Integrand size = 590, antiderivative size = 30 \[ \int \frac {-1000 x^2-600 x^3-620 x^4-308 x^5-60 x^6-4 x^7+\left (40 x-1192 x^2-660 x^3-1124 x^4-608 x^5-120 x^6-8 x^7+\left (20 x-96 x^2-30 x^3-2 x^4\right ) \log (2)\right ) \log (5)+\left (8 x-200 x^2-60 x^3-504 x^4-300 x^5-60 x^6-4 x^7+\left (8 x-100 x^2-30 x^3-2 x^4\right ) \log (2)+2 x \log ^2(2)\right ) \log ^2(5)+\left (\left (-80-16 x-40 x^2-8 x^3+\left (-40-8 x-20 x^2-4 x^3\right ) \log (2)\right ) \log (5)+\left (-16-40 x^2-8 x^3+\left (-16-20 x^2-4 x^3\right ) \log (2)-4 \log ^2(2)\right ) \log ^2(5)\right ) \log (x)+\left (600 x^2+240 x^3+324 x^4+120 x^5+12 x^6+\left (-8 x+680 x^2+252 x^3+624 x^4+240 x^5+24 x^6+\left (-4 x+40 x^2+6 x^3\right ) \log (2)\right ) \log (5)+\left (80 x^2+12 x^3+300 x^4+120 x^5+12 x^6+\left (40 x^2+6 x^3\right ) \log (2)\right ) \log ^2(5)\right ) \log ^2(x)+\left (\left (16+8 x^2+\left (8+4 x^2\right ) \log (2)\right ) \log (5)+\left (8 x^2+4 x^2 \log (2)\right ) \log ^2(5)\right ) \log ^3(x)+\left (-120 x^2-24 x^3-60 x^4-12 x^5+\left (-128 x^2-24 x^3-120 x^4-24 x^5-4 x^2 \log (2)\right ) \log (5)+\left (-8 x^2-60 x^4-12 x^5-4 x^2 \log (2)\right ) \log ^2(5)\right ) \log ^4(x)+\left (8 x^2+4 x^4+\left (8 x^2+8 x^4\right ) \log (5)+4 x^4 \log ^2(5)\right ) \log ^6(x)}{-125 x-75 x^2-15 x^3-x^4+\left (75 x+30 x^2+3 x^3\right ) \log ^2(x)+\left (-15 x-3 x^2\right ) \log ^4(x)+x \log ^6(x)} \, dx=\left (2+x^2+\log (5) \left (x^2+\frac {2+\log (2)}{5+x-\log ^2(x)}\right )\right )^2 \]
[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 {-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 \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int \frac {2 \left (x \left (30 x^5 (1+\log (5))^2+2 x^6 (1+\log (5))^2+x^3 (1+\log (5)) (310+(252+\log (2)) \log (5))+2 x^4 \left (77+152 \log (5)+75 \log ^2(5)\right )+2 x \left (250+(298+24 \log (2)) \log (5)+25 (2+\log (2)) \log ^2(5)\right )-(2+\log (2)) \log (5) (10+\log (2) \log (5)+\log (25))+15 x^2 (1+\log (5)) (20+\log (2) \log (5)+\log (25))\right )+\log (5) \left (10 x^2 (2+\log (2)) (1+\log (5))+x^3 (4+\log (4)) (1+\log (5))+x (8+\log (16))+2 (2+\log (2)) (10+\log (2) \log (5)+\log (25))\right ) \log (x)-x \left (-((4+\log (4)) \log (5))+60 x^4 (1+\log (5))^2+6 x^5 (1+\log (5))^2+6 x^3 \left (27+52 \log (5)+25 \log ^2(5)\right )+x^2 (1+\log (5)) (120+\log (5) (6+\log (8)))+20 x (1+\log (5)) (15+\log (2) \log (5)+\log (25))\right ) \log ^2(x)-\log (5) \left (8+x^2 (4+\log (4)) (1+\log (5))+\log (16)\right ) \log ^3(x)+x^2 (1+\log (5)) \left (60+12 x+\log (4) \log (5)+30 x^2 (1+\log (5))+6 x^3 (1+\log (5))+\log (625)\right ) \log ^4(x)-2 x^2 (1+\log (5)) \left (2+x^2 (1+\log (5))\right ) \log ^6(x)\right )}{x \left (5+x-\log ^2(x)\right )^3} \, dx \\ & = 2 \int \frac {x \left (30 x^5 (1+\log (5))^2+2 x^6 (1+\log (5))^2+x^3 (1+\log (5)) (310+(252+\log (2)) \log (5))+2 x^4 \left (77+152 \log (5)+75 \log ^2(5)\right )+2 x \left (250+(298+24 \log (2)) \log (5)+25 (2+\log (2)) \log ^2(5)\right )-(2+\log (2)) \log (5) (10+\log (2) \log (5)+\log (25))+15 x^2 (1+\log (5)) (20+\log (2) \log (5)+\log (25))\right )+\log (5) \left (10 x^2 (2+\log (2)) (1+\log (5))+x^3 (4+\log (4)) (1+\log (5))+x (8+\log (16))+2 (2+\log (2)) (10+\log (2) \log (5)+\log (25))\right ) \log (x)-x \left (-((4+\log (4)) \log (5))+60 x^4 (1+\log (5))^2+6 x^5 (1+\log (5))^2+6 x^3 \left (27+52 \log (5)+25 \log ^2(5)\right )+x^2 (1+\log (5)) (120+\log (5) (6+\log (8)))+20 x (1+\log (5)) (15+\log (2) \log (5)+\log (25))\right ) \log ^2(x)-\log (5) \left (8+x^2 (4+\log (4)) (1+\log (5))+\log (16)\right ) \log ^3(x)+x^2 (1+\log (5)) \left (60+12 x+\log (4) \log (5)+30 x^2 (1+\log (5))+6 x^3 (1+\log (5))+\log (625)\right ) \log ^4(x)-2 x^2 (1+\log (5)) \left (2+x^2 (1+\log (5))\right ) \log ^6(x)}{x \left (5+x-\log ^2(x)\right )^3} \, dx \\ & = 2 \int \left (2 x (1+\log (5)) \left (2+x^2 (1+\log (5))\right )+\frac {-x \log ^2(2) \log ^2(5) \left (1+\frac {\log (4) \log ^2(5)+\log (2) \log (5) \log (25)+\log ^2(25)}{\log ^2(2) \log ^2(5)}\right )+100 x^2 \log ^2(5) \left (1-\frac {\log (625) \log (298023223876953125)}{100 \log ^2(5)}\right )+\log ^2(5) \log (16) \left (1+\frac {\log ^2(2) \log (25)+\log (4) \log (25)+\log (390625)}{\log (5) \log (16)}\right ) \log (x)}{x \left (5+x-\log ^2(x)\right )^3}+\frac {-x \log (4) \log (5) \left (1+\frac {\log (625)}{\log (4) \log (5)}\right )-x^3 \log (2) \log (5) \left (1+\frac {(-6+\log (2)) \log ^2(5)+\log (25) (1+\log (625))}{\log (2) \log (5)}\right )-x^2 \log (625) \log (9765625) \left (1-\frac {\log (25) \log (95367431640625)}{\log (625) \log (9765625)}\right )+x^2 \log (4) \log (5) \left (1+\frac {(4+\log (4)) \log ^2(5)+\log (625)}{\log (4) \log (5)}\right ) \log (x)+\log (5) \log (16) \left (1+\frac {\log (390625)}{\log (5) \log (16)}\right ) \log (x)}{x \left (5+x-\log ^2(x)\right )^2}+\frac {x (1+\log (5)) (\log (4) \log (5)+\log (625))}{5+x-\log ^2(x)}\right ) \, dx \\ & = 2 \int \frac {-x \log ^2(2) \log ^2(5) \left (1+\frac {\log (4) \log ^2(5)+\log (2) \log (5) \log (25)+\log ^2(25)}{\log ^2(2) \log ^2(5)}\right )+100 x^2 \log ^2(5) \left (1-\frac {\log (625) \log (298023223876953125)}{100 \log ^2(5)}\right )+\log ^2(5) \log (16) \left (1+\frac {\log ^2(2) \log (25)+\log (4) \log (25)+\log (390625)}{\log (5) \log (16)}\right ) \log (x)}{x \left (5+x-\log ^2(x)\right )^3} \, dx+2 \int \frac {-x \log (4) \log (5) \left (1+\frac {\log (625)}{\log (4) \log (5)}\right )-x^3 \log (2) \log (5) \left (1+\frac {(-6+\log (2)) \log ^2(5)+\log (25) (1+\log (625))}{\log (2) \log (5)}\right )-x^2 \log (625) \log (9765625) \left (1-\frac {\log (25) \log (95367431640625)}{\log (625) \log (9765625)}\right )+x^2 \log (4) \log (5) \left (1+\frac {(4+\log (4)) \log ^2(5)+\log (625)}{\log (4) \log (5)}\right ) \log (x)+\log (5) \log (16) \left (1+\frac {\log (390625)}{\log (5) \log (16)}\right ) \log (x)}{x \left (5+x-\log ^2(x)\right )^2} \, dx+(4 (1+\log (5))) \int x \left (2+x^2 (1+\log (5))\right ) \, dx+(2 (4+\log (4)) \log (5) (1+\log (5))) \int \frac {x}{5+x-\log ^2(x)} \, dx \\ & = 2 \int \frac {-x \left (\log (4) \log (5)+\log (625)+x^2 \left (-6 \log ^2(5)+\log (2) \log (5) (1+\log (5))+\log (25) (1+\log (625))\right )+x (\log (625) \log (9765625)-\log (25) \log (95367431640625))\right )+\left (\log (5) \log (16)+x^2 \left (4 \log ^2(5)+\log (4) \log (5) (1+\log (5))+\log (625)\right )+\log (390625)\right ) \log (x)}{x \left (5+x-\log ^2(x)\right )^2} \, dx+2 \int \left (\frac {-\log ^2(2) \log ^2(5)-\log (4) \log ^2(5)-\log (2) \log (5) \log (25)-\log ^2(25)}{\left (5+x-\log ^2(x)\right )^3}+\frac {x \left (100 \log ^2(5)-\log (625) \log (298023223876953125)\right )}{\left (5+x-\log ^2(x)\right )^3}+\frac {\log (5) \left (\log (5) \log (16)+\log ^2(2) \log (25)+\log (4) \log (25)+\log (390625)\right ) \log (x)}{x \left (5+x-\log ^2(x)\right )^3}\right ) \, dx+(4 (1+\log (5))) \int \left (2 x+x^3 (1+\log (5))\right ) \, dx+(2 (4+\log (4)) \log (5) (1+\log (5))) \int \frac {x}{5+x-\log ^2(x)} \, dx \\ & = 4 x^2 (1+\log (5))+x^4 (1+\log (5))^2+2 \int \left (-\frac {\log (4) \log (5) \left (1+\frac {\log (625)}{\log (4) \log (5)}\right )}{\left (5+x-\log ^2(x)\right )^2}+\frac {x^2 \left (6 \log ^2(5)-\log (2) \log (5) (1+\log (5))-\log (25) (1+\log (625))\right )}{\left (5+x-\log ^2(x)\right )^2}-\frac {x (\log (625) \log (9765625)-\log (25) \log (95367431640625))}{\left (5+x-\log ^2(x)\right )^2}+\frac {x \left (4 \log ^2(5)+\log (4) \log (5) (1+\log (5))+\log (625)\right ) \log (x)}{\left (5+x-\log ^2(x)\right )^2}+\frac {\log (5) \log (16) \left (1+\frac {\log (390625)}{\log (5) \log (16)}\right ) \log (x)}{x \left (5+x-\log ^2(x)\right )^2}\right ) \, dx+(2 (4+\log (4)) \log (5) (1+\log (5))) \int \frac {x}{5+x-\log ^2(x)} \, dx+\left (4 \log ^2(5) \left (4+\log ^2(2)+\log (16)\right )\right ) \int \frac {\log (x)}{x \left (5+x-\log ^2(x)\right )^3} \, dx-\left (2 \left (\log ^2(2) \log ^2(5)+\log (4) \log ^2(5)+\log (2) \log (5) \log (25)+\log ^2(25)\right )\right ) \int \frac {1}{\left (5+x-\log ^2(x)\right )^3} \, dx+\left (2 \left (100 \log ^2(5)-\log (625) \log (298023223876953125)\right )\right ) \int \frac {x}{\left (5+x-\log ^2(x)\right )^3} \, dx \\ & = 4 x^2 (1+\log (5))+x^4 (1+\log (5))^2+(2 (4+\log (4)) \log (5) (1+\log (5))) \int \frac {x}{5+x-\log ^2(x)} \, dx+\left (4 \log ^2(5) \left (4+\log ^2(2)+\log (16)\right )\right ) \int \frac {\log (x)}{x \left (5+x-\log ^2(x)\right )^3} \, dx-\left (2 \left (\log ^2(2) \log ^2(5)+\log (4) \log ^2(5)+\log (2) \log (5) \log (25)+\log ^2(25)\right )\right ) \int \frac {1}{\left (5+x-\log ^2(x)\right )^3} \, dx+\left (2 \left (4 \log ^2(5)+\log (4) \log (5) (1+\log (5))+\log (625)\right )\right ) \int \frac {x \log (x)}{\left (5+x-\log ^2(x)\right )^2} \, dx-\left (2 \log (4) \log (5) \left (1+\frac {\log (625)}{\log (4) \log (5)}\right )\right ) \int \frac {1}{\left (5+x-\log ^2(x)\right )^2} \, dx+\left (2 \left (6 \log ^2(5)-\log (2) \log (5) (1+\log (5))-\log (25) (1+\log (625))\right )\right ) \int \frac {x^2}{\left (5+x-\log ^2(x)\right )^2} \, dx+\left (2 \log (5) \log (16) \left (1+\frac {\log (390625)}{\log (5) \log (16)}\right )\right ) \int \frac {\log (x)}{x \left (5+x-\log ^2(x)\right )^2} \, dx+\left (2 \left (100 \log ^2(5)-\log (625) \log (298023223876953125)\right )\right ) \int \frac {x}{\left (5+x-\log ^2(x)\right )^3} \, dx \\ \end{align*}
