3.2.86 \(\int \frac {-16 x^7+8 x^8-4 x^{11}+(112 x^6-56 x^7+40 x^{10}) \log (x^2 \log (3))+(-336 x^5+168 x^6-180 x^9) \log ^2(x^2 \log (3))+(560 x^4-280 x^5+480 x^8) \log ^3(x^2 \log (3))+(-560 x^3+280 x^4-840 x^7) \log ^4(x^2 \log (3))+(336 x^2-168 x^3+1008 x^6) \log ^5(x^2 \log (3))+(-112 x+56 x^2-840 x^5) \log ^6(x^2 \log (3))+(16-8 x+480 x^4) \log ^7(x^2 \log (3))-180 x^3 \log ^8(x^2 \log (3))+40 x^2 \log ^9(x^2 \log (3))-4 x \log ^{10}(x^2 \log (3))}{x+5 x^4+10 x^7+10 x^{10}+5 x^{13}+x^{16}+(-10 x^3-40 x^6-60 x^9-40 x^{12}-10 x^{15}) \log (x^2 \log (3))+(5 x^2+60 x^5+150 x^8+140 x^{11}+45 x^{14}) \log ^2(x^2 \log (3))+(-40 x^4-200 x^7-280 x^{10}-120 x^{13}) \log ^3(x^2 \log (3))+(10 x^3+150 x^6+350 x^9+210 x^{12}) \log ^4(x^2 \log (3))+(-60 x^5-280 x^8-252 x^{11}) \log ^5(x^2 \log (3))+(10 x^4+140 x^7+210 x^{10}) \log ^6(x^2 \log (3))+(-40 x^6-120 x^9) \log ^7(x^2 \log (3))+(5 x^5+45 x^8) \log ^8(x^2 \log (3))-10 x^7 \log ^9(x^2 \log (3))+x^6 \log ^{10}(x^2 \log (3))} \, dx\)
Optimal. Leaf size=17 \[ \frac {1}{\left (x+\frac {1}{\left (-x+\log \left (x^2 \log (3)\right )\right )^2}\right )^4} \]
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Rubi [F] time = 62.38, 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 {-16 x^7+8 x^8-4 x^{11}+\left (112 x^6-56 x^7+40 x^{10}\right ) \log \left (x^2 \log (3)\right )+\left (-336 x^5+168 x^6-180 x^9\right ) \log ^2\left (x^2 \log (3)\right )+\left (560 x^4-280 x^5+480 x^8\right ) \log ^3\left (x^2 \log (3)\right )+\left (-560 x^3+280 x^4-840 x^7\right ) \log ^4\left (x^2 \log (3)\right )+\left (336 x^2-168 x^3+1008 x^6\right ) \log ^5\left (x^2 \log (3)\right )+\left (-112 x+56 x^2-840 x^5\right ) \log ^6\left (x^2 \log (3)\right )+\left (16-8 x+480 x^4\right ) \log ^7\left (x^2 \log (3)\right )-180 x^3 \log ^8\left (x^2 \log (3)\right )+40 x^2 \log ^9\left (x^2 \log (3)\right )-4 x \log ^{10}\left (x^2 \log (3)\right )}{x+5 x^4+10 x^7+10 x^{10}+5 x^{13}+x^{16}+\left (-10 x^3-40 x^6-60 x^9-40 x^{12}-10 x^{15}\right ) \log \left (x^2 \log (3)\right )+\left (5 x^2+60 x^5+150 x^8+140 x^{11}+45 x^{14}\right ) \log ^2\left (x^2 \log (3)\right )+\left (-40 x^4-200 x^7-280 x^{10}-120 x^{13}\right ) \log ^3\left (x^2 \log (3)\right )+\left (10 x^3+150 x^6+350 x^9+210 x^{12}\right ) \log ^4\left (x^2 \log (3)\right )+\left (-60 x^5-280 x^8-252 x^{11}\right ) \log ^5\left (x^2 \log (3)\right )+\left (10 x^4+140 x^7+210 x^{10}\right ) \log ^6\left (x^2 \log (3)\right )+\left (-40 x^6-120 x^9\right ) \log ^7\left (x^2 \log (3)\right )+\left (5 x^5+45 x^8\right ) \log ^8\left (x^2 \log (3)\right )-10 x^7 \log ^9\left (x^2 \log (3)\right )+x^6 \log ^{10}\left (x^2 \log (3)\right )} \, dx \end {gather*}
Verification is not applicable to the result.
[In]
Int[(-16*x^7 + 8*x^8 - 4*x^11 + (112*x^6 - 56*x^7 + 40*x^10)*Log[x^2*Log[3]] + (-336*x^5 + 168*x^6 - 180*x^9)*
Log[x^2*Log[3]]^2 + (560*x^4 - 280*x^5 + 480*x^8)*Log[x^2*Log[3]]^3 + (-560*x^3 + 280*x^4 - 840*x^7)*Log[x^2*L
og[3]]^4 + (336*x^2 - 168*x^3 + 1008*x^6)*Log[x^2*Log[3]]^5 + (-112*x + 56*x^2 - 840*x^5)*Log[x^2*Log[3]]^6 +
(16 - 8*x + 480*x^4)*Log[x^2*Log[3]]^7 - 180*x^3*Log[x^2*Log[3]]^8 + 40*x^2*Log[x^2*Log[3]]^9 - 4*x*Log[x^2*Lo
g[3]]^10)/(x + 5*x^4 + 10*x^7 + 10*x^10 + 5*x^13 + x^16 + (-10*x^3 - 40*x^6 - 60*x^9 - 40*x^12 - 10*x^15)*Log[
x^2*Log[3]] + (5*x^2 + 60*x^5 + 150*x^8 + 140*x^11 + 45*x^14)*Log[x^2*Log[3]]^2 + (-40*x^4 - 200*x^7 - 280*x^1
0 - 120*x^13)*Log[x^2*Log[3]]^3 + (10*x^3 + 150*x^6 + 350*x^9 + 210*x^12)*Log[x^2*Log[3]]^4 + (-60*x^5 - 280*x
^8 - 252*x^11)*Log[x^2*Log[3]]^5 + (10*x^4 + 140*x^7 + 210*x^10)*Log[x^2*Log[3]]^6 + (-40*x^6 - 120*x^9)*Log[x
^2*Log[3]]^7 + (5*x^5 + 45*x^8)*Log[x^2*Log[3]]^8 - 10*x^7*Log[x^2*Log[3]]^9 + x^6*Log[x^2*Log[3]]^10),x]
[Out]
x^(-4) + 4*Defer[Int][1/(x^5*(1 + x^3 - 2*x^2*Log[x^2*Log[3]] + x*Log[x^2*Log[3]]^2)^5), x] + 16*Defer[Int][1/
(x^3*(1 + x^3 - 2*x^2*Log[x^2*Log[3]] + x*Log[x^2*Log[3]]^2)^5), x] - 8*Defer[Int][1/(x^2*(1 + x^3 - 2*x^2*Log
[x^2*Log[3]] + x*Log[x^2*Log[3]]^2)^5), x] - 16*Defer[Int][Log[x^2*Log[3]]/(x^4*(1 + x^3 - 2*x^2*Log[x^2*Log[3
]] + x*Log[x^2*Log[3]]^2)^5), x] + 8*Defer[Int][Log[x^2*Log[3]]/(x^3*(1 + x^3 - 2*x^2*Log[x^2*Log[3]] + x*Log[
x^2*Log[3]]^2)^5), x] - 20*Defer[Int][1/(x^5*(1 + x^3 - 2*x^2*Log[x^2*Log[3]] + x*Log[x^2*Log[3]]^2)^4), x] -
48*Defer[Int][1/(x^3*(1 + x^3 - 2*x^2*Log[x^2*Log[3]] + x*Log[x^2*Log[3]]^2)^4), x] + 24*Defer[Int][1/(x^2*(1
