3.61.66 \(\int \frac {10 x-20 x^2+30 x^3-20 x^4-2 x^5+10 x^6-20 x^7+20 x^8-10 x^9+2 x^{10}+(5 x-16 x^3+52 x^4-60 x^5+28 x^6-4 x^7) \log (3)+(-32 x+48 x^2-18 x^3+2 x^4) \log ^2(3)+(-10+10 x-20 x^2+8 x^4-32 x^5+48 x^6-32 x^7+8 x^8+(32 x^2-72 x^3+48 x^4-8 x^5) \log (3)) \log (x)+(-12 x^3+36 x^4-36 x^5+12 x^6+(-16 x+20 x^2-4 x^3) \log (3)) \log ^2(x)+(8 x^2-16 x^3+8 x^4) \log ^3(x)+(-2 x+2 x^2) \log ^4(x)}{x^5-4 x^6+6 x^7-4 x^8+x^9+(8 x^3-18 x^4+12 x^5-2 x^6) \log (3)+(16 x-8 x^2+x^3) \log ^2(3)+(-4 x^4+12 x^5-12 x^6+4 x^7+(-16 x^2+20 x^3-4 x^4) \log (3)) \log (x)+(6 x^3-12 x^4+6 x^5+(8 x-2 x^2) \log (3)) \log ^2(x)+(-4 x^2+4 x^3) \log ^3(x)+x \log ^4(x)} \, dx\)

Optimal. Leaf size=33 \[ -2 x+x^2+\frac {5}{(4-x) \log (3)+\left (x-x^2-\log (x)\right )^2} \]

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Rubi [F]  time = 5.62, 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 {10 x-20 x^2+30 x^3-20 x^4-2 x^5+10 x^6-20 x^7+20 x^8-10 x^9+2 x^{10}+\left (5 x-16 x^3+52 x^4-60 x^5+28 x^6-4 x^7\right ) \log (3)+\left (-32 x+48 x^2-18 x^3+2 x^4\right ) \log ^2(3)+\left (-10+10 x-20 x^2+8 x^4-32 x^5+48 x^6-32 x^7+8 x^8+\left (32 x^2-72 x^3+48 x^4-8 x^5\right ) \log (3)\right ) \log (x)+\left (-12 x^3+36 x^4-36 x^5+12 x^6+\left (-16 x+20 x^2-4 x^3\right ) \log (3)\right ) \log ^2(x)+\left (8 x^2-16 x^3+8 x^4\right ) \log ^3(x)+\left (-2 x+2 x^2\right ) \log ^4(x)}{x^5-4 x^6+6 x^7-4 x^8+x^9+\left (8 x^3-18 x^4+12 x^5-2 x^6\right ) \log (3)+\left (16 x-8 x^2+x^3\right ) \log ^2(3)+\left (-4 x^4+12 x^5-12 x^6+4 x^7+\left (-16 x^2+20 x^3-4 x^4\right ) \log (3)\right ) \log (x)+\left (6 x^3-12 x^4+6 x^5+\left (8 x-2 x^2\right ) \log (3)\right ) \log ^2(x)+\left (-4 x^2+4 x^3\right ) \log ^3(x)+x \log ^4(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(10*x - 20*x^2 + 30*x^3 - 20*x^4 - 2*x^5 + 10*x^6 - 20*x^7 + 20*x^8 - 10*x^9 + 2*x^10 + (5*x - 16*x^3 + 52
*x^4 - 60*x^5 + 28*x^6 - 4*x^7)*Log[3] + (-32*x + 48*x^2 - 18*x^3 + 2*x^4)*Log[3]^2 + (-10 + 10*x - 20*x^2 + 8
*x^4 - 32*x^5 + 48*x^6 - 32*x^7 + 8*x^8 + (32*x^2 - 72*x^3 + 48*x^4 - 8*x^5)*Log[3])*Log[x] + (-12*x^3 + 36*x^
4 - 36*x^5 + 12*x^6 + (-16*x + 20*x^2 - 4*x^3)*Log[3])*Log[x]^2 + (8*x^2 - 16*x^3 + 8*x^4)*Log[x]^3 + (-2*x +
2*x^2)*Log[x]^4)/(x^5 - 4*x^6 + 6*x^7 - 4*x^8 + x^9 + (8*x^3 - 18*x^4 + 12*x^5 - 2*x^6)*Log[3] + (16*x - 8*x^2
+ x^3)*Log[3]^2 + (-4*x^4 + 12*x^5 - 12*x^6 + 4*x^7 + (-16*x^2 + 20*x^3 - 4*x^4)*Log[3])*Log[x] + (6*x^3 - 12
*x^4 + 6*x^5 + (8*x - 2*x^2)*Log[3])*Log[x]^2 + (-4*x^2 + 4*x^3)*Log[x]^3 + x*Log[x]^4),x]

