3.38.83 \(\int \frac {(27 x-27 x^3+9 x^5-x^7) \log ^5(2)+(135 x^2-135 x^4+45 x^6-5 x^8) \log ^4(2) \log (x)+(270 x^3-270 x^5+90 x^7-10 x^9) \log ^3(2) \log ^2(x)+((-108+36 x^2) \log (2)+(270 x^4-270 x^6+90 x^8-10 x^{10}) \log ^2(2)) \log ^3(x)+(-36 x^2+135 x^5-135 x^7+45 x^9-5 x^{11}) \log (2) \log ^4(x)+(108 x-72 x^3+27 x^6-27 x^8+9 x^{10}-x^{12}) \log ^5(x)}{(-27 x+27 x^3-9 x^5+x^7) \log ^5(2)+(-135 x^2+135 x^4-45 x^6+5 x^8) \log ^4(2) \log (x)+(-270 x^3+270 x^5-90 x^7+10 x^9) \log ^3(2) \log ^2(x)+(-270 x^4+270 x^6-90 x^8+10 x^{10}) \log ^2(2) \log ^3(x)+(-135 x^5+135 x^7-45 x^9+5 x^{11}) \log (2) \log ^4(x)+(-27 x^6+27 x^8-9 x^{10}+x^{12}) \log ^5(x)} \, dx\)

Optimal. Leaf size=25 \[ 4-x+\frac {9}{\left (-3+x^2\right )^2 \left (x+\frac {\log (2)}{\log (x)}\right )^4} \]

________________________________________________________________________________________

Rubi [F]  time = 9.71, 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 {\left (27 x-27 x^3+9 x^5-x^7\right ) \log ^5(2)+\left (135 x^2-135 x^4+45 x^6-5 x^8\right ) \log ^4(2) \log (x)+\left (270 x^3-270 x^5+90 x^7-10 x^9\right ) \log ^3(2) \log ^2(x)+\left (\left (-108+36 x^2\right ) \log (2)+\left (270 x^4-270 x^6+90 x^8-10 x^{10}\right ) \log ^2(2)\right ) \log ^3(x)+\left (-36 x^2+135 x^5-135 x^7+45 x^9-5 x^{11}\right ) \log (2) \log ^4(x)+\left (108 x-72 x^3+27 x^6-27 x^8+9 x^{10}-x^{12}\right ) \log ^5(x)}{\left (-27 x+27 x^3-9 x^5+x^7\right ) \log ^5(2)+\left (-135 x^2+135 x^4-45 x^6+5 x^8\right ) \log ^4(2) \log (x)+\left (-270 x^3+270 x^5-90 x^7+10 x^9\right ) \log ^3(2) \log ^2(x)+\left (-270 x^4+270 x^6-90 x^8+10 x^{10}\right ) \log ^2(2) \log ^3(x)+\left (-135 x^5+135 x^7-45 x^9+5 x^{11}\right ) \log (2) \log ^4(x)+\left (-27 x^6+27 x^8-9 x^{10}+x^{12}\right ) \log ^5(x)} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[((27*x - 27*x^3 + 9*x^5 - x^7)*Log[2]^5 + (135*x^2 - 135*x^4 + 45*x^6 - 5*x^8)*Log[2]^4*Log[x] + (270*x^3
- 270*x^5 + 90*x^7 - 10*x^9)*Log[2]^3*Log[x]^2 + ((-108 + 36*x^2)*Log[2] + (270*x^4 - 270*x^6 + 90*x^8 - 10*x^
10)*Log[2]^2)*Log[x]^3 + (-36*x^2 + 135*x^5 - 135*x^7 + 45*x^9 - 5*x^11)*Log[2]*Log[x]^4 + (108*x - 72*x^3 + 2
7*x^6 - 27*x^8 + 9*x^10 - x^12)*Log[x]^5)/((-27*x + 27*x^3 - 9*x^5 + x^7)*Log[2]^5 + (-135*x^2 + 135*x^4 - 45*
x^6 + 5*x^8)*Log[2]^4*Log[x] + (-270*x^3 + 270*x^5 - 90*x^7 + 10*x^9)*Log[2]^3*Log[x]^2 + (-270*x^4 + 270*x^6
- 90*x^8 + 10*x^10)*Log[2]^2*Log[x]^3 + (-135*x^5 + 135*x^7 - 45*x^9 + 5*x^11)*Log[2]*Log[x]^4 + (-27*x^6 + 27
*x^8 - 9*x^10 + x^12)*Log[x]^5),x]

[Out]