+ x^3 - 2*x^2*Log[x^2*Log[3]] + x*Log[x^2*Log[3]]^2)^4), x] + 48*Defer[Int][Log[x^2*Log[3]]/(x^4*(1 + x^3 - 2*
x^2*Log[x^2*Log[3]] + x*Log[x^2*Log[3]]^2)^4), x] - 24*Defer[Int][Log[x^2*Log[3]]/(x^3*(1 + x^3 - 2*x^2*Log[x^
2*Log[3]] + x*Log[x^2*Log[3]]^2)^4), x] + 40*Defer[Int][1/(x^5*(1 + x^3 - 2*x^2*Log[x^2*Log[3]] + x*Log[x^2*Lo
g[3]]^2)^3), x] + 48*Defer[Int][1/(x^3*(1 + x^3 - 2*x^2*Log[x^2*Log[3]] + x*Log[x^2*Log[3]]^2)^3), x] - 24*Def
er[Int][1/(x^2*(1 + x^3 - 2*x^2*Log[x^2*Log[3]] + x*Log[x^2*Log[3]]^2)^3), x] - 48*Defer[Int][Log[x^2*Log[3]]/
(x^4*(1 + x^3 - 2*x^2*Log[x^2*Log[3]] + x*Log[x^2*Log[3]]^2)^3), x] + 24*Defer[Int][Log[x^2*Log[3]]/(x^3*(1 +
x^3 - 2*x^2*Log[x^2*Log[3]] + x*Log[x^2*Log[3]]^2)^3), x] - 40*Defer[Int][1/(x^5*(1 + x^3 - 2*x^2*Log[x^2*Log[
3]] + x*Log[x^2*Log[3]]^2)^2), x] - 16*Defer[Int][1/(x^3*(1 + x^3 - 2*x^2*Log[x^2*Log[3]] + x*Log[x^2*Log[3]]^
2)^2), x] + 8*Defer[Int][1/(x^2*(1 + x^3 - 2*x^2*Log[x^2*Log[3]] + x*Log[x^2*Log[3]]^2)^2), x] + 16*Defer[Int]
[Log[x^2*Log[3]]/(x^4*(1 + x^3 - 2*x^2*Log[x^2*Log[3]] + x*Log[x^2*Log[3]]^2)^2), x] - 8*Defer[Int][Log[x^2*Lo
g[3]]/(x^3*(1 + x^3 - 2*x^2*Log[x^2*Log[3]] + x*Log[x^2*Log[3]]^2)^2), x] + 20*Defer[Int][1/(x^5*(1 + x^3 - 2*
x^2*Log[x^2*Log[3]] + x*Log[x^2*Log[3]]^2)), x]
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {4 \left (x-\log \left (x^2 \log (3)\right )\right )^7 \left (-4+2 x-x^4+3 x^3 \log \left (x^2 \log (3)\right )-3 x^2 \log ^2\left (x^2 \log (3)\right )+x \log ^3\left (x^2 \log (3)\right )\right )}{x \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^5} \, dx\\ &=4 \int \frac {\left (x-\log \left (x^2 \log (3)\right )\right )^7 \left (-4+2 x-x^4+3 x^3 \log \left (x^2 \log (3)\right )-3 x^2 \log ^2\left (x^2 \log (3)\right )+x \log ^3\left (x^2 \log (3)\right )\right )}{x \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^5} \, dx\\ &=4 \int \left (-\frac {1}{x^5}+\frac {1+4 x^2-2 x^3-4 x \log \left (x^2 \log (3)\right )+2 x^2 \log \left (x^2 \log (3)\right )}{x^5 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^5}+\frac {-5-12 x^2+6 x^3+12 x \log \left (x^2 \log (3)\right )-6 x^2 \log \left (x^2 \log (3)\right )}{x^5 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^4}-\frac {2 \left (-5-6 x^2+3 x^3+6 x \log \left (x^2 \log (3)\right )-3 x^2 \log \left (x^2 \log (3)\right )\right )}{x^5 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^3}+\frac {2 \left (-5-2 x^2+x^3+2 x \log \left (x^2 \log (3)\right )-x^2 \log \left (x^2 \log (3)\right )\right )}{x^5 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^2}+\frac {5}{x^5 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )}\right ) \, dx\\ &=\frac {1}{x^4}+4 \int \frac {1+4 x^2-2 x^3-4 x \log \left (x^2 \log (3)\right )+2 x^2 \log \left (x^2 \log (3)\right )}{x^5 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^5} \, dx+4 \int \frac {-5-12 x^2+6 x^3+12 x \log \left (x^2 \log (3)\right )-6 x^2 \log \left (x^2 \log (3)\right )}{x^5 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^4} \, dx-8 \int \frac {-5-6 x^2+3 x^3+6 x \log \left (x^2 \log (3)\right )-3 x^2 \log \left (x^2 \log (3)\right )}{x^5 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^3} \, dx+8 \int \frac {-5-2 x^2+x^3+2 x \log \left (x^2 \log (3)\right )-x^2 \log \left (x^2 \log (3)\right )}{x^5 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^2} \, dx+20 \int \frac {1}{x^5 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )} \, dx\\ &=\frac {1}{x^4}+4 \int \frac {1+4 x^2-2 x^3+2 (-2+x) x \log \left (x^2 \log (3)\right )}{x^5 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^5} \, dx+4 \int \frac {-5-12 x^2+6 x^3-6 (-2+x) x \log \left (x^2 \log (3)\right )}{x^5 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^4} \, dx-8 \int \frac {-5-6 x^2+3 x^3-3 (-2+x) x \log \left (x^2 \log (3)\right )}{x^5 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^3} \, dx+8 \int \frac {-5-2 x^2+x^3-(-2+x) x \log \left (x^2 \log (3)\right )}{x^5 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^2} \, dx+20 \int \frac {1}{x^5 \left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}
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Mathematica [B] time = 0.10, size = 44, normalized size = 2.59 \begin {gather*} \frac {\left (x-\log \left (x^2 \log (3)\right )\right )^8}{\left (1+x^3-2 x^2 \log \left (x^2 \log (3)\right )+x \log ^2\left (x^2 \log (3)\right )\right )^4} \end {gather*}
Antiderivative was successfully verified.