[Out]

(-1 + x)^2 + (10 - 32*Log[3]^2 + 2*Log[81]^2 + Log[243])*Defer[Int][(x^2 - 2*x^3 + x^4 - x*Log[3] + Log[81] -
2*x*Log[x] + 2*x^2*Log[x] + Log[x]^2)^(-2), x] - (20 - 48*Log[3]^2 + 3*Log[81]^2)*Defer[Int][x/(x^2 - 2*x^3 +
x^4 - x*Log[3] + Log[81] - 2*x*Log[x] + 2*x^2*Log[x] + Log[x]^2)^2, x] + (30 - 16*Log[3]^2 + Log[81]^2)*Defer[
Int][x^2/(x^2 - 2*x^3 + x^4 - x*Log[3] + Log[81] - 2*x*Log[x] + 2*x^2*Log[x] + Log[x]^2)^2, x] - 20*Defer[Int]
[x^3/(x^2 - 2*x^3 + x^4 - x*Log[3] + Log[81] - 2*x*Log[x] + 2*x^2*Log[x] + Log[x]^2)^2, x] + 10*Defer[Int][Log
[x]/(x^2 - 2*x^3 + x^4 - x*Log[3] + Log[81] - 2*x*Log[x] + 2*x^2*Log[x] + Log[x]^2)^2, x] - 10*Defer[Int][Log[
x]/(x*(x^2 - 2*x^3 + x^4 - x*Log[3] + Log[81] - 2*x*Log[x] + 2*x^2*Log[x] + Log[x]^2)^2), x] - 20*Defer[Int][(
x*Log[x])/(x^2 - 2*x^3 + x^4 - x*Log[3] + Log[81] - 2*x*Log[x] + 2*x^2*Log[x] + Log[x]^2)^2, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {x \left (10+20 x^7-10 x^8+2 x^9-32 \log ^2(3)-4 x^6 (5+\log (3))+2 x^5 (5+14 \log (3))-2 x^4 (1+30 \log (3))+2 x^3 \left (-10+26 \log (3)+\log ^2(3)\right )-2 x^2 \left (-15+8 \log (3)+9 \log ^2(3)\right )+4 x \left (-5+12 \log ^2(3)\right )+\log (243)\right )+2 \left (-5+5 x+24 x^6-16 x^7+4 x^8-36 x^3 \log (3)-4 x^5 (4+\log (3))+2 x^2 (-5+8 \log (3))+4 x^4 (1+\log (729))\right ) \log (x)+4 (-1+x) x \left (3 x^2-6 x^3+3 x^4-x \log (3)+\log (81)\right ) \log ^2(x)+8 (-1+x)^2 x^2 \log ^3(x)+2 (-1+x) x \log ^4(x)}{x \left (x^2-2 x^3+x^4-x \log (3)+\log (81)+2 (-1+x) x \log (x)+\log ^2(x)\right )^2} \, dx\\ &=\int \left (2 (-1+x)+\frac {-20 x^4+30 x^3 \left (1+\frac {1}{30} \left (-16 \log ^2(3)+\log ^2(81)\right )\right )-20 x^2 \left (1+\frac {3}{20} \left (-16 \log ^2(3)+\log ^2(81)\right )\right )+10 x \left (1+\frac {1}{10} \left (-32 \log ^2(3)+2 \log ^2(81)+\log (243)\right )\right )-10 \log (x)+10 x \log (x)-20 x^2 \log (x)}{x \left (x^2-2 x^3+x^4-x \log (3)+\log (81)-2 x \log (x)+2 x^2 \log (x)+\log ^2(x)\right )^2}\right ) \, dx\\ &=(-1+x)^2+\int \frac {-20 x^4+30 x^3 \left (1+\frac {1}{30} \left (-16 \log ^2(3)+\log ^2(81)\right )\right )-20 x^2 \left (1+\frac {3}{20} \left (-16 \log ^2(3)+\log ^2(81)\right )\right )+10 x \left (1+\frac {1}{10} \left (-32 \log ^2(3)+2 \log ^2(81)+\log (243)\right )\right )-10 \log (x)+10 x \log (x)-20 x^2 \log (x)}{x \left (x^2-2 x^3+x^4-x \log (3)+\log (81)-2 x \log (x)+2 x^2 \log (x)+\log ^2(x)\right )^2} \, dx\\ &=(-1+x)^2+\int \left (-\frac {20 x^3}{\left (x^2-2 x^3+x^4-x \log (3)+\log (81)-2 x \log (x)+2 x^2 \log (x)+\log ^2(x)\right )^2}+\frac {x \left (-20+48 \log ^2(3)-3 \log ^2(81)\right )}{\left (x^2-2 x^3+x^4-x \log (3)+\log (81)-2 x \log (x)+2 x^2 \log (x)+\log ^2(x)\right )^2}-\frac {x^2 \left (-30+16 \log ^2(3)-\log ^2(81)\right )}{\left (x^2-2 x^3+x^4-x \log (3)+\log (81)-2 x \log (x)+2 x^2 \log (x)+\log ^2(x)\right )^2}+\frac {10-32 \log ^2(3)+2 \log ^2(81)+\log (243)}{\left (x^2-2 x^3+x^4-x \log (3)+\log (81)-2 x \log (x)+2 x^2 \log (x)+\log ^2(x)\right )^2}+\frac {10 \log (x)}{\left (x^2-2 x^3+x^4-x \log (3)+\log (81)-2 x \log (x)+2 x^2 \log (x)+\log ^2(x)\right )^2}-\frac {10 \log (x)}{x \left (x^2-2 x^3+x^4-x \log (3)+\log (81)-2 x \log (x)+2 x^2 \log (x)+\log ^2(x)\right )^2}-\frac {20 x \log (x)}{\left (x^2-2 x^3+x^4-x \log (3)+\log (81)-2 x \log (x)+2 x^2 \log (x)+\log ^2(x)\right )^2}\right ) \, dx\\ &=(-1+x)^2+10 \int \frac {\log (x)}{\left (x^2-2 x^3+x^4-x \log (3)+\log (81)-2 x \log (x)+2 x^2 \log (x)+\log ^2(x)\right )^2} \, dx-10 \int \frac {\log (x)}{x \left (x^2-2 x^3+x^4-x \log (3)+\log (81)-2 x \log (x)+2 x^2 \log (x)+\log ^2(x)\right )^2} \, dx-20 \int \frac {x^3}{\left (x^2-2 x^3+x^4-x \log (3)+\log (81)-2 x \log (x)+2 x^2 \log (x)+\log ^2(x)\right )^2} \, dx-20 \int \frac {x \log (x)}{\left (x^2-2 x^3+x^4-x \log (3)+\log (81)-2 x \log (x)+2 x^2 \log (x)+\log ^2(x)\right )^2} \, dx+\left (-20+48 \log ^2(3)-3 \log ^2(81)\right ) \int \frac {x}{\left (x^2-2 x^3+x^4-x \log (3)+\log (81)-2 x \log (x)+2 x^2 \log (x)+\log ^2(x)\right )^2} \, dx+\left (30-16 \log ^2(3)+\log ^2(81)\right ) \int \frac {x^2}{\left (x^2-2 x^3+x^4-x \log (3)+\log (81)-2 x \log (x)+2 x^2 \log (x)+\log ^2(x)\right )^2} \, dx+\left (10-32 \log ^2(3)+2 \log ^2(81)+\log (243)\right ) \int \frac {1}{\left (x^2-2 x^3+x^4-x \log (3)+\log (81)-2 x \log (x)+2 x^2 \log (x)+\log ^2(x)\right )^2} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [B]  time = 0.73, size = 570, normalized size = 17.27 \begin {gather*} \frac {16 x^{11} \log (3)-20 \log (81)+x^3 \left (-48 \log ^3(3)+88 \log (81)+(84+\log (9)) \log ^2(81)+6 \log ^2(3) (28+\log (81))-24 \log (3) (-5+6 \log (81))-4 \log (243)\right )+4 x \left (10 \log (81)+2 \log ^2(81)+\log (243)\right )-x^8 \left (136 \log (3)+17 \log ^2(3)+300 \log (81)-80 \log (729)\right )+4 x^9 (89 \log (3)+38 \log (81)-20 \log (729))+4 x^7 \left (41 \log ^2(3)+\log (3) (-30+\log (81))+86 \log (81)-12 \log (729)\right )+x^4 \left (14 \log ^3(3)-112 \log ^2(81)-\log ^2(3) (228+5 \log (81))+2 \log (3) (-43+50 \log (81))+6 \log (243)+4 \log (81) (-31+4 \log (729))\right )+x^5 \left (258 \log ^2(3)+\log ^3(3)+108 \log ^2(81)-4 \log (243)+4 \log (81) (34-4 \log (729))-4 \log (3) (6+17 \log (81)+4 \log (729))\right )+x^6 \left (-73 \log ^2(3)-8 \left (5 \log ^2(81)+\log (81) (33-4 \log (729))-2 \log (729)\right )-4 \log (3) (53 \log (81)-4 (12+\log (729)))\right )-16 x^{10} \log (19683)+x^2 \left (-64 \log ^2(3)+32 \log ^3(3)-100 \log (81)-(32+\log (9)) \log ^2(81)+\log (3) (-50+48 \log (81)-\log (243))+\log (59049)\right )+2 x^2 \left (2-3 x+x^2\right ) \left (16 x^5 \log (3)-4 \log (81)+9 x \log (81)-x^2 \left (8 \log (3)+\log ^2(3)+20 \log (81)\right )-16 x^4 \log (243)+4 x^3 (4 \log (81)+\log (243))\right ) \log (x)+(-2+x) x \left (16 x^5 \log (3)-4 \log (81)+9 x \log (81)-x^2 \left (8 \log (3)+\log ^2(3)+20 \log (81)\right )-16 x^4 \log (243)+4 x^3 (4 \log (81)+\log (243))\right ) \log ^2(x)}{\left (16 x^5 \log (3)-4 \log (81)+9 x \log (81)-x^2 \left (8 \log (3)+\log ^2(3)+20 \log (81)\right )-16 x^4 \log (243)+4 x^3 (4 \log (81)+\log (243))\right ) \left (x^2-2 x^3+x^4-x \log (3)+\log (81)+2 (-1+x) x \log (x)+\log ^2(x)\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(10*x - 20*x^2 + 30*x^3 - 20*x^4 - 2*x^5 + 10*x^6 - 20*x^7 + 20*x^8 - 10*x^9 + 2*x^10 + (5*x - 16*x^
3 + 52*x^4 - 60*x^5 + 28*x^6 - 4*x^7)*Log[3] + (-32*x + 48*x^2 - 18*x^3 + 2*x^4)*Log[3]^2 + (-10 + 10*x - 20*x
^2 + 8*x^4 - 32*x^5 + 48*x^6 - 32*x^7 + 8*x^8 + (32*x^2 - 72*x^3 + 48*x^4 - 8*x^5)*Log[3])*Log[x] + (-12*x^3 +
36*x^4 - 36*x^5 + 12*x^6 + (-16*x + 20*x^2 - 4*x^3)*Log[3])*Log[x]^2 + (8*x^2 - 16*x^3 + 8*x^4)*Log[x]^3 + (-
2*x + 2*x^2)*Log[x]^4)/(x^5 - 4*x^6 + 6*x^7 - 4*x^8 + x^9 + (8*x^3 - 18*x^4 + 12*x^5 - 2*x^6)*Log[3] + (16*x -
8*x^2 + x^3)*Log[3]^2 + (-4*x^4 + 12*x^5 - 12*x^6 + 4*x^7 + (-16*x^2 + 20*x^3 - 4*x^4)*Log[3])*Log[x] + (6*x^
3 - 12*x^4 + 6*x^5 + (8*x - 2*x^2)*Log[3])*Log[x]^2 + (-4*x^2 + 4*x^3)*Log[x]^3 + x*Log[x]^4),x]

