3.53.64 \(\int \frac {-1000 x^2-600 x^3-620 x^4-308 x^5-60 x^6-4 x^7+(40 x-1192 x^2-660 x^3-1124 x^4-608 x^5-120 x^6-8 x^7+(20 x-96 x^2-30 x^3-2 x^4) \log (2)) \log (5)+(8 x-200 x^2-60 x^3-504 x^4-300 x^5-60 x^6-4 x^7+(8 x-100 x^2-30 x^3-2 x^4) \log (2)+2 x \log ^2(2)) \log ^2(5)+((-80-16 x-40 x^2-8 x^3+(-40-8 x-20 x^2-4 x^3) \log (2)) \log (5)+(-16-40 x^2-8 x^3+(-16-20 x^2-4 x^3) \log (2)-4 \log ^2(2)) \log ^2(5)) \log (x)+(600 x^2+240 x^3+324 x^4+120 x^5+12 x^6+(-8 x+680 x^2+252 x^3+624 x^4+240 x^5+24 x^6+(-4 x+40 x^2+6 x^3) \log (2)) \log (5)+(80 x^2+12 x^3+300 x^4+120 x^5+12 x^6+(40 x^2+6 x^3) \log (2)) \log ^2(5)) \log ^2(x)+((16+8 x^2+(8+4 x^2) \log (2)) \log (5)+(8 x^2+4 x^2 \log (2)) \log ^2(5)) \log ^3(x)+(-120 x^2-24 x^3-60 x^4-12 x^5+(-128 x^2-24 x^3-120 x^4-24 x^5-4 x^2 \log (2)) \log (5)+(-8 x^2-60 x^4-12 x^5-4 x^2 \log (2)) \log ^2(5)) \log ^4(x)+(8 x^2+4 x^4+(8 x^2+8 x^4) \log (5)+4 x^4 \log ^2(5)) \log ^6(x)}{-125 x-75 x^2-15 x^3-x^4+(75 x+30 x^2+3 x^3) \log ^2(x)+(-15 x-3 x^2) \log ^4(x)+x \log ^6(x)} \, dx\)

Optimal. Leaf size=30 \[ \left (2+x^2+\log (5) \left (x^2+\frac {2+\log (2)}{5+x-\log ^2(x)}\right )\right )^2 \]

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Rubi [F]  time = 10.93, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \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 \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-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 - 30
0*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)*Lo
g[x]^2 + (-15*x - 3*x^2)*Log[x]^4 + x*Log[x]^6),x]

[Out]

4*x^2*(1 + Log[5]) + x^4*(1 + Log[5])^2 - 2*(Log[2]^2*Log[5]^2 + Log[4]*Log[5]^2 + Log[2]*Log[5]*Log[25] + Log
[25]^2)*Defer[Int][(5 + x - Log[x]^2)^(-3), x] + 2*(100*Log[5]^2 - Log[625]*Log[298023223876953125])*Defer[Int
][x/(5 + x - Log[x]^2)^3, x] + 4*Log[5]^2*(4 + Log[2]^2 + Log[16])*Defer[Int][Log[x]/(x*(5 + x - Log[x]^2)^3),
x] - 2*(4 + Log[4])*Log[5]*Defer[Int][(5 + x - Log[x]^2)^(-2), x] + 2*(6*Log[5]^2 - Log[2]*Log[5]*(1 + Log[5]
) - Log[25]*(1 + Log[625]))*Defer[Int][x^2/(5 + x - Log[x]^2)^2, x] + 2*Log[5]*(8 + Log[16])*Defer[Int][Log[x]
/(x*(5 + x - Log[x]^2)^2), x] + 2*(4*Log[5]^2 + Log[4]*Log[5]*(1 + Log[5]) + Log[625])*Defer[Int][(x*Log[x])/(
5 + x - Log[x]^2)^2, x] + 2*(4 + Log[4])*Log[5]*(1 + Log[5])*Defer[Int][x/(5 + x - Log[x]^2), x]

Rubi steps

\begin {gather*} \begin {aligned} \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 {aligned} \end {gather*}

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Mathematica [B]  time = 0.88, size = 495, normalized size = 16.50 \begin {gather*} 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 )} \end {gather*}

Antiderivative was successfully verified.