[In]
Integrate[(-16*x^7 + 8*x^8 - 4*x^11 + (112*x^6 - 56*x^7 + 40*x^10)*Log[x^2*Log[3]] + (-336*x^5 + 168*x^6 - 180
*x^9)*Log[x^2*Log[3]]^2 + (560*x^4 - 280*x^5 + 480*x^8)*Log[x^2*Log[3]]^3 + (-560*x^3 + 280*x^4 - 840*x^7)*Log
[x^2*Log[3]]^4 + (336*x^2 - 168*x^3 + 1008*x^6)*Log[x^2*Log[3]]^5 + (-112*x + 56*x^2 - 840*x^5)*Log[x^2*Log[3]
]^6 + (16 - 8*x + 480*x^4)*Log[x^2*Log[3]]^7 - 180*x^3*Log[x^2*Log[3]]^8 + 40*x^2*Log[x^2*Log[3]]^9 - 4*x*Log[
x^2*Log[3]]^10)/(x + 5*x^4 + 10*x^7 + 10*x^10 + 5*x^13 + x^16 + (-10*x^3 - 40*x^6 - 60*x^9 - 40*x^12 - 10*x^15
)*Log[x^2*Log[3]] + (5*x^2 + 60*x^5 + 150*x^8 + 140*x^11 + 45*x^14)*Log[x^2*Log[3]]^2 + (-40*x^4 - 200*x^7 - 2
80*x^10 - 120*x^13)*Log[x^2*Log[3]]^3 + (10*x^3 + 150*x^6 + 350*x^9 + 210*x^12)*Log[x^2*Log[3]]^4 + (-60*x^5 -
280*x^8 - 252*x^11)*Log[x^2*Log[3]]^5 + (10*x^4 + 140*x^7 + 210*x^10)*Log[x^2*Log[3]]^6 + (-40*x^6 - 120*x^9)
*Log[x^2*Log[3]]^7 + (5*x^5 + 45*x^8)*Log[x^2*Log[3]]^8 - 10*x^7*Log[x^2*Log[3]]^9 + x^6*Log[x^2*Log[3]]^10),x
]
[Out]
(x - Log[x^2*Log[3]])^8/(1 + x^3 - 2*x^2*Log[x^2*Log[3]] + x*Log[x^2*Log[3]]^2)^4
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fricas [B] time = 0.85, size = 307, normalized size = 18.06 \begin {gather*} \frac {x^{8} - 8 \, x^{7} \log \left (x^{2} \log \relax (3)\right ) + 28 \, x^{6} \log \left (x^{2} \log \relax (3)\right )^{2} - 56 \, x^{5} \log \left (x^{2} \log \relax (3)\right )^{3} + 70 \, x^{4} \log \left (x^{2} \log \relax (3)\right )^{4} - 56 \, x^{3} \log \left (x^{2} \log \relax (3)\right )^{5} + 28 \, x^{2} \log \left (x^{2} \log \relax (3)\right )^{6} - 8 \, x \log \left (x^{2} \log \relax (3)\right )^{7} + \log \left (x^{2} \log \relax (3)\right )^{8}}{x^{12} - 8 \, x^{5} \log \left (x^{2} \log \relax (3)\right )^{7} + x^{4} \log \left (x^{2} \log \relax (3)\right )^{8} + 4 \, x^{9} + 4 \, {\left (7 \, x^{6} + x^{3}\right )} \log \left (x^{2} \log \relax (3)\right )^{6} + 6 \, x^{6} - 8 \, {\left (7 \, x^{7} + 3 \, x^{4}\right )} \log \left (x^{2} \log \relax (3)\right )^{5} + 2 \, {\left (35 \, x^{8} + 30 \, x^{5} + 3 \, x^{2}\right )} \log \left (x^{2} \log \relax (3)\right )^{4} - 8 \, {\left (7 \, x^{9} + 10 \, x^{6} + 3 \, x^{3}\right )} \log \left (x^{2} \log \relax (3)\right )^{3} + 4 \, x^{3} + 4 \, {\left (7 \, x^{10} + 15 \, x^{7} + 9 \, x^{4} + x\right )} \log \left (x^{2} \log \relax (3)\right )^{2} - 8 \, {\left (x^{11} + 3 \, x^{8} + 3 \, x^{5} + x^{2}\right )} \log \left (x^{2} \log \relax (3)\right ) + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((-4*x*log(x^2*log(3))^10+40*x^2*log(x^2*log(3))^9-180*x^3*log(x^2*log(3))^8+(480*x^4-8*x+16)*log(x^2
*log(3))^7+(-840*x^5+56*x^2-112*x)*log(x^2*log(3))^6+(1008*x^6-168*x^3+336*x^2)*log(x^2*log(3))^5+(-840*x^7+28
0*x^4-560*x^3)*log(x^2*log(3))^4+(480*x^8-280*x^5+560*x^4)*log(x^2*log(3))^3+(-180*x^9+168*x^6-336*x^5)*log(x^
2*log(3))^2+(40*x^10-56*x^7+112*x^6)*log(x^2*log(3))-4*x^11+8*x^8-16*x^7)/(x^6*log(x^2*log(3))^10-10*x^7*log(x
^2*log(3))^9+(45*x^8+5*x^5)*log(x^2*log(3))^8+(-120*x^9-40*x^6)*log(x^2*log(3))^7+(210*x^10+140*x^7+10*x^4)*lo
g(x^2*log(3))^6+(-252*x^11-280*x^8-60*x^5)*log(x^2*log(3))^5+(210*x^12+350*x^9+150*x^6+10*x^3)*log(x^2*log(3))
^4+(-120*x^13-280*x^10-200*x^7-40*x^4)*log(x^2*log(3))^3+(45*x^14+140*x^11+150*x^8+60*x^5+5*x^2)*log(x^2*log(3
))^2+(-10*x^15-40*x^12-60*x^9-40*x^6-10*x^3)*log(x^2*log(3))+x^16+5*x^13+10*x^10+10*x^7+5*x^4+x),x, algorithm=
"fricas")
[Out]
(x^8 - 8*x^7*log(x^2*log(3)) + 28*x^6*log(x^2*log(3))^2 - 56*x^5*log(x^2*log(3))^3 + 70*x^4*log(x^2*log(3))^4