x^(-4) + 2/(3*x^2) - x + 2/(3*(3 - x^2)) + (-3 + x^2)^(-2) - (4*Log[2]^4*Defer[Int][1/((Sqrt[3] - x)*(Log[2] +
x*Log[x])^5), x])/(3*Sqrt[3]) + (Log[2]^4*Log[262144]*Defer[Int][1/((Sqrt[3] - x)*(Log[2] + x*Log[x])^5), x])
/27 + (2*Log[2]^4*Log[262144]*Defer[Int][1/(x^5*(Log[2] + x*Log[x])^5), x])/9 - 4*Log[2]^4*Defer[Int][1/(x^4*(
Log[2] + x*Log[x])^5), x] + (4*Log[2]^4*Log[262144]*Defer[Int][1/(x^3*(Log[2] + x*Log[x])^5), x])/27 - (8*Log[
2]^4*Defer[Int][1/(x^2*(Log[2] + x*Log[x])^5), x])/3 + (2*Log[2]^4*Log[262144]*Defer[Int][1/(x*(Log[2] + x*Log
[x])^5), x])/27 - (4*Log[2]^4*Defer[Int][1/((Sqrt[3] + x)*(Log[2] + x*Log[x])^5), x])/(3*Sqrt[3]) - (Log[2]^4*
Log[262144]*Defer[Int][1/((Sqrt[3] + x)*(Log[2] + x*Log[x])^5), x])/27 - 4*Log[2]^4*Defer[Int][1/((-3 + x^2)^2
*(Log[2] + x*Log[x])^5), x] + (2*Log[2]^4*Log[262144]*Defer[Int][x/((-3 + x^2)^2*(Log[2] + x*Log[x])^5), x])/2
7 + (4*Log[2]^3*Defer[Int][1/((Sqrt[3] - x)*(Log[2] + x*Log[x])^4), x])/Sqrt[3] - (Log[2]^3*Log[16777216]*Defe
r[Int][1/((Sqrt[3] - x)*(Log[2] + x*Log[x])^4), x])/9 - (2*Log[2]^3*Log[1073741824]*Defer[Int][1/(x^5*(Log[2]
+ x*Log[x])^4), x])/3 + 12*Log[2]^3*Defer[Int][1/(x^4*(Log[2] + x*Log[x])^4), x] - (2*Log[2]^3*Log[262144]*Def
er[Int][1/(x^3*(Log[2] + x*Log[x])^4), x])/3 + 8*Log[2]^3*Defer[Int][1/(x^2*(Log[2] + x*Log[x])^4), x] - (2*Lo
g[2]^3*Log[16777216]*Defer[Int][1/(x*(Log[2] + x*Log[x])^4), x])/9 + (4*Log[2]^3*Defer[Int][1/((Sqrt[3] + x)*(
Log[2] + x*Log[x])^4), x])/Sqrt[3] + (Log[2]^3*Log[16777216]*Defer[Int][1/((Sqrt[3] + x)*(Log[2] + x*Log[x])^4
), x])/9 - (2*Log[2]^3*Log[64]*Defer[Int][x/((-3 + x^2)^3*(Log[2] + x*Log[x])^4), x])/3 + 12*Log[2]^3*Defer[In
t][1/((-3 + x^2)^2*(Log[2] + x*Log[x])^4), x] - (2*Log[2]^3*Log[64]*Defer[Int][x/((-3 + x^2)^2*(Log[2] + x*Log
[x])^4), x])/3 - (4*Log[2]^2*Defer[Int][1/((Sqrt[3] - x)*(Log[2] + x*Log[x])^3), x])/Sqrt[3] + 4*Log[2]^3*Defe
r[Int][1/((Sqrt[3] - x)*(Log[2] + x*Log[x])^3), x] + 40*Log[2]^3*Defer[Int][1/(x^5*(Log[2] + x*Log[x])^3), x]
- 12*Log[2]^2*Defer[Int][1/(x^4*(Log[2] + x*Log[x])^3), x] + (64*Log[2]^3*Defer[Int][1/(x^3*(Log[2] + x*Log[x]
)^3), x])/3 - 8*Log[2]^2*Defer[Int][1/(x^2*(Log[2] + x*Log[x])^3), x] + 8*Log[2]^3*Defer[Int][1/(x*(Log[2] + x
*Log[x])^3), x] - (4*Log[2]^2*Defer[Int][1/((Sqrt[3] + x)*(Log[2] + x*Log[x])^3), x])/Sqrt[3] - 4*Log[2]^3*Def
er[Int][1/((Sqrt[3] + x)*(Log[2] + x*Log[x])^3), x] + 16*Log[2]^3*Defer[Int][x/((-3 + x^2)^3*(Log[2] + x*Log[x
])^3), x] - 12*Log[2]^2*Defer[Int][1/((-3 + x^2)^2*(Log[2] + x*Log[x])^3), x] + (4*Log[2]^2*Log[4]*Defer[Int][
x/((-3 + x^2)^2*(Log[2] + x*Log[x])^3), x])/3 + (4*Log[2]*Defer[Int][1/((Sqrt[3] - x)*(Log[2] + x*Log[x])^2),
x])/(3*Sqrt[3]) - (4*Log[2]*Log[4]*Defer[Int][1/((Sqrt[3] - x)*(Log[2] + x*Log[x])^2), x])/3 - 40*Log[2]^2*Def
er[Int][1/(x^5*(Log[2] + x*Log[x])^2), x] + 4*Log[2]*Defer[Int][1/(x^4*(Log[2] + x*Log[x])^2), x] - (56*Log[2]
^2*Defer[Int][1/(x^3*(Log[2] + x*Log[x])^2), x])/3 + (8*Log[2]*Defer[Int][1/(x^2*(Log[2] + x*Log[x])^2), x])/3
- (16*Log[2]^2*Defer[Int][1/(x*(Log[2] + x*Log[x])^2), x])/3 + (4*Log[2]*Defer[Int][1/((Sqrt[3] + x)*(Log[2]
+ x*Log[x])^2), x])/(3*Sqrt[3]) + (4*Log[2]*Log[4]*Defer[Int][1/((Sqrt[3] + x)*(Log[2] + x*Log[x])^2), x])/3 -
24*Log[2]^2*Defer[Int][x/((-3 + x^2)^3*(Log[2] + x*Log[x])^2), x] + 4*Log[2]*Defer[Int][1/((-3 + x^2)^2*(Log[
2] + x*Log[x])^2), x] + (4*Log[2]*Log[4]*Defer[Int][x/((-3 + x^2)^2*(Log[2] + x*Log[x])^2), x])/3 + (2*Log[2]*
Defer[Int][1/((Sqrt[3] - x)*(Log[2] + x*Log[x])), x])/3 + 20*Log[2]*Defer[Int][1/(x^5*(Log[2] + x*Log[x])), x]
+ 8*Log[2]*Defer[Int][1/(x^3*(Log[2] + x*Log[x])), x] + (4*Log[2]*Defer[Int][1/(x*(Log[2] + x*Log[x])), x])/3
- (2*Log[2]*Defer[Int][1/((Sqrt[3] + x)*(Log[2] + x*Log[x])), x])/3 + 16*Log[2]*Defer[Int][x/((-3 + x^2)^3*(L