[In]

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]

[Out]

4*x^2*(1 + Log[5]) + x^4*(1 + Log[5])^2 + (x^2*(Log[2]^2*Log[5]^2 + 5*Log[4]*Log[5]*(9 + 10*Log[5]) + Log[25]^
2 + Log[2]*Log[5]*(-90 - 98*Log[5] + Log[25])) + x^4*(1 + Log[5])*(Log[8]*Log[3125] - Log[5]*Log[32768]) - 10*
Log[5]*(Log[5]*Log[16] + Log[2]^2*Log[25] + Log[4]*Log[25] + Log[390625]) - 2*x*Log[5]*(Log[5]*Log[16] + Log[2
]^2*Log[25] + Log[4]*Log[25] + Log[390625]) + x^3*(-100*Log[5]^2 + Log[625]*Log[298023223876953125]))/((-20 -
4*x + x^2)*(5 + x - Log[x]^2)^2) + (-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*L
og[16] + 4000*Log[25] + 300*Log[5]*(16 + Log[256]) - 2000*Log[625]) + x^6*(Log[5]^2*(-524 + 390*Log[2] - 39*Lo
g[4] - 112*Log[8]) + 360*Log[25] + Log[5]*(-516 + 392*Log[2] - 38*Log[4] - 112*Log[8] + 360*Log[25] - 61*Log[6
25]) - 61*Log[625]) + x^8*(1 + Log[5])*(Log[4]*Log[5] + Log[625]) + 4*x^5*(2*Log[5]^2*(-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])) + x^4*(-20*Log[5]^2*(-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*Lo
g[625])) - 2*x^7*(1 + Log[5])*(15*Log[25] + 8*Log[625] + Log[5]*(-38 + Log[4096])))/((-20 - 4*x + x^2)^3*(5 +
x - Log[x]^2))

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fricas [B]  time = 0.54, size = 262, normalized size = 8.73 \begin {gather*} \frac {x^{6} + 10 \, x^{5} + {\left (x^{4} \log \relax (5)^{2} + x^{4} + 4 \, x^{2} + 2 \, {\left (x^{4} + 2 \, x^{2}\right )} \log \relax (5)\right )} \log \relax (x)^{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 \relax (2) + \log \relax (2)^{2} + 4\right )} \log \relax (5)^{2} - 2 \, {\left (x^{5} + 5 \, x^{4} + 4 \, x^{3} + {\left (x^{5} + 5 \, x^{4} + x^{2} \log \relax (2) + 2 \, x^{2}\right )} \log \relax (5)^{2} + 20 \, x^{2} + {\left (2 \, x^{5} + 10 \, x^{4} + 4 \, x^{3} + 22 \, x^{2} + {\left (x^{2} + 2\right )} \log \relax (2) + 4\right )} \log \relax (5)\right )} \log \relax (x)^{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 \relax (2) + 4 \, x + 20\right )} \log \relax (5)}{\log \relax (x)^{4} - 2 \, {\left (x + 5\right )} \log \relax (x)^{2} + x^{2} + 10 \, x + 25} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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)*lo
g(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^3-96*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)*log(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^2-15*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, algorithm="fricas")

[Out]

(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)

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giac [B]  time = 0.49, size = 242, normalized size = 8.07 \begin {gather*} {\left (\log \relax (5)^{2} + 2 \, \log \relax (5) + 1\right )} x^{4} + 4 \, x^{2} {\left (\log \relax (5) + 1\right )} - \frac {2 \, x^{2} \log \relax (5)^{2} \log \relax (2) \log \relax (x)^{2} - 2 \, x^{3} \log \relax (5)^{2} \log \relax (2) + 4 \, x^{2} \log \relax (5)^{2} \log \relax (x)^{2} + 2 \, x^{2} \log \relax (5) \log \relax (2) \log \relax (x)^{2} - 4 \, x^{3} \log \relax (5)^{2} - 2 \, x^{3} \log \relax (5) \log \relax (2) - 10 \, x^{2} \log \relax (5)^{2} \log \relax (2) + 4 \, x^{2} \log \relax (5) \log \relax (x)^{2} - 4 \, x^{3} \log \relax (5) - 20 \, x^{2} \log \relax (5)^{2} - 10 \, x^{2} \log \relax (5) \log \relax (2) - \log \relax (5)^{2} \log \relax (2)^{2} + 4 \, \log \relax (5) \log \relax (2) \log \relax (x)^{2} - 20 \, x^{2} \log \relax (5) - 4 \, x \log \relax (5) \log \relax (2) - 4 \, \log \relax (5)^{2} \log \relax (2) + 8 \, \log \relax (5) \log \relax (x)^{2} - 8 \, x \log \relax (5) - 4 \, \log \relax (5)^{2} - 20 \, \log \relax (5) \log \relax (2) - 40 \, \log \relax (5)}{\log \relax (x)^{4} - 2 \, x \log \relax (x)^{2} + x^{2} - 10 \, \log \relax (x)^{2} + 10 \, x + 25} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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)*lo
g(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^3-96*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)*log(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^2-15*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, algorithm="giac")