- 56*x^3*log(x^2*log(3))^5 + 28*x^2*log(x^2*log(3))^6 - 8*x*log(x^2*log(3))^7 + log(x^2*log(3))^8)/(x^12 - 8*x
^5*log(x^2*log(3))^7 + x^4*log(x^2*log(3))^8 + 4*x^9 + 4*(7*x^6 + x^3)*log(x^2*log(3))^6 + 6*x^6 - 8*(7*x^7 +
3*x^4)*log(x^2*log(3))^5 + 2*(35*x^8 + 30*x^5 + 3*x^2)*log(x^2*log(3))^4 - 8*(7*x^9 + 10*x^6 + 3*x^3)*log(x^2*
log(3))^3 + 4*x^3 + 4*(7*x^10 + 15*x^7 + 9*x^4 + x)*log(x^2*log(3))^2 - 8*(x^11 + 3*x^8 + 3*x^5 + x^2)*log(x^2
*log(3)) + 1)
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giac [B] time = 9.93, size = 478, normalized size = 28.12 \begin {gather*} -\frac {4 \, x^{9} - 24 \, x^{8} \log \left (x^{2} \log \relax (3)\right ) + 60 \, x^{7} \log \left (x^{2} \log \relax (3)\right )^{2} - 80 \, x^{6} \log \left (x^{2} \log \relax (3)\right )^{3} + 60 \, x^{5} \log \left (x^{2} \log \relax (3)\right )^{4} - 24 \, x^{4} \log \left (x^{2} \log \relax (3)\right )^{5} + 4 \, x^{3} \log \left (x^{2} \log \relax (3)\right )^{6} + 6 \, x^{6} - 24 \, x^{5} \log \left (x^{2} \log \relax (3)\right ) + 36 \, x^{4} \log \left (x^{2} \log \relax (3)\right )^{2} - 24 \, x^{3} \log \left (x^{2} \log \relax (3)\right )^{3} + 6 \, x^{2} \log \left (x^{2} \log \relax (3)\right )^{4} + 4 \, x^{3} - 8 \, x^{2} \log \left (x^{2} \log \relax (3)\right ) + 4 \, x \log \left (x^{2} \log \relax (3)\right )^{2} + 1}{x^{16} - 8 \, x^{15} \log \left (x^{2} \log \relax (3)\right ) + 28 \, x^{14} \log \left (x^{2} \log \relax (3)\right )^{2} - 56 \, x^{13} \log \left (x^{2} \log \relax (3)\right )^{3} + 70 \, x^{12} \log \left (x^{2} \log \relax (3)\right )^{4} - 56 \, x^{11} \log \left (x^{2} \log \relax (3)\right )^{5} + 28 \, x^{10} \log \left (x^{2} \log \relax (3)\right )^{6} - 8 \, x^{9} \log \left (x^{2} \log \relax (3)\right )^{7} + x^{8} \log \left (x^{2} \log \relax (3)\right )^{8} + 4 \, x^{13} - 24 \, x^{12} \log \left (x^{2} \log \relax (3)\right ) + 60 \, x^{11} \log \left (x^{2} \log \relax (3)\right )^{2} - 80 \, x^{10} \log \left (x^{2} \log \relax (3)\right )^{3} + 60 \, x^{9} \log \left (x^{2} \log \relax (3)\right )^{4} - 24 \, x^{8} \log \left (x^{2} \log \relax (3)\right )^{5} + 4 \, x^{7} \log \left (x^{2} \log \relax (3)\right )^{6} + 6 \, x^{10} - 24 \, x^{9} \log \left (x^{2} \log \relax (3)\right ) + 36 \, x^{8} \log \left (x^{2} \log \relax (3)\right )^{2} - 24 \, x^{7} \log \left (x^{2} \log \relax (3)\right )^{3} + 6 \, x^{6} \log \left (x^{2} \log \relax (3)\right )^{4} + 4 \, x^{7} - 8 \, x^{6} \log \left (x^{2} \log \relax (3)\right ) + 4 \, x^{5} \log \left (x^{2} \log \relax (3)\right )^{2} + x^{4}} + \frac {1}{x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((-4*x*log(x^2*log(3))^10+40*x^2*log(x^2*log(3))^9-180*x^3*log(x^2*log(3))^8+(480*x^4-8*x+16)*log(x^2
*log(3))^7+(-840*x^5+56*x^2-112*x)*log(x^2*log(3))^6+(1008*x^6-168*x^3+336*x^2)*log(x^2*log(3))^5+(-840*x^7+28
0*x^4-560*x^3)*log(x^2*log(3))^4+(480*x^8-280*x^5+560*x^4)*log(x^2*log(3))^3+(-180*x^9+168*x^6-336*x^5)*log(x^
2*log(3))^2+(40*x^10-56*x^7+112*x^6)*log(x^2*log(3))-4*x^11+8*x^8-16*x^7)/(x^6*log(x^2*log(3))^10-10*x^7*log(x
^2*log(3))^9+(45*x^8+5*x^5)*log(x^2*log(3))^8+(-120*x^9-40*x^6)*log(x^2*log(3))^7+(210*x^10+140*x^7+10*x^4)*lo
g(x^2*log(3))^6+(-252*x^11-280*x^8-60*x^5)*log(x^2*log(3))^5+(210*x^12+350*x^9+150*x^6+10*x^3)*log(x^2*log(3))
^4+(-120*x^13-280*x^10-200*x^7-40*x^4)*log(x^2*log(3))^3+(45*x^14+140*x^11+150*x^8+60*x^5+5*x^2)*log(x^2*log(3
))^2+(-10*x^15-40*x^12-60*x^9-40*x^6-10*x^3)*log(x^2*log(3))+x^16+5*x^13+10*x^10+10*x^7+5*x^4+x),x, algorithm=
"giac")
[Out]