og[2] + x*Log[x])), x] - 4*Log[2]*Defer[Int][x/((-3 + x^2)^2*(Log[2] + x*Log[x])), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {x \left (-3+x^2\right )^3 \log ^5(2)+5 x^2 \left (-3+x^2\right )^3 \log ^4(2) \log (x)+10 x^3 \left (-3+x^2\right )^3 \log ^3(2) \log ^2(x)+2 \left (-3+x^2\right ) \log (2) \left (-18+45 x^4 \log (2)-30 x^6 \log (2)+x^8 \log (32)\right ) \log ^3(x)+x^2 \left (36-135 x^3+135 x^5-45 x^7+5 x^9\right ) \log (2) \log ^4(x)+x \left (-108+72 x^2-27 x^5+27 x^7-9 x^9+x^{11}\right ) \log ^5(x)}{x \left (3-x^2\right )^3 (\log (2)+x \log (x))^5} \, dx\\ &=\int \left (\frac {108-72 x^2+27 x^5-27 x^7+9 x^9-x^{11}}{x^5 \left (-3+x^2\right )^3}-\frac {2 \log ^4(2) (18 x-\log (262144))}{x^5 \left (-3+x^2\right )^2 (\log (2)+x \log (x))^5}+\frac {18 \log ^3(2) \left (-18 x+6 x^3-x^2 \log (4096)+\log (1073741824)\right )}{x^5 \left (-3+x^2\right )^3 (\log (2)+x \log (x))^4}-\frac {36 \log ^2(2) \left (-9 x+3 x^3+30 \log (2)-14 x^2 \log (2)\right )}{x^5 \left (-3+x^2\right )^3 (\log (2)+x \log (x))^3}+\frac {36 \log (2) \left (-3 x+x^3+30 \log (2)-16 x^2 \log (2)\right )}{x^5 \left (-3+x^2\right )^3 (\log (2)+x \log (x))^2}+\frac {108 \left (-5+3 x^2\right ) \log (2)}{x^5 \left (-3+x^2\right )^3 (\log (2)+x \log (x))}\right ) \, dx\\ &=(36 \log (2)) \int \frac {-3 x+x^3+30 \log (2)-16 x^2 \log (2)}{x^5 \left (-3+x^2\right )^3 (\log (2)+x \log (x))^2} \, dx+(108 \log (2)) \int \frac {-5+3 x^2}{x^5 \left (-3+x^2\right )^3 (\log (2)+x \log (x))} \, dx-\left (36 \log ^2(2)\right ) \int \frac {-9 x+3 x^3+30 \log (2)-14 x^2 \log (2)}{x^5 \left (-3+x^2\right )^3 (\log (2)+x \log (x))^3} \, dx+\left (18 \log ^3(2)\right ) \int \frac {-18 x+6 x^3-x^2 \log (4096)+\log (1073741824)}{x^5 \left (-3+x^2\right )^3 (\log (2)+x \log (x))^4} \, dx-\left (2 \log ^4(2)\right ) \int \frac {18 x-\log (262144)}{x^5 \left (-3+x^2\right )^2 (\log (2)+x \log (x))^5} \, dx+\int \frac {108-72 x^2+27 x^5-27 x^7+9 x^9-x^{11}}{x^5 \left (-3+x^2\right )^3} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [B]  time = 0.89, size = 628, normalized size = 25.12 \begin {gather*} \frac {1}{x^4}+\frac {2}{3 x^2}-x+\frac {1}{\left (-3+x^2\right )^2}-\frac {2}{3 \left (-3+x^2\right )}+\frac {9 \log ^4(2)}{x^4 \left (-3+x^2\right )^2 (\log (2)+x \log (x))^4}-\frac {36 \log ^3(2)}{x^4 \left (-3+x^2\right )^2 (\log (2)+x \log (x))^3}-\frac {3 \log ^2(2) \left (180 x^8 \log (2)-1620 x \log ^4(2)+324 \log ^5(2)-216 x^2 \log ^3(2) \left (-15+\log ^2(2)\right )+1080 x^3 \log ^2(2) \left (-3+\log ^2(2)\right )-72 x^7 \left (-3+5 \log ^2(2)\right )+36 x^4 \log (2) \left (45-60 \log ^2(2)+\log ^4(2)\right )-36 x^5 \left (9-60 \log ^2(2)+5 \log ^4(2)\right )+360 x^6 \left (\log ^3(2)-\log (8)\right )+x^9 \left (-36-155 \log ^5(2)+31 \log ^4(2) \log (32)\right )\right )}{2 x^4 \left (-3+x^2\right )^4 (x-\log (2))^5 (\log (2)+x \log (x))^2}-\frac {3 \log (2) \left (-9072 x \log ^6(2)+1296 \log ^7(2)-1296 x^2 \log ^5(2) \left (-21+\log ^2(2)\right )+9072 x^3 \log ^4(2) \left (-5+\log ^2(2)\right )+432 x^4 \log ^3(2) \left (105-63 \log ^2(2)+\log ^4(2)\right )-3024 x^5 \log ^2(2) \left (9-15 \log ^2(2)+\log ^4(2)\right )-48 x^6 \log (2) \left (-189+945 \log ^2(2)-189 \log ^4(2)+\log ^6(2)\right )+48 x^7 \left (-27+567 \log ^2(2)-315 \log ^4(2)+7 \log ^6(2)\right )-4 x^{12} \log (2) \left (84-5310 \log ^3(2)+505 \log ^5(2)+1062 \log ^2(2) \log (32)-101 \log ^4(2) \log (32)\right )+48 x^{10} \log (2) \left (63-35 \log ^2(2)+260 \log ^5(2)-52 \log ^4(2) \log (32)\right )-6 x^9 \left (-216+1512 \log ^2(2)-280 \log ^4(2)+525 \log ^7(2)-105 \log ^6(2) \log (32)\right )+3 x^{11} \left (-144+336 \log ^2(2)-7385 \log ^5(2)+70 \log ^7(2)+1477 \log ^4(2) \log (32)-14 \log ^6(2) \log (32)\right )+x^{13} \left (48-11520 \log ^3(2)+6635 \log ^5(2)-50 \log ^7(2)+2304 \log ^2(2) \log (32)-1327 \log ^4(2) \log (32)+10 \log ^6(2) \log (32)\right )-1008 x^8 \left (-15 \log ^3(2)+\log ^5(2)+\log (512)\right )\right )}{4 x^4 \left (-3+x^2\right )^5 (x-\log (2))^7 (\log (2)+x \log (x))} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[((27*x - 27*x^3 + 9*x^5 - x^7)*Log[2]^5 + (135*x^2 - 135*x^4 + 45*x^6 - 5*x^8)*Log[2]^4*Log[x] + (27
0*x^3 - 270*x^5 + 90*x^7 - 10*x^9)*Log[2]^3*Log[x]^2 + ((-108 + 36*x^2)*Log[2] + (270*x^4 - 270*x^6 + 90*x^8 -
10*x^10)*Log[2]^2)*Log[x]^3 + (-36*x^2 + 135*x^5 - 135*x^7 + 45*x^9 - 5*x^11)*Log[2]*Log[x]^4 + (108*x - 72*x
^3 + 27*x^6 - 27*x^8 + 9*x^10 - x^12)*Log[x]^5)/((-27*x + 27*x^3 - 9*x^5 + x^7)*Log[2]^5 + (-135*x^2 + 135*x^4
- 45*x^6 + 5*x^8)*Log[2]^4*Log[x] + (-270*x^3 + 270*x^5 - 90*x^7 + 10*x^9)*Log[2]^3*Log[x]^2 + (-270*x^4 + 27
0*x^6 - 90*x^8 + 10*x^10)*Log[2]^2*Log[x]^3 + (-135*x^5 + 135*x^7 - 45*x^9 + 5*x^11)*Log[2]*Log[x]^4 + (-27*x^
6 + 27*x^8 - 9*x^10 + x^12)*Log[x]^5),x]