[Out]

(16*x^11*Log[3] - 20*Log[81] + x^3*(-48*Log[3]^3 + 88*Log[81] + (84 + Log[9])*Log[81]^2 + 6*Log[3]^2*(28 + Log
[81]) - 24*Log[3]*(-5 + 6*Log[81]) - 4*Log[243]) + 4*x*(10*Log[81] + 2*Log[81]^2 + Log[243]) - x^8*(136*Log[3]
+ 17*Log[3]^2 + 300*Log[81] - 80*Log[729]) + 4*x^9*(89*Log[3] + 38*Log[81] - 20*Log[729]) + 4*x^7*(41*Log[3]^
2 + Log[3]*(-30 + Log[81]) + 86*Log[81] - 12*Log[729]) + x^4*(14*Log[3]^3 - 112*Log[81]^2 - Log[3]^2*(228 + 5*
Log[81]) + 2*Log[3]*(-43 + 50*Log[81]) + 6*Log[243] + 4*Log[81]*(-31 + 4*Log[729])) + x^5*(258*Log[3]^2 + Log[
3]^3 + 108*Log[81]^2 - 4*Log[243] + 4*Log[81]*(34 - 4*Log[729]) - 4*Log[3]*(6 + 17*Log[81] + 4*Log[729])) + x^
6*(-73*Log[3]^2 - 8*(5*Log[81]^2 + Log[81]*(33 - 4*Log[729]) - 2*Log[729]) - 4*Log[3]*(53*Log[81] - 4*(12 + Lo
g[729]))) - 16*x^10*Log[19683] + x^2*(-64*Log[3]^2 + 32*Log[3]^3 - 100*Log[81] - (32 + Log[9])*Log[81]^2 + Log
[3]*(-50 + 48*Log[81] - Log[243]) + Log[59049]) + 2*x^2*(2 - 3*x + x^2)*(16*x^5*Log[3] - 4*Log[81] + 9*x*Log[8
1] - x^2*(8*Log[3] + Log[3]^2 + 20*Log[81]) - 16*x^4*Log[243] + 4*x^3*(4*Log[81] + Log[243]))*Log[x] + (-2 + x
)*x*(16*x^5*Log[3] - 4*Log[81] + 9*x*Log[81] - x^2*(8*Log[3] + Log[3]^2 + 20*Log[81]) - 16*x^4*Log[243] + 4*x^
3*(4*Log[81] + Log[243]))*Log[x]^2)/((16*x^5*Log[3] - 4*Log[81] + 9*x*Log[81] - x^2*(8*Log[3] + Log[3]^2 + 20*
Log[81]) - 16*x^4*Log[243] + 4*x^3*(4*Log[81] + Log[243]))*(x^2 - 2*x^3 + x^4 - x*Log[3] + Log[81] + 2*(-1 + x
)*x*Log[x] + Log[x]^2))

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fricas [B]  time = 0.71, size = 103, normalized size = 3.12 \begin {gather*} \frac {x^{6} - 4 \, x^{5} + 5 \, x^{4} - 2 \, x^{3} + {\left (x^{2} - 2 \, x\right )} \log \relax (x)^{2} - {\left (x^{3} - 6 \, x^{2} + 8 \, x\right )} \log \relax (3) + 2 \, {\left (x^{4} - 3 \, x^{3} + 2 \, x^{2}\right )} \log \relax (x) + 5}{x^{4} - 2 \, x^{3} + x^{2} - {\left (x - 4\right )} \log \relax (3) + 2 \, {\left (x^{2} - x\right )} \log \relax (x) + \log \relax (x)^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x^2-2*x)*log(x)^4+(8*x^4-16*x^3+8*x^2)*log(x)^3+((-4*x^3+20*x^2-16*x)*log(3)+12*x^6-36*x^5+36*x^
4-12*x^3)*log(x)^2+((-8*x^5+48*x^4-72*x^3+32*x^2)*log(3)+8*x^8-32*x^7+48*x^6-32*x^5+8*x^4-20*x^2+10*x-10)*log(
x)+(2*x^4-18*x^3+48*x^2-32*x)*log(3)^2+(-4*x^7+28*x^6-60*x^5+52*x^4-16*x^3+5*x)*log(3)+2*x^10-10*x^9+20*x^8-20
*x^7+10*x^6-2*x^5-20*x^4+30*x^3-20*x^2+10*x)/(x*log(x)^4+(4*x^3-4*x^2)*log(x)^3+((-2*x^2+8*x)*log(3)+6*x^5-12*
x^4+6*x^3)*log(x)^2+((-4*x^4+20*x^3-16*x^2)*log(3)+4*x^7-12*x^6+12*x^5-4*x^4)*log(x)+(x^3-8*x^2+16*x)*log(3)^2
+(-2*x^6+12*x^5-18*x^4+8*x^3)*log(3)+x^9-4*x^8+6*x^7-4*x^6+x^5),x, algorithm="fricas")

[Out]

(x^6 - 4*x^5 + 5*x^4 - 2*x^3 + (x^2 - 2*x)*log(x)^2 - (x^3 - 6*x^2 + 8*x)*log(3) + 2*(x^4 - 3*x^3 + 2*x^2)*log
(x) + 5)/(x^4 - 2*x^3 + x^2 - (x - 4)*log(3) + 2*(x^2 - x)*log(x) + log(x)^2)