[Out]

(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*l
og(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)

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maple [B]  time = 0.31, size = 191, normalized size = 6.37

method	result	size
risch	\(x^{4} \ln \relax (5)^{2}+2 x^{4} \ln \relax (5)+x^{4}+4 x^{2} \ln \relax (5)+4 x^{2}+\frac {\ln \relax (5) \left (-2 \ln \relax (x )^{2} \ln \relax (5) \ln \relax (2) x^{2}+2 \ln \relax (5) \ln \relax (2) x^{3}-4 \ln \relax (x )^{2} \ln \relax (5) x^{2}-2 x^{2} \ln \relax (2) \ln \relax (x )^{2}+10 x^{2} \ln \relax (2) \ln \relax (5)+4 x^{3} \ln \relax (5)+2 x^{3} \ln \relax (2)-4 x^{2} \ln \relax (x )^{2}+\ln \relax (2)^{2} \ln \relax (5)+20 x^{2} \ln \relax (5)+10 x^{2} \ln \relax (2)-4 \ln \relax (2) \ln \relax (x )^{2}+4 x^{3}+4 \ln \relax (2) \ln \relax (5)+4 x \ln \relax (2)+20 x^{2}-8 \ln \relax (x )^{2}+4 \ln \relax (5)+20 \ln \relax (2)+8 x +40\right )}{\left (5+x -\ln \relax (x )^{2}\right )^{2}}\)	\(191\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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+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+7
5*x)*ln(x)^2-x^4-15*x^3-75*x^2-125*x),x,method=_RETURNVERBOSE)

[Out]

x^4*ln(5)^2+2*x^4*ln(5)+x^4+4*x^2*ln(5)+4*x^2+ln(5)*(-2*ln(x)^2*ln(5)*ln(2)*x^2+2*ln(5)*ln(2)*x^3-4*ln(x)^2*ln
(5)*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

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maxima [B]  time = 0.57, size = 279, normalized size = 9.30 \begin {gather*} \frac {{\left (\log \relax (5)^{2} + 2 \, \log \relax (5) + 1\right )} x^{6} + 10 \, {\left (\log \relax (5)^{2} + 2 \, \log \relax (5) + 1\right )} x^{5} + {\left (25 \, \log \relax (5)^{2} + 54 \, \log \relax (5) + 29\right )} x^{4} + {\left ({\left (\log \relax (5)^{2} + 2 \, \log \relax (5) + 1\right )} x^{4} + 4 \, x^{2} {\left (\log \relax (5) + 1\right )}\right )} \log \relax (x)^{4} + 2 \, {\left (2 \, \log \relax (5)^{2} + {\left (\log \relax (5)^{2} + \log \relax (5)\right )} \log \relax (2) + 22 \, \log \relax (5) + 20\right )} x^{3} + \log \relax (5)^{2} \log \relax (2)^{2} + 10 \, {\left (2 \, \log \relax (5)^{2} + {\left (\log \relax (5)^{2} + \log \relax (5)\right )} \log \relax (2) + 12 \, \log \relax (5) + 10\right )} x^{2} - 2 \, {\left ({\left (\log \relax (5)^{2} + 2 \, \log \relax (5) + 1\right )} x^{5} + 5 \, {\left (\log \relax (5)^{2} + 2 \, \log \relax (5) + 1\right )} x^{4} + 4 \, x^{3} {\left (\log \relax (5) + 1\right )} + {\left (2 \, \log \relax (5)^{2} + {\left (\log \relax (5)^{2} + \log \relax (5)\right )} \log \relax (2) + 22 \, \log \relax (5) + 20\right )} x^{2} + 2 \, \log \relax (5) \log \relax (2) + 4 \, \log \relax (5)\right )} \log \relax (x)^{2} + 4 \, {\left (\log \relax (5) \log \relax (2) + 2 \, \log \relax (5)\right )} x + 4 \, \log \relax (5)^{2} + 4 \, {\left (\log \relax (5)^{2} + 5 \, \log \relax (5)\right )} \log \relax (2) + 40 \, \log \relax (5)}{\log \relax (x)^{4} - 2 \, {\left (x + 5\right )} \log \relax (x)^{2} + x^{2} + 10 \, x + 25} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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)*lo
g(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^3-96*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)*log(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^2-15*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, algorithm="maxima")