[Out]

x^(-4) + 2/(3*x^2) - x + (-3 + x^2)^(-2) - 2/(3*(-3 + x^2)) + (9*Log[2]^4)/(x^4*(-3 + x^2)^2*(Log[2] + x*Log[x
])^4) - (36*Log[2]^3)/(x^4*(-3 + x^2)^2*(Log[2] + x*Log[x])^3) - (3*Log[2]^2*(180*x^8*Log[2] - 1620*x*Log[2]^4
+ 324*Log[2]^5 - 216*x^2*Log[2]^3*(-15 + Log[2]^2) + 1080*x^3*Log[2]^2*(-3 + Log[2]^2) - 72*x^7*(-3 + 5*Log[2
]^2) + 36*x^4*Log[2]*(45 - 60*Log[2]^2 + Log[2]^4) - 36*x^5*(9 - 60*Log[2]^2 + 5*Log[2]^4) + 360*x^6*(Log[2]^3
- Log[8]) + x^9*(-36 - 155*Log[2]^5 + 31*Log[2]^4*Log[32])))/(2*x^4*(-3 + x^2)^4*(x - Log[2])^5*(Log[2] + x*L
og[x])^2) - (3*Log[2]*(-9072*x*Log[2]^6 + 1296*Log[2]^7 - 1296*x^2*Log[2]^5*(-21 + Log[2]^2) + 9072*x^3*Log[2]
^4*(-5 + Log[2]^2) + 432*x^4*Log[2]^3*(105 - 63*Log[2]^2 + Log[2]^4) - 3024*x^5*Log[2]^2*(9 - 15*Log[2]^2 + Lo
g[2]^4) - 48*x^6*Log[2]*(-189 + 945*Log[2]^2 - 189*Log[2]^4 + Log[2]^6) + 48*x^7*(-27 + 567*Log[2]^2 - 315*Log
[2]^4 + 7*Log[2]^6) - 4*x^12*Log[2]*(84 - 5310*Log[2]^3 + 505*Log[2]^5 + 1062*Log[2]^2*Log[32] - 101*Log[2]^4*
Log[32]) + 48*x^10*Log[2]*(63 - 35*Log[2]^2 + 260*Log[2]^5 - 52*Log[2]^4*Log[32]) - 6*x^9*(-216 + 1512*Log[2]^
2 - 280*Log[2]^4 + 525*Log[2]^7 - 105*Log[2]^6*Log[32]) + 3*x^11*(-144 + 336*Log[2]^2 - 7385*Log[2]^5 + 70*Log
[2]^7 + 1477*Log[2]^4*Log[32] - 14*Log[2]^6*Log[32]) + x^13*(48 - 11520*Log[2]^3 + 6635*Log[2]^5 - 50*Log[2]^7
+ 2304*Log[2]^2*Log[32] - 1327*Log[2]^4*Log[32] + 10*Log[2]^6*Log[32]) - 1008*x^8*(-15*Log[2]^3 + Log[2]^5 +
Log[512])))/(4*x^4*(-3 + x^2)^5*(x - Log[2])^7*(Log[2] + x*Log[x]))