\[ \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 \]
[In]
[Out]
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 | \(\frac {\ln \left (5\right )^{2} \ln \left (x \right )^{4} x^{4}-2 \ln \left (5\right )^{2} \ln \left (x \right )^{2} x^{5}+2 \ln \left (5\right ) \ln \left (x \right )^{4} x^{4}-4 \ln \left (5\right ) \ln \left (x \right )^{2} x^{5}+4 \ln \left (5\right ) \ln \left (x \right )^{4} x^{2}-20 \ln \left (5\right ) \ln \left (x \right )^{2} x^{4}-10 \ln \left (5\right )^{2} x^{4} \ln \left (x \right )^{2}+2 \ln \left (5\right )^{2} \ln \left (2\right ) x^{3}-8 \ln \left (5\right ) \ln \left (x \right )^{2} x^{3}-44 \ln \left (5\right ) \ln \left (x \right )^{2} x^{2}-4 \ln \left (5\right ) \ln \left (x \right )^{2} \ln \left (2\right )-4 x^{2} \ln \left (5\right )^{2} \ln \left (x \right )^{2}+x^{6} \ln \left (5\right )^{2}+10 x^{5} \ln \left (5\right )^{2}+4 x^{3} \ln \left (5\right )^{2}+4 x \ln \left (2\right ) \ln \left (5\right )-10 x^{4} \ln \left (x \right )^{2}+20 x^{5} \ln \left (5\right )+2 x^{6} \ln \left (5\right )+20 \ln \left (2\right ) \ln \left (5\right )+8 x \ln \left (5\right )+20 x^{2} \ln \left (5\right )^{2}+44 x^{3} \ln \left (5\right )+\ln \left (2\right )^{2} \ln \left (5\right )^{2}-2 \ln \left (5\right )^{2} \ln \left (x \right )^{2} \ln \left (2\right ) x^{2}+25 x^{4} \ln \left (5\right )^{2}+x^{4} \ln \left (x \right )^{4}-2 x^{2} \ln \left (5\right ) \ln \left (x \right )^{2} \ln \left (2\right )-2 x^{5} \ln \left (x \right )^{2}+54 x^{4} \ln \left (5\right )-8 x^{3} \ln \left (x \right )^{2}+120 x^{2} \ln \left (5\right )-40 x^{2} \ln \left (x \right )^{2}+4 x^{2} \ln \left (x \right )^{4}+40 \ln \left (5\right )+4 \ln \left (5\right )^{2}+10 x^{2} \ln \left (2\right ) \ln \left (5\right )+x^{6}+10 x^{5}+29 x^{4}+40 x^{3}+100 x^{2}-8 \ln \left (5\right ) \ln \left (x \right )^{2}+2 \ln \left (5\right ) \ln \left (2\right ) x^{3}+4 \ln \left (5\right )^{2} \ln \left (2\right )+10 \ln \left (5\right )^{2} \ln \left (2\right ) x^{2}}{\ln \left (x \right )^{4}-2 x \ln \left (x \right )^{2}-10 \ln \left (x \right )^{2}+x^{2}+10 x +25}\) | \(433\) |
[In]
[Out]
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} \]
[In]
[Out]
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} \]
[In]
[Out]
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} \]
[In]
[Out]
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} \]
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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 \]
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