*x^6-300*x^5-504*x^4-60*x^3-200*x^2+8*x)*log(5)^2+((-2*x^4-30*x^3-9 6*x^2+20*x)*log(2)-8*x^7-120*x^6-608*x^5-1124*x^4-660*x^3-1192*x^2+40*x)*l og(5)-4*x^7-60*x^6-308*x^5-620*x^4-600*x^3-1000*x^2)/(x*log(x)^6+(-3*x^2-1 5*x)*log(x)^4+(3*x^3+30*x^2+75*x)*log(x)^2-x^4-15*x^3-75*x^2-125*x),x, alg orithm=\
(log(5)^2 + 2*log(5) + 1)*x^4 + 4*x^2*(log(5) + 1) - (2*x^2*log(5)^2*log(2 )*log(x)^2 - 2*x^3*log(5)^2*log(2) + 4*x^2*log(5)^2*log(x)^2 + 2*x^2*log(5 )*log(2)*log(x)^2 - 4*x^3*log(5)^2 - 2*x^3*log(5)*log(2) - 10*x^2*log(5)^2 *log(2) + 4*x^2*log(5)*log(x)^2 - 4*x^3*log(5) - 20*x^2*log(5)^2 - 10*x^2* log(5)*log(2) - log(5)^2*log(2)^2 + 4*log(5)*log(2)*log(x)^2 - 20*x^2*log( 5) - 4*x*log(5)*log(2) - 4*log(5)^2*log(2) + 8*log(5)*log(x)^2 - 8*x*log(5 ) - 4*log(5)^2 - 20*log(5)*log(2) - 40*log(5))/(log(x)^4 - 2*x*log(x)^2 + x^2 - 10*log(x)^2 + 10*x + 25)
Timed out. \[ \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=\int \frac {\ln \left (x\right )\,\left ({\ln \left (5\right )}^2\,\left (\ln \left (2\right )\,\left (4\,x^3+20\,x^2+16\right )+4\,{\ln \left (2\right )}^2+40\,x^2+8\,x^3+16\right )+\ln \left (5\right )\,\left (16\,x+\ln \left (2\right )\,\left (4\,x^3+20\,x^2+8\,x+40\right )+40\,x^2+8\,x^3+80\right )\right )-{\ln \left (x\right )}^3\,\left ({\ln \left (5\right )}^2\,\left (4\,x^2\,\ln \left (2\right )+8\,x^2\right )+\ln \left (5\right )\,\left (\ln \left (2\right )\,\left (4\,x^2+8\right )+8\,x^2+16\right )\right )-{\ln \left (x\right )}^6\,\left (4\,x^4\,{\ln \left (5\right )}^2+\ln \left (5\right )\,\left (8\,x^4+8\,x^2\right )+8\,x^2+4\,x^4\right )+{\ln \left (x\right )}^4\,\left (\ln \left (5\right )\,\left (4\,x^2\,\ln \left (2\right )+128\,x^2+24\,x^3+120\,x^4+24\,x^5\right )+{\ln \left (5\right )}^2\,\left (4\,x^2\,\ln \left (2\right )+8\,x^2+60\,x^4+12\,x^5\right )+120\,x^2+24\,x^3+60\,x^4+12\,x^5\right )-{\ln \left (x\right )}^2\,\left ({\ln \left (5\right )}^2\,\left (\ln \left (2\right )\,\left (6\,x^3+40\,x^2\right )+80\,x^2+12\,x^3+300\,x^4+120\,x^5+12\,x^6\right )+\ln \left (5\right )\,\left (\ln \left (2\right )\,\left (6\,x^3+40\,x^2-4\,x\right )-8\,x+680\,x^2+252\,x^3+624\,x^4+240\,x^5+24\,x^6\right )+600\,x^2+240\,x^3+324\,x^4+120\,x^5+12\,x^6\right )+1000\,x^2+600\,x^3+620\,x^4+308\,x^5+60\,x^6+4\,x^7+\ln \left (5\right )\,\left (\ln \left (2\right )\,\left (2\,x^4+30\,x^3+96\,x^2-20\,x\right )-40\,x+1192\,x^2+660\,x^3+1124\,x^4+608\,x^5+120\,x^6+8\,x^7\right )+{\ln \left (5\right )}^2\,\left (\ln \left (2\right )\,\left (2\,x^4+30\,x^3+100\,x^2-8\,x\right )-2\,x\,{\ln \left (2\right )}^2-8\,x+200\,x^2+60\,x^3+504\,x^4+300\,x^5+60\,x^6+4\,x^7\right )}{125\,x+{\ln \left (x\right )}^4\,\left (3\,x^2+15\,x\right )-x\,{\ln \left (x\right )}^6-{\ln \left (x\right )}^2\,\left (3\,x^3+30\,x^2+75\,x\right )+75\,x^2+15\,x^3+x^4} \,d x \]