________________________________________________________________________________________

fricas [B]  time = 0.92, size = 211, normalized size = 8.44 \begin {gather*} -\frac {{\left (x^{5} - 6 \, x^{3} + 9 \, x\right )} \log \relax (2)^{4} + 4 \, {\left (x^{6} - 6 \, x^{4} + 9 \, x^{2}\right )} \log \relax (2)^{3} \log \relax (x) + 6 \, {\left (x^{7} - 6 \, x^{5} + 9 \, x^{3}\right )} \log \relax (2)^{2} \log \relax (x)^{2} + 4 \, {\left (x^{8} - 6 \, x^{6} + 9 \, x^{4}\right )} \log \relax (2) \log \relax (x)^{3} + {\left (x^{9} - 6 \, x^{7} + 9 \, x^{5} - 9\right )} \log \relax (x)^{4}}{{\left (x^{4} - 6 \, x^{2} + 9\right )} \log \relax (2)^{4} + 4 \, {\left (x^{5} - 6 \, x^{3} + 9 \, x\right )} \log \relax (2)^{3} \log \relax (x) + 6 \, {\left (x^{6} - 6 \, x^{4} + 9 \, x^{2}\right )} \log \relax (2)^{2} \log \relax (x)^{2} + 4 \, {\left (x^{7} - 6 \, x^{5} + 9 \, x^{3}\right )} \log \relax (2) \log \relax (x)^{3} + {\left (x^{8} - 6 \, x^{6} + 9 \, x^{4}\right )} \log \relax (x)^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-x^12+9*x^10-27*x^8+27*x^6-72*x^3+108*x)*log(x)^5+(-5*x^11+45*x^9-135*x^7+135*x^5-36*x^2)*log(2)*l
og(x)^4+((-10*x^10+90*x^8-270*x^6+270*x^4)*log(2)^2+(36*x^2-108)*log(2))*log(x)^3+(-10*x^9+90*x^7-270*x^5+270*
x^3)*log(2)^3*log(x)^2+(-5*x^8+45*x^6-135*x^4+135*x^2)*log(2)^4*log(x)+(-x^7+9*x^5-27*x^3+27*x)*log(2)^5)/((x^
12-9*x^10+27*x^8-27*x^6)*log(x)^5+(5*x^11-45*x^9+135*x^7-135*x^5)*log(2)*log(x)^4+(10*x^10-90*x^8+270*x^6-270*
x^4)*log(2)^2*log(x)^3+(10*x^9-90*x^7+270*x^5-270*x^3)*log(2)^3*log(x)^2+(5*x^8-45*x^6+135*x^4-135*x^2)*log(2)
^4*log(x)+(x^7-9*x^5+27*x^3-27*x)*log(2)^5),x, algorithm="fricas")

[Out]

-((x^5 - 6*x^3 + 9*x)*log(2)^4 + 4*(x^6 - 6*x^4 + 9*x^2)*log(2)^3*log(x) + 6*(x^7 - 6*x^5 + 9*x^3)*log(2)^2*lo
g(x)^2 + 4*(x^8 - 6*x^6 + 9*x^4)*log(2)*log(x)^3 + (x^9 - 6*x^7 + 9*x^5 - 9)*log(x)^4)/((x^4 - 6*x^2 + 9)*log(
2)^4 + 4*(x^5 - 6*x^3 + 9*x)*log(2)^3*log(x) + 6*(x^6 - 6*x^4 + 9*x^2)*log(2)^2*log(x)^2 + 4*(x^7 - 6*x^5 + 9*
x^3)*log(2)*log(x)^3 + (x^8 - 6*x^6 + 9*x^4)*log(x)^4)

________________________________________________________________________________________

giac [B]  time = 1.23, size = 237, normalized size = 9.48 \begin {gather*} -x - \frac {9 \, {\left (4 \, x^{3} \log \relax (2) \log \relax (x)^{3} + 6 \, x^{2} \log \relax (2)^{2} \log \relax (x)^{2} + 4 \, x \log \relax (2)^{3} \log \relax (x) + \log \relax (2)^{4}\right )}}{x^{12} \log \relax (x)^{4} + 4 \, x^{11} \log \relax (2) \log \relax (x)^{3} + 6 \, x^{10} \log \relax (2)^{2} \log \relax (x)^{2} - 6 \, x^{10} \log \relax (x)^{4} + 4 \, x^{9} \log \relax (2)^{3} \log \relax (x) - 24 \, x^{9} \log \relax (2) \log \relax (x)^{3} + x^{8} \log \relax (2)^{4} - 36 \, x^{8} \log \relax (2)^{2} \log \relax (x)^{2} + 9 \, x^{8} \log \relax (x)^{4} - 24 \, x^{7} \log \relax (2)^{3} \log \relax (x) + 36 \, x^{7} \log \relax (2) \log \relax (x)^{3} - 6 \, x^{6} \log \relax (2)^{4} + 54 \, x^{6} \log \relax (2)^{2} \log \relax (x)^{2} + 36 \, x^{5} \log \relax (2)^{3} \log \relax (x) + 9 \, x^{4} \log \relax (2)^{4}} - \frac {2 \, x^{2} - 9}{3 \, {\left (x^{4} - 6 \, x^{2} + 9\right )}} + \frac {2 \, x^{2} + 3}{3 \, x^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-x^12+9*x^10-27*x^8+27*x^6-72*x^3+108*x)*log(x)^5+(-5*x^11+45*x^9-135*x^7+135*x^5-36*x^2)*log(2)*l
og(x)^4+((-10*x^10+90*x^8-270*x^6+270*x^4)*log(2)^2+(36*x^2-108)*log(2))*log(x)^3+(-10*x^9+90*x^7-270*x^5+270*
x^3)*log(2)^3*log(x)^2+(-5*x^8+45*x^6-135*x^4+135*x^2)*log(2)^4*log(x)+(-x^7+9*x^5-27*x^3+27*x)*log(2)^5)/((x^
12-9*x^10+27*x^8-27*x^6)*log(x)^5+(5*x^11-45*x^9+135*x^7-135*x^5)*log(2)*log(x)^4+(10*x^10-90*x^8+270*x^6-270*
x^4)*log(2)^2*log(x)^3+(10*x^9-90*x^7+270*x^5-270*x^3)*log(2)^3*log(x)^2+(5*x^8-45*x^6+135*x^4-135*x^2)*log(2)
^4*log(x)+(x^7-9*x^5+27*x^3-27*x)*log(2)^5),x, algorithm="giac")