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giac [A]  time = 1.37, size = 48, normalized size = 1.45 \begin {gather*} x^{2} - 2 \, x + \frac {5}{x^{4} - 2 \, x^{3} + 2 \, x^{2} \log \relax (x) + x^{2} - x \log \relax (3) - 2 \, x \log \relax (x) + \log \relax (x)^{2} + 4 \, \log \relax (3)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x^2-2*x)*log(x)^4+(8*x^4-16*x^3+8*x^2)*log(x)^3+((-4*x^3+20*x^2-16*x)*log(3)+12*x^6-36*x^5+36*x^
4-12*x^3)*log(x)^2+((-8*x^5+48*x^4-72*x^3+32*x^2)*log(3)+8*x^8-32*x^7+48*x^6-32*x^5+8*x^4-20*x^2+10*x-10)*log(
x)+(2*x^4-18*x^3+48*x^2-32*x)*log(3)^2+(-4*x^7+28*x^6-60*x^5+52*x^4-16*x^3+5*x)*log(3)+2*x^10-10*x^9+20*x^8-20
*x^7+10*x^6-2*x^5-20*x^4+30*x^3-20*x^2+10*x)/(x*log(x)^4+(4*x^3-4*x^2)*log(x)^3+((-2*x^2+8*x)*log(3)+6*x^5-12*
x^4+6*x^3)*log(x)^2+((-4*x^4+20*x^3-16*x^2)*log(3)+4*x^7-12*x^6+12*x^5-4*x^4)*log(x)+(x^3-8*x^2+16*x)*log(3)^2
+(-2*x^6+12*x^5-18*x^4+8*x^3)*log(3)+x^9-4*x^8+6*x^7-4*x^6+x^5),x, algorithm="giac")

[Out]

x^2 - 2*x + 5/(x^4 - 2*x^3 + 2*x^2*log(x) + x^2 - x*log(3) - 2*x*log(x) + log(x)^2 + 4*log(3))

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maple [A]  time = 0.07, size = 54, normalized size = 1.64

method	result	size
risch	\(x^{2}-2 x -\frac {5}{-x^{4}+2 x^{3}-2 x^{2} \ln \relax (x )+x \ln \relax (3)-x^{2}+2 x \ln \relax (x )-\ln \relax (x )^{2}-4 \ln \relax (3)}\)	\(54\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((2*x^2-2*x)*ln(x)^4+(8*x^4-16*x^3+8*x^2)*ln(x)^3+((-4*x^3+20*x^2-16*x)*ln(3)+12*x^6-36*x^5+36*x^4-12*x^3)
*ln(x)^2+((-8*x^5+48*x^4-72*x^3+32*x^2)*ln(3)+8*x^8-32*x^7+48*x^6-32*x^5+8*x^4-20*x^2+10*x-10)*ln(x)+(2*x^4-18
*x^3+48*x^2-32*x)*ln(3)^2+(-4*x^7+28*x^6-60*x^5+52*x^4-16*x^3+5*x)*ln(3)+2*x^10-10*x^9+20*x^8-20*x^7+10*x^6-2*
x^5-20*x^4+30*x^3-20*x^2+10*x)/(x*ln(x)^4+(4*x^3-4*x^2)*ln(x)^3+((-2*x^2+8*x)*ln(3)+6*x^5-12*x^4+6*x^3)*ln(x)^
2+((-4*x^4+20*x^3-16*x^2)*ln(3)+4*x^7-12*x^6+12*x^5-4*x^4)*ln(x)+(x^3-8*x^2+16*x)*ln(3)^2+(-2*x^6+12*x^5-18*x^
4+8*x^3)*ln(3)+x^9-4*x^8+6*x^7-4*x^6+x^5),x,method=_RETURNVERBOSE)

[Out]