-(4*x^9 - 24*x^8*log(x^2*log(3)) + 60*x^7*log(x^2*log(3))^2 - 80*x^6*log(x^2*log(3))^3 + 60*x^5*log(x^2*log(3)
)^4 - 24*x^4*log(x^2*log(3))^5 + 4*x^3*log(x^2*log(3))^6 + 6*x^6 - 24*x^5*log(x^2*log(3)) + 36*x^4*log(x^2*log
(3))^2 - 24*x^3*log(x^2*log(3))^3 + 6*x^2*log(x^2*log(3))^4 + 4*x^3 - 8*x^2*log(x^2*log(3)) + 4*x*log(x^2*log(
3))^2 + 1)/(x^16 - 8*x^15*log(x^2*log(3)) + 28*x^14*log(x^2*log(3))^2 - 56*x^13*log(x^2*log(3))^3 + 70*x^12*lo
g(x^2*log(3))^4 - 56*x^11*log(x^2*log(3))^5 + 28*x^10*log(x^2*log(3))^6 - 8*x^9*log(x^2*log(3))^7 + x^8*log(x^
2*log(3))^8 + 4*x^13 - 24*x^12*log(x^2*log(3)) + 60*x^11*log(x^2*log(3))^2 - 80*x^10*log(x^2*log(3))^3 + 60*x^
9*log(x^2*log(3))^4 - 24*x^8*log(x^2*log(3))^5 + 4*x^7*log(x^2*log(3))^6 + 6*x^10 - 24*x^9*log(x^2*log(3)) + 3
6*x^8*log(x^2*log(3))^2 - 24*x^7*log(x^2*log(3))^3 + 6*x^6*log(x^2*log(3))^4 + 4*x^7 - 8*x^6*log(x^2*log(3)) +
4*x^5*log(x^2*log(3))^2 + x^4) + 1/x^4
________________________________________________________________________________________
maple [B] time = 0.22, size = 217, normalized size = 12.76
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\(\frac {1}{x^{4}}-\frac {4 x^{9}-24 \ln \left (x^{2} \ln \relax (3)\right ) x^{8}+60 \ln \left (x^{2} \ln \relax (3)\right )^{2} x^{7}-80 \ln \left (x^{2} \ln \relax (3)\right )^{3} x^{6}+60 \ln \left (x^{2} \ln \relax (3)\right )^{4} x^{5}-24 x^{4} \ln \left (x^{2} \ln \relax (3)\right )^{5}+4 x^{3} \ln \left (x^{2} \ln \relax (3)\right )^{6}+6 x^{6}-24 x^{5} \ln \left (x^{2} \ln \relax (3)\right )+36 x^{4} \ln \left (x^{2} \ln \relax (3)\right )^{2}-24 x^{3} \ln \left (x^{2} \ln \relax (3)\right )^{3}+6 x^{2} \ln \left (x^{2} \ln \relax (3)\right )^{4}+4 x^{3}-8 x^{2} \ln \left (x^{2} \ln \relax (3)\right )+4 x \ln \left (x^{2} \ln \relax (3)\right )^{2}+1}{x^{4} \left (x \ln \left (x^{2} \ln \relax (3)\right )^{2}-2 x^{2} \ln \left (x^{2} \ln \relax (3)\right )+x^{3}+1\right )^{4}}\) |
\(217\) |
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Verification of antiderivative is not currently implemented for this CAS.
[In]
int((-4*x*ln(x^2*ln(3))^10+40*x^2*ln(x^2*ln(3))^9-180*x^3*ln(x^2*ln(3))^8+(480*x^4-8*x+16)*ln(x^2*ln(3))^7+(-8
40*x^5+56*x^2-112*x)*ln(x^2*ln(3))^6+(1008*x^6-168*x^3+336*x^2)*ln(x^2*ln(3))^5+(-840*x^7+280*x^4-560*x^3)*ln(
x^2*ln(3))^4+(480*x^8-280*x^5+560*x^4)*ln(x^2*ln(3))^3+(-180*x^9+168*x^6-336*x^5)*ln(x^2*ln(3))^2+(40*x^10-56*
x^7+112*x^6)*ln(x^2*ln(3))-4*x^11+8*x^8-16*x^7)/(x^6*ln(x^2*ln(3))^10-10*x^7*ln(x^2*ln(3))^9+(45*x^8+5*x^5)*ln
(x^2*ln(3))^8+(-120*x^9-40*x^6)*ln(x^2*ln(3))^7+(210*x^10+140*x^7+10*x^4)*ln(x^2*ln(3))^6+(-252*x^11-280*x^8-6
0*x^5)*ln(x^2*ln(3))^5+(210*x^12+350*x^9+150*x^6+10*x^3)*ln(x^2*ln(3))^4+(-120*x^13-280*x^10-200*x^7-40*x^4)*l
n(x^2*ln(3))^3+(45*x^14+140*x^11+150*x^8+60*x^5+5*x^2)*ln(x^2*ln(3))^2+(-10*x^15-40*x^12-60*x^9-40*x^6-10*x^3)
*ln(x^2*ln(3))+x^16+5*x^13+10*x^10+10*x^7+5*x^4+x),x,method=_RETURNVERBOSE)
[Out]
1/x^4-(4*x^9-24*ln(x^2*ln(3))*x^8+60*ln(x^2*ln(3))^2*x^7-80*ln(x^2*ln(3))^3*x^6+60*ln(x^2*ln(3))^4*x^5-24*x^4*
ln(x^2*ln(3))^5+4*x^3*ln(x^2*ln(3))^6+6*x^6-24*x^5*ln(x^2*ln(3))+36*x^4*ln(x^2*ln(3))^2-24*x^3*ln(x^2*ln(3))^3
+6*x^2*ln(x^2*ln(3))^4+4*x^3-8*x^2*ln(x^2*ln(3))+4*x*ln(x^2*ln(3))^2+1)/x^4/(x*ln(x^2*ln(3))^2-2*x^2*ln(x^2*ln
(3))+x^3+1)^4
________________________________________________________________________________________
maxima [B] time = 1.31, size = 1150, normalized size = 67.65 result too large to
display
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((-4*x*log(x^2*log(3))^10+40*x^2*log(x^2*log(3))^9-180*x^3*log(x^2*log(3))^8+(480*x^4-8*x+16)*log(x^2