[Out]

-x - 9*(4*x^3*log(2)*log(x)^3 + 6*x^2*log(2)^2*log(x)^2 + 4*x*log(2)^3*log(x) + log(2)^4)/(x^12*log(x)^4 + 4*x
^11*log(2)*log(x)^3 + 6*x^10*log(2)^2*log(x)^2 - 6*x^10*log(x)^4 + 4*x^9*log(2)^3*log(x) - 24*x^9*log(2)*log(x
)^3 + x^8*log(2)^4 - 36*x^8*log(2)^2*log(x)^2 + 9*x^8*log(x)^4 - 24*x^7*log(2)^3*log(x) + 36*x^7*log(2)*log(x)
^3 - 6*x^6*log(2)^4 + 54*x^6*log(2)^2*log(x)^2 + 36*x^5*log(2)^3*log(x) + 9*x^4*log(2)^4) - 1/3*(2*x^2 - 9)/(x
^4 - 6*x^2 + 9) + 1/3*(2*x^2 + 3)/x^4

________________________________________________________________________________________

maple [B]  time = 0.19, size = 96, normalized size = 3.84

method	result	size
risch	\(-\frac {x^{9}-6 x^{7}+9 x^{5}-9}{x^{4} \left (x^{4}-6 x^{2}+9\right )}-\frac {9 \ln \relax (2) \left (4 x^{3} \ln \relax (x )^{3}+6 x^{2} \ln \relax (2) \ln \relax (x )^{2}+4 \ln \relax (2)^{2} x \ln \relax (x )+\ln \relax (2)^{3}\right )}{x^{4} \left (x^{4}-6 x^{2}+9\right ) \left (x \ln \relax (x )+\ln \relax (2)\right )^{4}}\)	\(96\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-x^12+9*x^10-27*x^8+27*x^6-72*x^3+108*x)*ln(x)^5+(-5*x^11+45*x^9-135*x^7+135*x^5-36*x^2)*ln(2)*ln(x)^4+(
(-10*x^10+90*x^8-270*x^6+270*x^4)*ln(2)^2+(36*x^2-108)*ln(2))*ln(x)^3+(-10*x^9+90*x^7-270*x^5+270*x^3)*ln(2)^3
*ln(x)^2+(-5*x^8+45*x^6-135*x^4+135*x^2)*ln(2)^4*ln(x)+(-x^7+9*x^5-27*x^3+27*x)*ln(2)^5)/((x^12-9*x^10+27*x^8-
27*x^6)*ln(x)^5+(5*x^11-45*x^9+135*x^7-135*x^5)*ln(2)*ln(x)^4+(10*x^10-90*x^8+270*x^6-270*x^4)*ln(2)^2*ln(x)^3
+(10*x^9-90*x^7+270*x^5-270*x^3)*ln(2)^3*ln(x)^2+(5*x^8-45*x^6+135*x^4-135*x^2)*ln(2)^4*ln(x)+(x^7-9*x^5+27*x^
3-27*x)*ln(2)^5),x,method=_RETURNVERBOSE)

[Out]

-(x^9-6*x^7+9*x^5-9)/x^4/(x^4-6*x^2+9)-9*ln(2)*(4*x^3*ln(x)^3+6*x^2*ln(2)*ln(x)^2+4*ln(2)^2*x*ln(x)+ln(2)^3)/x
^4/(x^4-6*x^2+9)/(x*ln(x)+ln(2))^4