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

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maxima [B]  time = 0.51, size = 105, normalized size = 3.18 \begin {gather*} \frac {x^{6} - 4 \, x^{5} + 5 \, x^{4} - x^{3} {\left (\log \relax (3) + 2\right )} + 6 \, x^{2} \log \relax (3) + {\left (x^{2} - 2 \, x\right )} \log \relax (x)^{2} - 8 \, x \log \relax (3) + 2 \, {\left (x^{4} - 3 \, x^{3} + 2 \, x^{2}\right )} \log \relax (x) + 5}{x^{4} - 2 \, x^{3} + x^{2} - x \log \relax (3) + 2 \, {\left (x^{2} - x\right )} \log \relax (x) + \log \relax (x)^{2} + 4 \, \log \relax (3)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x^2-2*x)*log(x)^4+(8*x^4-16*x^3+8*x^2)*log(x)^3+((-4*x^3+20*x^2-16*x)*log(3)+12*x^6-36*x^5+36*x^
4-12*x^3)*log(x)^2+((-8*x^5+48*x^4-72*x^3+32*x^2)*log(3)+8*x^8-32*x^7+48*x^6-32*x^5+8*x^4-20*x^2+10*x-10)*log(
x)+(2*x^4-18*x^3+48*x^2-32*x)*log(3)^2+(-4*x^7+28*x^6-60*x^5+52*x^4-16*x^3+5*x)*log(3)+2*x^10-10*x^9+20*x^8-20
*x^7+10*x^6-2*x^5-20*x^4+30*x^3-20*x^2+10*x)/(x*log(x)^4+(4*x^3-4*x^2)*log(x)^3+((-2*x^2+8*x)*log(3)+6*x^5-12*
x^4+6*x^3)*log(x)^2+((-4*x^4+20*x^3-16*x^2)*log(3)+4*x^7-12*x^6+12*x^5-4*x^4)*log(x)+(x^3-8*x^2+16*x)*log(3)^2
+(-2*x^6+12*x^5-18*x^4+8*x^3)*log(3)+x^9-4*x^8+6*x^7-4*x^6+x^5),x, algorithm="maxima")

[Out]

(x^6 - 4*x^5 + 5*x^4 - x^3*(log(3) + 2) + 6*x^2*log(3) + (x^2 - 2*x)*log(x)^2 - 8*x*log(3) + 2*(x^4 - 3*x^3 +
2*x^2)*log(x) + 5)/(x^4 - 2*x^3 + x^2 - x*log(3) + 2*(x^2 - x)*log(x) + log(x)^2 + 4*log(3))

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mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int \frac {10\,x-{\ln \relax (3)}^2\,\left (-2\,x^4+18\,x^3-48\,x^2+32\,x\right )-{\ln \relax (x)}^4\,\left (2\,x-2\,x^2\right )+\ln \relax (3)\,\left (-4\,x^7+28\,x^6-60\,x^5+52\,x^4-16\,x^3+5\,x\right )-{\ln \relax (x)}^2\,\left (\ln \relax (3)\,\left (4\,x^3-20\,x^2+16\,x\right )+12\,x^3-36\,x^4+36\,x^5-12\,x^6\right )+{\ln \relax (x)}^3\,\left (8\,x^4-16\,x^3+8\,x^2\right )+\ln \relax (x)\,\left (10\,x+\ln \relax (3)\,\left (-8\,x^5+48\,x^4-72\,x^3+32\,x^2\right )-20\,x^2+8\,x^4-32\,x^5+48\,x^6-32\,x^7+8\,x^8-10\right )-20\,x^2+30\,x^3-20\,x^4-2\,x^5+10\,x^6-20\,x^7+20\,x^8-10\,x^9+2\,x^{10}}{\ln \relax (3)\,\left (-2\,x^6+12\,x^5-18\,x^4+8\,x^3\right )+x\,{\ln \relax (x)}^4-\ln \relax (x)\,\left (\ln \relax (3)\,\left (4\,x^4-20\,x^3+16\,x^2\right )+4\,x^4-12\,x^5+12\,x^6-4\,x^7\right )-{\ln \relax (x)}^3\,\left (4\,x^2-4\,x^3\right )+{\ln \relax (3)}^2\,\left (x^3-8\,x^2+16\,x\right )+x^5-4\,x^6+6\,x^7-4\,x^8+x^9+{\ln \relax (x)}^2\,\left (\ln \relax (3)\,\left (8\,x-2\,x^2\right )+6\,x^3-12\,x^4+6\,x^5\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((10*x - log(3)^2*(32*x - 48*x^2 + 18*x^3 - 2*x^4) - log(x)^4*(2*x - 2*x^2) + log(3)*(5*x - 16*x^3 + 52*x^4
- 60*x^5 + 28*x^6 - 4*x^7) - log(x)^2*(log(3)*(16*x - 20*x^2 + 4*x^3) + 12*x^3 - 36*x^4 + 36*x^5 - 12*x^6) +
log(x)^3*(8*x^2 - 16*x^3 + 8*x^4) + log(x)*(10*x + log(3)*(32*x^2 - 72*x^3 + 48*x^4 - 8*x^5) - 20*x^2 + 8*x^4
- 32*x^5 + 48*x^6 - 32*x^7 + 8*x^8 - 10) - 20*x^2 + 30*x^3 - 20*x^4 - 2*x^5 + 10*x^6 - 20*x^7 + 20*x^8 - 10*x^
9 + 2*x^10)/(log(3)*(8*x^3 - 18*x^4 + 12*x^5 - 2*x^6) + x*log(x)^4 - log(x)*(log(3)*(16*x^2 - 20*x^3 + 4*x^4)
+ 4*x^4 - 12*x^5 + 12*x^6 - 4*x^7) - log(x)^3*(4*x^2 - 4*x^3) + log(3)^2*(16*x - 8*x^2 + x^3) + x^5 - 4*x^6 +
6*x^7 - 4*x^8 + x^9 + log(x)^2*(log(3)*(8*x - 2*x^2) + 6*x^3 - 12*x^4 + 6*x^5)),x)