*log(3))^7+(-840*x^5+56*x^2-112*x)*log(x^2*log(3))^6+(1008*x^6-168*x^3+336*x^2)*log(x^2*log(3))^5+(-840*x^7+28
0*x^4-560*x^3)*log(x^2*log(3))^4+(480*x^8-280*x^5+560*x^4)*log(x^2*log(3))^3+(-180*x^9+168*x^6-336*x^5)*log(x^
2*log(3))^2+(40*x^10-56*x^7+112*x^6)*log(x^2*log(3))-4*x^11+8*x^8-16*x^7)/(x^6*log(x^2*log(3))^10-10*x^7*log(x
^2*log(3))^9+(45*x^8+5*x^5)*log(x^2*log(3))^8+(-120*x^9-40*x^6)*log(x^2*log(3))^7+(210*x^10+140*x^7+10*x^4)*lo
g(x^2*log(3))^6+(-252*x^11-280*x^8-60*x^5)*log(x^2*log(3))^5+(210*x^12+350*x^9+150*x^6+10*x^3)*log(x^2*log(3))
^4+(-120*x^13-280*x^10-200*x^7-40*x^4)*log(x^2*log(3))^3+(45*x^14+140*x^11+150*x^8+60*x^5+5*x^2)*log(x^2*log(3
))^2+(-10*x^15-40*x^12-60*x^9-40*x^6-10*x^3)*log(x^2*log(3))+x^16+5*x^13+10*x^10+10*x^7+5*x^4+x),x, algorithm=
"maxima")
[Out]
(x^8 - 1024*(x - log(log(3)))*log(x)^7 + 256*log(x)^8 - 8*x^7*log(log(3)) + 28*x^6*log(log(3))^2 - 56*x^5*log(
log(3))^3 + 70*x^4*log(log(3))^4 - 56*x^3*log(log(3))^5 + 28*x^2*log(log(3))^6 - 8*x*log(log(3))^7 + log(log(3
))^8 + 1792*(x^2 - 2*x*log(log(3)) + log(log(3))^2)*log(x)^6 - 1792*(x^3 - 3*x^2*log(log(3)) + 3*x*log(log(3))
^2 - log(log(3))^3)*log(x)^5 + 1120*(x^4 - 4*x^3*log(log(3)) + 6*x^2*log(log(3))^2 - 4*x*log(log(3))^3 + log(l
og(3))^4)*log(x)^4 - 448*(x^5 - 5*x^4*log(log(3)) + 10*x^3*log(log(3))^2 - 10*x^2*log(log(3))^3 + 5*x*log(log(
3))^4 - log(log(3))^5)*log(x)^3 + 112*(x^6 - 6*x^5*log(log(3)) + 15*x^4*log(log(3))^2 - 20*x^3*log(log(3))^3 +
15*x^2*log(log(3))^4 - 6*x*log(log(3))^5 + log(log(3))^6)*log(x)^2 - 16*(x^7 - 7*x^6*log(log(3)) + 21*x^5*log
(log(3))^2 - 35*x^4*log(log(3))^3 + 35*x^3*log(log(3))^4 - 21*x^2*log(log(3))^5 + 7*x*log(log(3))^6 - log(log(
3))^7)*log(x))/(x^12 + 256*x^4*log(x)^8 - 8*x^11*log(log(3)) + 28*x^10*log(log(3))^2 - 4*(14*log(log(3))^3 - 1
)*x^9 + 2*(35*log(log(3))^4 - 12*log(log(3)))*x^8 - 4*(14*log(log(3))^5 - 15*log(log(3))^2)*x^7 - 1024*(x^5 -
x^4*log(log(3)))*log(x)^7 + 2*(14*log(log(3))^6 - 40*log(log(3))^3 + 3)*x^6 + 256*(7*x^6 - 14*x^5*log(log(3))
+ 7*x^4*log(log(3))^2 + x^3)*log(x)^6 - 4*(2*log(log(3))^7 - 15*log(log(3))^4 + 6*log(log(3)))*x^5 - 256*(7*x^
7 - 21*x^6*log(log(3)) + 21*x^5*log(log(3))^2 - (7*log(log(3))^3 - 3)*x^4 - 3*x^3*log(log(3)))*log(x)^5 + (log
(log(3))^8 - 24*log(log(3))^5 + 36*log(log(3))^2)*x^4 + 32*(35*x^8 - 140*x^7*log(log(3)) + 210*x^6*log(log(3))
^2 - 10*(14*log(log(3))^3 - 3)*x^5 + 5*(7*log(log(3))^4 - 12*log(log(3)))*x^4 + 30*x^3*log(log(3))^2 + 3*x^2)*
log(x)^4 + 4*(log(log(3))^6 - 6*log(log(3))^3 + 1)*x^3 - 64*(7*x^9 - 35*x^8*log(log(3)) + 70*x^7*log(log(3))^2
- 10*(7*log(log(3))^3 - 1)*x^6 + 5*(7*log(log(3))^4 - 6*log(log(3)))*x^5 - (7*log(log(3))^5 - 30*log(log(3))^
2)*x^4 - (10*log(log(3))^3 - 3)*x^3 - 3*x^2*log(log(3)))*log(x)^3 + 2*(3*log(log(3))^4 - 4*log(log(3)))*x^2 +
16*(7*x^10 - 42*x^9*log(log(3)) + 105*x^8*log(log(3))^2 - 5*(28*log(log(3))^3 - 3)*x^7 + 15*(7*log(log(3))^4 -
4*log(log(3)))*x^6 - 6*(7*log(log(3))^5 - 15*log(log(3))^2)*x^5 + (7*log(log(3))^6 - 60*log(log(3))^3 + 9)*x^
4 + 3*(5*log(log(3))^4 - 6*log(log(3)))*x^3 + 9*x^2*log(log(3))^2 + x)*log(x)^2 + 4*x*log(log(3))^2 - 16*(x^11
- 7*x^10*log(log(3)) + 21*x^9*log(log(3))^2 - (35*log(log(3))^3 - 3)*x^8 + 5*(7*log(log(3))^4 - 3*log(log(3))
)*x^7 - 3*(7*log(log(3))^5 - 10*log(log(3))^2)*x^6 + (7*log(log(3))^6 - 30*log(log(3))^3 + 3)*x^5 - (log(log(3
))^7 - 15*log(log(3))^4 + 9*log(log(3)))*x^4 - 3*(log(log(3))^5 - 3*log(log(3))^2)*x^3 - (3*log(log(3))^3 - 1)