________________________________________________________________________________________

maxima [B]  time = 0.81, size = 272, normalized size = 10.88 \begin {gather*} -\frac {x^{5} \log \relax (2)^{4} - 6 \, x^{3} \log \relax (2)^{4} + 9 \, x \log \relax (2)^{4} + {\left (x^{9} - 6 \, x^{7} + 9 \, x^{5} - 9\right )} \log \relax (x)^{4} + 4 \, {\left (x^{8} \log \relax (2) - 6 \, x^{6} \log \relax (2) + 9 \, x^{4} \log \relax (2)\right )} \log \relax (x)^{3} + 6 \, {\left (x^{7} \log \relax (2)^{2} - 6 \, x^{5} \log \relax (2)^{2} + 9 \, x^{3} \log \relax (2)^{2}\right )} \log \relax (x)^{2} + 4 \, {\left (x^{6} \log \relax (2)^{3} - 6 \, x^{4} \log \relax (2)^{3} + 9 \, x^{2} \log \relax (2)^{3}\right )} \log \relax (x)}{x^{4} \log \relax (2)^{4} - 6 \, x^{2} \log \relax (2)^{4} + {\left (x^{8} - 6 \, x^{6} + 9 \, x^{4}\right )} \log \relax (x)^{4} + 9 \, \log \relax (2)^{4} + 4 \, {\left (x^{7} \log \relax (2) - 6 \, x^{5} \log \relax (2) + 9 \, x^{3} \log \relax (2)\right )} \log \relax (x)^{3} + 6 \, {\left (x^{6} \log \relax (2)^{2} - 6 \, x^{4} \log \relax (2)^{2} + 9 \, x^{2} \log \relax (2)^{2}\right )} \log \relax (x)^{2} + 4 \, {\left (x^{5} \log \relax (2)^{3} - 6 \, x^{3} \log \relax (2)^{3} + 9 \, x \log \relax (2)^{3}\right )} \log \relax (x)} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-x^12+9*x^10-27*x^8+27*x^6-72*x^3+108*x)*log(x)^5+(-5*x^11+45*x^9-135*x^7+135*x^5-36*x^2)*log(2)*l
og(x)^4+((-10*x^10+90*x^8-270*x^6+270*x^4)*log(2)^2+(36*x^2-108)*log(2))*log(x)^3+(-10*x^9+90*x^7-270*x^5+270*
x^3)*log(2)^3*log(x)^2+(-5*x^8+45*x^6-135*x^4+135*x^2)*log(2)^4*log(x)+(-x^7+9*x^5-27*x^3+27*x)*log(2)^5)/((x^
12-9*x^10+27*x^8-27*x^6)*log(x)^5+(5*x^11-45*x^9+135*x^7-135*x^5)*log(2)*log(x)^4+(10*x^10-90*x^8+270*x^6-270*
x^4)*log(2)^2*log(x)^3+(10*x^9-90*x^7+270*x^5-270*x^3)*log(2)^3*log(x)^2+(5*x^8-45*x^6+135*x^4-135*x^2)*log(2)
^4*log(x)+(x^7-9*x^5+27*x^3-27*x)*log(2)^5),x, algorithm="maxima")

[Out]

-(x^5*log(2)^4 - 6*x^3*log(2)^4 + 9*x*log(2)^4 + (x^9 - 6*x^7 + 9*x^5 - 9)*log(x)^4 + 4*(x^8*log(2) - 6*x^6*lo
g(2) + 9*x^4*log(2))*log(x)^3 + 6*(x^7*log(2)^2 - 6*x^5*log(2)^2 + 9*x^3*log(2)^2)*log(x)^2 + 4*(x^6*log(2)^3
- 6*x^4*log(2)^3 + 9*x^2*log(2)^3)*log(x))/(x^4*log(2)^4 - 6*x^2*log(2)^4 + (x^8 - 6*x^6 + 9*x^4)*log(x)^4 + 9
*log(2)^4 + 4*(x^7*log(2) - 6*x^5*log(2) + 9*x^3*log(2))*log(x)^3 + 6*(x^6*log(2)^2 - 6*x^4*log(2)^2 + 9*x^2*l
og(2)^2)*log(x)^2 + 4*(x^5*log(2)^3 - 6*x^3*log(2)^3 + 9*x*log(2)^3)*log(x))

________________________________________________________________________________________

mupad [F]  time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} -\int \frac {\left (-x^{12}+9\,x^{10}-27\,x^8+27\,x^6-72\,x^3+108\,x\right )\,{\ln \relax (x)}^5-\ln \relax (2)\,\left (5\,x^{11}-45\,x^9+135\,x^7-135\,x^5+36\,x^2\right )\,{\ln \relax (x)}^4+\left (\ln \relax (2)\,\left (36\,x^2-108\right )+{\ln \relax (2)}^2\,\left (-10\,x^{10}+90\,x^8-270\,x^6+270\,x^4\right )\right )\,{\ln \relax (x)}^3+{\ln \relax (2)}^3\,\left (-10\,x^9+90\,x^7-270\,x^5+270\,x^3\right )\,{\ln \relax (x)}^2+{\ln \relax (2)}^4\,\left (-5\,x^8+45\,x^6-135\,x^4+135\,x^2\right )\,\ln \relax (x)+{\ln \relax (2)}^5\,\left (-x^7+9\,x^5-27\,x^3+27\,x\right )}{\left (-x^{12}+9\,x^{10}-27\,x^8+27\,x^6\right )\,{\ln \relax (x)}^5+\ln \relax (2)\,\left (-5\,x^{11}+45\,x^9-135\,x^7+135\,x^5\right )\,{\ln \relax (x)}^4+{\ln \relax (2)}^2\,\left (-10\,x^{10}+90\,x^8-270\,x^6+270\,x^4\right )\,{\ln \relax (x)}^3+{\ln \relax (2)}^3\,\left (-10\,x^9+90\,x^7-270\,x^5+270\,x^3\right )\,{\ln \relax (x)}^2+{\ln \relax (2)}^4\,\left (-5\,x^8+45\,x^6-135\,x^4+135\,x^2\right )\,\ln \relax (x)+{\ln \relax (2)}^5\,\left (-x^7+9\,x^5-27\,x^3+27\,x\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(log(2)^5*(27*x - 27*x^3 + 9*x^5 - x^7) + log(x)^3*(log(2)*(36*x^2 - 108) + log(2)^2*(270*x^4 - 270*x^6 +
90*x^8 - 10*x^10)) + log(x)^5*(108*x - 72*x^3 + 27*x^6 - 27*x^8 + 9*x^10 - x^12) + log(2)^4*log(x)*(135*x^2 -
135*x^4 + 45*x^6 - 5*x^8) - log(2)*log(x)^4*(36*x^2 - 135*x^5 + 135*x^7 - 45*x^9 + 5*x^11) + log(2)^3*log(x)^
2*(270*x^3 - 270*x^5 + 90*x^7 - 10*x^9))/(log(2)^5*(27*x - 27*x^3 + 9*x^5 - x^7) + log(x)^5*(27*x^6 - 27*x^8 +
9*x^10 - x^12) + log(2)^4*log(x)*(135*x^2 - 135*x^4 + 45*x^6 - 5*x^8) + log(2)*log(x)^4*(135*x^5 - 135*x^7 +
45*x^9 - 5*x^11) + log(2)^3*log(x)^2*(270*x^3 - 270*x^5 + 90*x^7 - 10*x^9) + log(2)^2*log(x)^3*(270*x^4 - 270*
x^6 + 90*x^8 - 10*x^10)),x)