int((log(x)*(log(5)^2*(log(2)*(20*x^2 + 4*x^3 + 16) + 4*log(2)^2 + 40*x^2 + 8*x^3 + 16) + log(5)*(16*x + log(2)*(8*x + 20*x^2 + 4*x^3 + 40) + 40*x^2 + 8*x^3 + 80)) - log(x)^3*(log(5)^2*(4*x^2*log(2) + 8*x^2) + log(5)*(log( 2)*(4*x^2 + 8) + 8*x^2 + 16)) - log(x)^6*(4*x^4*log(5)^2 + log(5)*(8*x^2 + 8*x^4) + 8*x^2 + 4*x^4) + log(x)^4*(log(5)*(4*x^2*log(2) + 128*x^2 + 24*x ^3 + 120*x^4 + 24*x^5) + log(5)^2*(4*x^2*log(2) + 8*x^2 + 60*x^4 + 12*x^5) + 120*x^2 + 24*x^3 + 60*x^4 + 12*x^5) - log(x)^2*(log(5)^2*(log(2)*(40*x^ 2 + 6*x^3) + 80*x^2 + 12*x^3 + 300*x^4 + 120*x^5 + 12*x^6) + log(5)*(log(2 )*(40*x^2 - 4*x + 6*x^3) - 8*x + 680*x^2 + 252*x^3 + 624*x^4 + 240*x^5 + 2 4*x^6) + 600*x^2 + 240*x^3 + 324*x^4 + 120*x^5 + 12*x^6) + 1000*x^2 + 600* x^3 + 620*x^4 + 308*x^5 + 60*x^6 + 4*x^7 + log(5)*(log(2)*(96*x^2 - 20*x + 30*x^3 + 2*x^4) - 40*x + 1192*x^2 + 660*x^3 + 1124*x^4 + 608*x^5 + 120*x^ 6 + 8*x^7) + log(5)^2*(log(2)*(100*x^2 - 8*x + 30*x^3 + 2*x^4) - 2*x*log(2 )^2 - 8*x + 200*x^2 + 60*x^3 + 504*x^4 + 300*x^5 + 60*x^6 + 4*x^7))/(125*x + log(x)^4*(15*x + 3*x^2) - x*log(x)^6 - log(x)^2*(75*x + 30*x^2 + 3*x^3) + 75*x^2 + 15*x^3 + x^4),x)
int((log(x)*(log(5)^2*(log(2)*(20*x^2 + 4*x^3 + 16) + 4*log(2)^2 + 40*x^2 + 8*x^3 + 16) + log(5)*(16*x + log(2)*(8*x + 20*x^2 + 4*x^3 + 40) + 40*x^2 + 8*x^3 + 80)) - log(x)^3*(log(5)^2*(4*x^2*log(2) + 8*x^2) + log(5)*(log( 2)*(4*x^2 + 8) + 8*x^2 + 16)) - log(x)^6*(4*x^4*log(5)^2 + log(5)*(8*x^2 + 8*x^4) + 8*x^2 + 4*x^4) + log(x)^4*(log(5)*(4*x^2*log(2) + 128*x^2 + 24*x ^3 + 120*x^4 + 24*x^5) + log(5)^2*(4*x^2*log(2) + 8*x^2 + 60*x^4 + 12*x^5) + 120*x^2 + 24*x^3 + 60*x^4 + 12*x^5) - log(x)^2*(log(5)^2*(log(2)*(40*x^ 2 + 6*x^3) + 80*x^2 + 12*x^3 + 300*x^4 + 120*x^5 + 12*x^6) + log(5)*(log(2 )*(40*x^2 - 4*x + 6*x^3) - 8*x + 680*x^2 + 252*x^3 + 624*x^4 + 240*x^5 + 2 4*x^6) + 600*x^2 + 240*x^3 + 324*x^4 + 120*x^5 + 12*x^6) + 1000*x^2 + 600* x^3 + 620*x^4 + 308*x^5 + 60*x^6 + 4*x^7 + log(5)*(log(2)*(96*x^2 - 20*x + 30*x^3 + 2*x^4) - 40*x + 1192*x^2 + 660*x^3 + 1124*x^4 + 608*x^5 + 120*x^ 6 + 8*x^7) + log(5)^2*(log(2)*(100*x^2 - 8*x + 30*x^3 + 2*x^4) - 2*x*log(2 )^2 - 8*x + 200*x^2 + 60*x^3 + 504*x^4 + 300*x^5 + 60*x^6 + 4*x^7))/(125*x + log(x)^4*(15*x + 3*x^2) - x*log(x)^6 - log(x)^2*(75*x + 30*x^2 + 3*x^3) + 75*x^2 + 15*x^3 + x^4), x)