*x^2 - x*log(log(3)))*log(x) + 1)
________________________________________________________________________________________
mupad [F] time = 0.00, size = -1, normalized size = -0.06 \begin {gather*} \int -\frac {4\,x\,{\ln \left (x^2\,\ln \relax (3)\right )}^{10}-{\ln \left (x^2\,\ln \relax (3)\right )}^7\,\left (480\,x^4-8\,x+16\right )-\ln \left (x^2\,\ln \relax (3)\right )\,\left (40\,x^{10}-56\,x^7+112\,x^6\right )+{\ln \left (x^2\,\ln \relax (3)\right )}^6\,\left (840\,x^5-56\,x^2+112\,x\right )-40\,x^2\,{\ln \left (x^2\,\ln \relax (3)\right )}^9+180\,x^3\,{\ln \left (x^2\,\ln \relax (3)\right )}^8+{\ln \left (x^2\,\ln \relax (3)\right )}^2\,\left (180\,x^9-168\,x^6+336\,x^5\right )-{\ln \left (x^2\,\ln \relax (3)\right )}^3\,\left (480\,x^8-280\,x^5+560\,x^4\right )-{\ln \left (x^2\,\ln \relax (3)\right )}^5\,\left (1008\,x^6-168\,x^3+336\,x^2\right )+{\ln \left (x^2\,\ln \relax (3)\right )}^4\,\left (840\,x^7-280\,x^4+560\,x^3\right )+16\,x^7-8\,x^8+4\,x^{11}}{x-{\ln \left (x^2\,\ln \relax (3)\right )}^3\,\left (120\,x^{13}+280\,x^{10}+200\,x^7+40\,x^4\right )+{\ln \left (x^2\,\ln \relax (3)\right )}^4\,\left (210\,x^{12}+350\,x^9+150\,x^6+10\,x^3\right )+{\ln \left (x^2\,\ln \relax (3)\right )}^2\,\left (45\,x^{14}+140\,x^{11}+150\,x^8+60\,x^5+5\,x^2\right )+{\ln \left (x^2\,\ln \relax (3)\right )}^8\,\left (45\,x^8+5\,x^5\right )-{\ln \left (x^2\,\ln \relax (3)\right )}^7\,\left (120\,x^9+40\,x^6\right )+x^6\,{\ln \left (x^2\,\ln \relax (3)\right )}^{10}-10\,x^7\,{\ln \left (x^2\,\ln \relax (3)\right )}^9+{\ln \left (x^2\,\ln \relax (3)\right )}^6\,\left (210\,x^{10}+140\,x^7+10\,x^4\right )-{\ln \left (x^2\,\ln \relax (3)\right )}^5\,\left (252\,x^{11}+280\,x^8+60\,x^5\right )+5\,x^4+10\,x^7+10\,x^{10}+5\,x^{13}+x^{16}-\ln \left (x^2\,\ln \relax (3)\right )\,\left (10\,x^{15}+40\,x^{12}+60\,x^9+40\,x^6+10\,x^3\right )} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
int(-(4*x*log(x^2*log(3))^10 - log(x^2*log(3))^7*(480*x^4 - 8*x + 16) - log(x^2*log(3))*(112*x^6 - 56*x^7 + 40
*x^10) + log(x^2*log(3))^6*(112*x - 56*x^2 + 840*x^5) - 40*x^2*log(x^2*log(3))^9 + 180*x^3*log(x^2*log(3))^8 +
log(x^2*log(3))^2*(336*x^5 - 168*x^6 + 180*x^9) - log(x^2*log(3))^3*(560*x^4 - 280*x^5 + 480*x^8) - log(x^2*l
og(3))^5*(336*x^2 - 168*x^3 + 1008*x^6) + log(x^2*log(3))^4*(560*x^3 - 280*x^4 + 840*x^7) + 16*x^7 - 8*x^8 + 4
*x^11)/(x - log(x^2*log(3))^3*(40*x^4 + 200*x^7 + 280*x^10 + 120*x^13) + log(x^2*log(3))^4*(10*x^3 + 150*x^6 +
350*x^9 + 210*x^12) + log(x^2*log(3))^2*(5*x^2 + 60*x^5 + 150*x^8 + 140*x^11 + 45*x^14) + log(x^2*log(3))^8*(
5*x^5 + 45*x^8) - log(x^2*log(3))^7*(40*x^6 + 120*x^9) + x^6*log(x^2*log(3))^10 - 10*x^7*log(x^2*log(3))^9 + l
og(x^2*log(3))^6*(10*x^4 + 140*x^7 + 210*x^10) - log(x^2*log(3))^5*(60*x^5 + 280*x^8 + 252*x^11) + 5*x^4 + 10*
x^7 + 10*x^10 + 5*x^13 + x^16 - log(x^2*log(3))*(10*x^3 + 40*x^6 + 60*x^9 + 40*x^12 + 10*x^15)),x)
[Out]
int(-(4*x*log(x^2*log(3))^10 - log(x^2*log(3))^7*(480*x^4 - 8*x + 16) - log(x^2*log(3))*(112*x^6 - 56*x^7 + 40
*x^10) + log(x^2*log(3))^6*(112*x - 56*x^2 + 840*x^5) - 40*x^2*log(x^2*log(3))^9 + 180*x^3*log(x^2*log(3))^8 +
log(x^2*log(3))^2*(336*x^5 - 168*x^6 + 180*x^9) - log(x^2*log(3))^3*(560*x^4 - 280*x^5 + 480*x^8) - log(x^2*l
og(3))^5*(336*x^2 - 168*x^3 + 1008*x^6) + log(x^2*log(3))^4*(560*x^3 - 280*x^4 + 840*x^7) + 16*x^7 - 8*x^8 + 4
*x^11)/(x - log(x^2*log(3))^3*(40*x^4 + 200*x^7 + 280*x^10 + 120*x^13) + log(x^2*log(3))^4*(10*x^3 + 150*x^6 +
350*x^9 + 210*x^12) + log(x^2*log(3))^2*(5*x^2 + 60*x^5 + 150*x^8 + 140*x^11 + 45*x^14) + log(x^2*log(3))^8*(