[Out]

((log(5)^2 + 2*log(5) + 1)*x^6 + 10*(log(5)^2 + 2*log(5) + 1)*x^5 + (25*log(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*((lo
g(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)

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mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int \frac {\ln \relax (x)\,\left ({\ln \relax (5)}^2\,\left (\ln \relax (2)\,\left (4\,x^3+20\,x^2+16\right )+4\,{\ln \relax (2)}^2+40\,x^2+8\,x^3+16\right )+\ln \relax (5)\,\left (16\,x+\ln \relax (2)\,\left (4\,x^3+20\,x^2+8\,x+40\right )+40\,x^2+8\,x^3+80\right )\right )-{\ln \relax (x)}^3\,\left ({\ln \relax (5)}^2\,\left (4\,x^2\,\ln \relax (2)+8\,x^2\right )+\ln \relax (5)\,\left (\ln \relax (2)\,\left (4\,x^2+8\right )+8\,x^2+16\right )\right )-{\ln \relax (x)}^6\,\left (4\,x^4\,{\ln \relax (5)}^2+\ln \relax (5)\,\left (8\,x^4+8\,x^2\right )+8\,x^2+4\,x^4\right )+{\ln \relax (x)}^4\,\left (\ln \relax (5)\,\left (4\,x^2\,\ln \relax (2)+128\,x^2+24\,x^3+120\,x^4+24\,x^5\right )+{\ln \relax (5)}^2\,\left (4\,x^2\,\ln \relax (2)+8\,x^2+60\,x^4+12\,x^5\right )+120\,x^2+24\,x^3+60\,x^4+12\,x^5\right )-{\ln \relax (x)}^2\,\left ({\ln \relax (5)}^2\,\left (\ln \relax (2)\,\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 \relax (5)\,\left (\ln \relax (2)\,\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 \relax (5)\,\left (\ln \relax (2)\,\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 \relax (5)}^2\,\left (\ln \relax (2)\,\left (2\,x^4+30\,x^3+100\,x^2-8\,x\right )-2\,x\,{\ln \relax (2)}^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 \relax (x)}^4\,\left (3\,x^2+15\,x\right )-x\,{\ln \relax (x)}^6-{\ln \relax (x)}^2\,\left (3\,x^3+30\,x^2+75\,x\right )+75\,x^2+15\,x^3+x^4} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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)*(lo
g(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 + 3
00*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 + 24*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)

[Out]

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)*(lo
g(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 + 3
00*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 + 24*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)

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sympy [B]  time = 2.60, size = 260, normalized size = 8.67 \begin {gather*} x^{4} \left (1 + \log {\relax (5 )}^{2} + 2 \log {\relax (5 )}\right ) + x^{2} \left (4 + 4 \log {\relax (5 )}\right ) + \frac {2 x^{3} \log {\relax (2 )} \log {\relax (5 )} + 2 x^{3} \log {\relax (2 )} \log {\relax (5 )}^{2} + 4 x^{3} \log {\relax (5 )} + 4 x^{3} \log {\relax (5 )}^{2} + 10 x^{2} \log {\relax (2 )} \log {\relax (5 )} + 10 x^{2} \log {\relax (2 )} \log {\relax (5 )}^{2} + 20 x^{2} \log {\relax (5 )} + 20 x^{2} \log {\relax (5 )}^{2} + 4 x \log {\relax (2 )} \log {\relax (5 )} + 8 x \log {\relax (5 )} + \left (- 4 x^{2} \log {\relax (5 )}^{2} - 4 x^{2} \log {\relax (5 )} - 2 x^{2} \log {\relax (2 )} \log {\relax (5 )}^{2} - 2 x^{2} \log {\relax (2 )} \log {\relax (5 )} - 8 \log {\relax (5 )} - 4 \log {\relax (2 )} \log {\relax (5 )}\right ) \log {\relax (x )}^{2} + \log {\relax (2 )}^{2} \log {\relax (5 )}^{2} + 4 \log {\relax (2 )} \log {\relax (5 )}^{2} + 4 \log {\relax (5 )}^{2} + 20 \log {\relax (2 )} \log {\relax (5 )} + 40 \log {\relax (5 )}}{x^{2} + 10 x + \left (- 2 x - 10\right ) \log {\relax (x )}^{2} + \log {\relax (x )}^{4} + 25} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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**5-120*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+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+6
80*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)

[Out]

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)*log(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)

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