[Out]

int((10*x - log(3)^2*(32*x - 48*x^2 + 18*x^3 - 2*x^4) - log(x)^4*(2*x - 2*x^2) + log(3)*(5*x - 16*x^3 + 52*x^4
- 60*x^5 + 28*x^6 - 4*x^7) - log(x)^2*(log(3)*(16*x - 20*x^2 + 4*x^3) + 12*x^3 - 36*x^4 + 36*x^5 - 12*x^6) +
log(x)^3*(8*x^2 - 16*x^3 + 8*x^4) + log(x)*(10*x + log(3)*(32*x^2 - 72*x^3 + 48*x^4 - 8*x^5) - 20*x^2 + 8*x^4
- 32*x^5 + 48*x^6 - 32*x^7 + 8*x^8 - 10) - 20*x^2 + 30*x^3 - 20*x^4 - 2*x^5 + 10*x^6 - 20*x^7 + 20*x^8 - 10*x^
9 + 2*x^10)/(log(3)*(8*x^3 - 18*x^4 + 12*x^5 - 2*x^6) + x*log(x)^4 - log(x)*(log(3)*(16*x^2 - 20*x^3 + 4*x^4)
+ 4*x^4 - 12*x^5 + 12*x^6 - 4*x^7) - log(x)^3*(4*x^2 - 4*x^3) + log(3)^2*(16*x - 8*x^2 + x^3) + x^5 - 4*x^6 +
6*x^7 - 4*x^8 + x^9 + log(x)^2*(log(3)*(8*x - 2*x^2) + 6*x^3 - 12*x^4 + 6*x^5)), x)

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sympy [A]  time = 0.38, size = 46, normalized size = 1.39 \begin {gather*} x^{2} - 2 x + \frac {5}{x^{4} - 2 x^{3} + x^{2} - x \log {\relax (3 )} + \left (2 x^{2} - 2 x\right ) \log {\relax (x )} + \log {\relax (x )}^{2} + 4 \log {\relax (3 )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((2*x**2-2*x)*ln(x)**4+(8*x**4-16*x**3+8*x**2)*ln(x)**3+((-4*x**3+20*x**2-16*x)*ln(3)+12*x**6-36*x**
5+36*x**4-12*x**3)*ln(x)**2+((-8*x**5+48*x**4-72*x**3+32*x**2)*ln(3)+8*x**8-32*x**7+48*x**6-32*x**5+8*x**4-20*
x**2+10*x-10)*ln(x)+(2*x**4-18*x**3+48*x**2-32*x)*ln(3)**2+(-4*x**7+28*x**6-60*x**5+52*x**4-16*x**3+5*x)*ln(3)
+2*x**10-10*x**9+20*x**8-20*x**7+10*x**6-2*x**5-20*x**4+30*x**3-20*x**2+10*x)/(x*ln(x)**4+(4*x**3-4*x**2)*ln(x
)**3+((-2*x**2+8*x)*ln(3)+6*x**5-12*x**4+6*x**3)*ln(x)**2+((-4*x**4+20*x**3-16*x**2)*ln(3)+4*x**7-12*x**6+12*x
**5-4*x**4)*ln(x)+(x**3-8*x**2+16*x)*ln(3)**2+(-2*x**6+12*x**5-18*x**4+8*x**3)*ln(3)+x**9-4*x**8+6*x**7-4*x**6
+x**5),x)

[Out]

x**2 - 2*x + 5/(x**4 - 2*x**3 + x**2 - x*log(3) + (2*x**2 - 2*x)*log(x) + log(x)**2 + 4*log(3))

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