5*x^5 + 45*x^8) - log(x^2*log(3))^7*(40*x^6 + 120*x^9) + x^6*log(x^2*log(3))^10 - 10*x^7*log(x^2*log(3))^9 + l
og(x^2*log(3))^6*(10*x^4 + 140*x^7 + 210*x^10) - log(x^2*log(3))^5*(60*x^5 + 280*x^8 + 252*x^11) + 5*x^4 + 10*
x^7 + 10*x^10 + 5*x^13 + x^16 - log(x^2*log(3))*(10*x^3 + 40*x^6 + 60*x^9 + 40*x^12 + 10*x^15)), x)
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sympy [B] time = 3.54, size = 350, normalized size = 20.59 \begin {gather*} \frac {- 4 x^{9} - 6 x^{6} + 24 x^{4} \log {\left (x^{2} \log {\relax (3 )} \right )}^{5} - 4 x^{3} \log {\left (x^{2} \log {\relax (3 )} \right )}^{6} - 4 x^{3} + \left (- 60 x^{5} - 6 x^{2}\right ) \log {\left (x^{2} \log {\relax (3 )} \right )}^{4} + \left (80 x^{6} + 24 x^{3}\right ) \log {\left (x^{2} \log {\relax (3 )} \right )}^{3} + \left (- 60 x^{7} - 36 x^{4} - 4 x\right ) \log {\left (x^{2} \log {\relax (3 )} \right )}^{2} + \left (24 x^{8} + 24 x^{5} + 8 x^{2}\right ) \log {\left (x^{2} \log {\relax (3 )} \right )} - 1}{x^{16} + 4 x^{13} + 6 x^{10} - 8 x^{9} \log {\left (x^{2} \log {\relax (3 )} \right )}^{7} + x^{8} \log {\left (x^{2} \log {\relax (3 )} \right )}^{8} + 4 x^{7} + x^{4} + \left (28 x^{10} + 4 x^{7}\right ) \log {\left (x^{2} \log {\relax (3 )} \right )}^{6} + \left (- 56 x^{11} - 24 x^{8}\right ) \log {\left (x^{2} \log {\relax (3 )} \right )}^{5} + \left (70 x^{12} + 60 x^{9} + 6 x^{6}\right ) \log {\left (x^{2} \log {\relax (3 )} \right )}^{4} + \left (- 56 x^{13} - 80 x^{10} - 24 x^{7}\right ) \log {\left (x^{2} \log {\relax (3 )} \right )}^{3} + \left (28 x^{14} + 60 x^{11} + 36 x^{8} + 4 x^{5}\right ) \log {\left (x^{2} \log {\relax (3 )} \right )}^{2} + \left (- 8 x^{15} - 24 x^{12} - 24 x^{9} - 8 x^{6}\right ) \log {\left (x^{2} \log {\relax (3 )} \right )}} + \frac {1}{x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((-4*x*ln(x**2*ln(3))**10+40*x**2*ln(x**2*ln(3))**9-180*x**3*ln(x**2*ln(3))**8+(480*x**4-8*x+16)*ln(x
**2*ln(3))**7+(-840*x**5+56*x**2-112*x)*ln(x**2*ln(3))**6+(1008*x**6-168*x**3+336*x**2)*ln(x**2*ln(3))**5+(-84
0*x**7+280*x**4-560*x**3)*ln(x**2*ln(3))**4+(480*x**8-280*x**5+560*x**4)*ln(x**2*ln(3))**3+(-180*x**9+168*x**6
-336*x**5)*ln(x**2*ln(3))**2+(40*x**10-56*x**7+112*x**6)*ln(x**2*ln(3))-4*x**11+8*x**8-16*x**7)/(x**6*ln(x**2*
ln(3))**10-10*x**7*ln(x**2*ln(3))**9+(45*x**8+5*x**5)*ln(x**2*ln(3))**8+(-120*x**9-40*x**6)*ln(x**2*ln(3))**7+
(210*x**10+140*x**7+10*x**4)*ln(x**2*ln(3))**6+(-252*x**11-280*x**8-60*x**5)*ln(x**2*ln(3))**5+(210*x**12+350*
x**9+150*x**6+10*x**3)*ln(x**2*ln(3))**4+(-120*x**13-280*x**10-200*x**7-40*x**4)*ln(x**2*ln(3))**3+(45*x**14+1
40*x**11+150*x**8+60*x**5+5*x**2)*ln(x**2*ln(3))**2+(-10*x**15-40*x**12-60*x**9-40*x**6-10*x**3)*ln(x**2*ln(3)
)+x**16+5*x**13+10*x**10+10*x**7+5*x**4+x),x)
[Out]
(-4*x**9 - 6*x**6 + 24*x**4*log(x**2*log(3))**5 - 4*x**3*log(x**2*log(3))**6 - 4*x**3 + (-60*x**5 - 6*x**2)*lo
g(x**2*log(3))**4 + (80*x**6 + 24*x**3)*log(x**2*log(3))**3 + (-60*x**7 - 36*x**4 - 4*x)*log(x**2*log(3))**2 +
(24*x**8 + 24*x**5 + 8*x**2)*log(x**2*log(3)) - 1)/(x**16 + 4*x**13 + 6*x**10 - 8*x**9*log(x**2*log(3))**7 +
x**8*log(x**2*log(3))**8 + 4*x**7 + x**4 + (28*x**10 + 4*x**7)*log(x**2*log(3))**6 + (-56*x**11 - 24*x**8)*log
(x**2*log(3))**5 + (70*x**12 + 60*x**9 + 6*x**6)*log(x**2*log(3))**4 + (-56*x**13 - 80*x**10 - 24*x**7)*log(x*
*2*log(3))**3 + (28*x**14 + 60*x**11 + 36*x**8 + 4*x**5)*log(x**2*log(3))**2 + (-8*x**15 - 24*x**12 - 24*x**9
- 8*x**6)*log(x**2*log(3))) + x**(-4)
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