[Out]

-int((log(2)^5*(27*x - 27*x^3 + 9*x^5 - x^7) + log(x)^3*(log(2)*(36*x^2 - 108) + log(2)^2*(270*x^4 - 270*x^6 +
90*x^8 - 10*x^10)) + log(x)^5*(108*x - 72*x^3 + 27*x^6 - 27*x^8 + 9*x^10 - x^12) + log(2)^4*log(x)*(135*x^2 -
135*x^4 + 45*x^6 - 5*x^8) - log(2)*log(x)^4*(36*x^2 - 135*x^5 + 135*x^7 - 45*x^9 + 5*x^11) + log(2)^3*log(x)^
2*(270*x^3 - 270*x^5 + 90*x^7 - 10*x^9))/(log(2)^5*(27*x - 27*x^3 + 9*x^5 - x^7) + log(x)^5*(27*x^6 - 27*x^8 +
9*x^10 - x^12) + log(2)^4*log(x)*(135*x^2 - 135*x^4 + 45*x^6 - 5*x^8) + log(2)*log(x)^4*(135*x^5 - 135*x^7 +
45*x^9 - 5*x^11) + log(2)^3*log(x)^2*(270*x^3 - 270*x^5 + 90*x^7 - 10*x^9) + log(2)^2*log(x)^3*(270*x^4 - 270*
x^6 + 90*x^8 - 10*x^10)), x)

________________________________________________________________________________________

sympy [B]  time = 0.60, size = 212, normalized size = 8.48 \begin {gather*} - x + \frac {- 36 x^{3} \log {\relax (2 )} \log {\relax (x )}^{3} - 54 x^{2} \log {\relax (2 )}^{2} \log {\relax (x )}^{2} - 36 x \log {\relax (2 )}^{3} \log {\relax (x )} - 9 \log {\relax (2 )}^{4}}{x^{8} \log {\relax (2 )}^{4} - 6 x^{6} \log {\relax (2 )}^{4} + 9 x^{4} \log {\relax (2 )}^{4} + \left (x^{12} - 6 x^{10} + 9 x^{8}\right ) \log {\relax (x )}^{4} + \left (4 x^{9} \log {\relax (2 )}^{3} - 24 x^{7} \log {\relax (2 )}^{3} + 36 x^{5} \log {\relax (2 )}^{3}\right ) \log {\relax (x )} + \left (6 x^{10} \log {\relax (2 )}^{2} - 36 x^{8} \log {\relax (2 )}^{2} + 54 x^{6} \log {\relax (2 )}^{2}\right ) \log {\relax (x )}^{2} + \left (4 x^{11} \log {\relax (2 )} - 24 x^{9} \log {\relax (2 )} + 36 x^{7} \log {\relax (2 )}\right ) \log {\relax (x )}^{3}} + \frac {9}{x^{8} - 6 x^{6} + 9 x^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-x**12+9*x**10-27*x**8+27*x**6-72*x**3+108*x)*ln(x)**5+(-5*x**11+45*x**9-135*x**7+135*x**5-36*x**2
)*ln(2)*ln(x)**4+((-10*x**10+90*x**8-270*x**6+270*x**4)*ln(2)**2+(36*x**2-108)*ln(2))*ln(x)**3+(-10*x**9+90*x*
*7-270*x**5+270*x**3)*ln(2)**3*ln(x)**2+(-5*x**8+45*x**6-135*x**4+135*x**2)*ln(2)**4*ln(x)+(-x**7+9*x**5-27*x*
*3+27*x)*ln(2)**5)/((x**12-9*x**10+27*x**8-27*x**6)*ln(x)**5+(5*x**11-45*x**9+135*x**7-135*x**5)*ln(2)*ln(x)**
4+(10*x**10-90*x**8+270*x**6-270*x**4)*ln(2)**2*ln(x)**3+(10*x**9-90*x**7+270*x**5-270*x**3)*ln(2)**3*ln(x)**2
+(5*x**8-45*x**6+135*x**4-135*x**2)*ln(2)**4*ln(x)+(x**7-9*x**5+27*x**3-27*x)*ln(2)**5),x)

[Out]

-x + (-36*x**3*log(2)*log(x)**3 - 54*x**2*log(2)**2*log(x)**2 - 36*x*log(2)**3*log(x) - 9*log(2)**4)/(x**8*log
(2)**4 - 6*x**6*log(2)**4 + 9*x**4*log(2)**4 + (x**12 - 6*x**10 + 9*x**8)*log(x)**4 + (4*x**9*log(2)**3 - 24*x
**7*log(2)**3 + 36*x**5*log(2)**3)*log(x) + (6*x**10*log(2)**2 - 36*x**8*log(2)**2 + 54*x**6*log(2)**2)*log(x)
**2 + (4*x**11*log(2) - 24*x**9*log(2) + 36*x**7*log(2))*log(x)**3) + 9/(x**8 - 6*x**6 + 9*x**4)

________________________________________________________________________________________