3.28.37 \(\int \frac {-48 x^2+12 x^3+(16+28 x-8 x^2+(16-4 x) \log (x)) \log (\log (2))+(4 x^2+3 x^3+(-4 x-3 x^2+(-4-3 x) \log (x)) \log (\log (2))) \log (\frac {x^3+(-x^2-x \log (x)) \log (\log (2))}{\log (\log (2))})}{(1024 x^2-1280 x^3+640 x^4-160 x^5+20 x^6-x^7+(-1024 x+1280 x^2-640 x^3+160 x^4-20 x^5+x^6+(-1024+1280 x-640 x^2+160 x^3-20 x^4+x^5) \log (x)) \log (\log (2))) \log ^5(\frac {x^3+(-x^2-x \log (x)) \log (\log (2))}{\log (\log (2))})} \, dx\)

Optimal. Leaf size=29 \[ \frac {x}{(-4+x)^4 \log ^4\left (x \left (-x-\log (x)+\frac {x^2}{\log (\log (2))}\right )\right )} \]

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Rubi [F]  time = 16.22, 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 {-48 x^2+12 x^3+\left (16+28 x-8 x^2+(16-4 x) \log (x)\right ) \log (\log (2))+\left (4 x^2+3 x^3+\left (-4 x-3 x^2+(-4-3 x) \log (x)\right ) \log (\log (2))\right ) \log \left (\frac {x^3+\left (-x^2-x \log (x)\right ) \log (\log (2))}{\log (\log (2))}\right )}{\left (1024 x^2-1280 x^3+640 x^4-160 x^5+20 x^6-x^7+\left (-1024 x+1280 x^2-640 x^3+160 x^4-20 x^5+x^6+\left (-1024+1280 x-640 x^2+160 x^3-20 x^4+x^5\right ) \log (x)\right ) \log (\log (2))\right ) \log ^5\left (\frac {x^3+\left (-x^2-x \log (x)\right ) \log (\log (2))}{\log (\log (2))}\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-48*x^2 + 12*x^3 + (16 + 28*x - 8*x^2 + (16 - 4*x)*Log[x])*Log[Log[2]] + (4*x^2 + 3*x^3 + (-4*x - 3*x^2 +
(-4 - 3*x)*Log[x])*Log[Log[2]])*Log[(x^3 + (-x^2 - x*Log[x])*Log[Log[2]])/Log[Log[2]]])/((1024*x^2 - 1280*x^3
+ 640*x^4 - 160*x^5 + 20*x^6 - x^7 + (-1024*x + 1280*x^2 - 640*x^3 + 160*x^4 - 20*x^5 + x^6 + (-1024 + 1280*x
- 640*x^2 + 160*x^3 - 20*x^4 + x^5)*Log[x])*Log[Log[2]])*Log[(x^3 + (-x^2 - x*Log[x])*Log[Log[2]])/Log[Log[2]
]]^5),x]

[Out]

768*Defer[Int][1/((4 - x)^5*(x^2 - x*Log[Log[2]] - Log[x]*Log[Log[2]])*Log[-(x*Log[x]) + x^2*(-1 + x/Log[Log[2
]])]^5), x] + 128*Log[Log[2]]*Defer[Int][1/((4 - x)^5*(x^2 - x*Log[Log[2]] - Log[x]*Log[Log[2]])*Log[-(x*Log[x
]) + x^2*(-1 + x/Log[Log[2]])]^5), x] + 64*(6 + Log[Log[2]])*Defer[Int][1/((4 - x)^4*(x^2 - x*Log[Log[2]] - Lo
g[x]*Log[Log[2]])*Log[-(x*Log[x]) + x^2*(-1 + x/Log[Log[2]])]^5), x] + 144*Defer[Int][1/((4 - x)^3*(x^2 - x*Lo
g[Log[2]] - Log[x]*Log[Log[2]])*Log[-(x*Log[x]) + x^2*(-1 + x/Log[Log[2]])]^5), x] + 128*(6 + Log[Log[2]])*Def
er[Int][1/((-4 + x)^5*(x^2 - x*Log[Log[2]] - Log[x]*Log[Log[2]])*Log[-(x*Log[x]) + x^2*(-1 + x/Log[Log[2]])]^5
), x] + 8*(6 + Log[Log[2]])*Defer[Int][1/((-4 + x)^3*(x^2 - x*Log[Log[2]] - Log[x]*Log[Log[2]])*Log[-(x*Log[x]
) + x^2*(-1 + x/Log[Log[2]])]^5), x] + 16*Log[Log[2]]*Defer[Int][Log[x]/((4 - x)^5*(x^2 - x*Log[Log[2]] - Log[
x]*Log[Log[2]])*Log[-(x*Log[x]) + x^2*(-1 + x/Log[Log[2]])]^5), x] + 4*Log[Log[2]]*Defer[Int][Log[x]/((4 - x)^
4*(x^2 - x*Log[Log[2]] - Log[x]*Log[Log[2]])*Log[-(x*Log[x]) + x^2*(-1 + x/Log[Log[2]])]^5), x] + 16*Log[Log[2
]]*Defer[Int][Log[x]/((-4 + x)^5*(x^2 - x*Log[Log[2]] - Log[x]*Log[Log[2]])*Log[-(x*Log[x]) + x^2*(-1 + x/Log[
Log[2]])]^5), x] + 576*Defer[Int][1/((4 - x)^4*(-x^2 + x*Log[Log[2]] + Log[x]*Log[Log[2]])*Log[-(x*Log[x]) + x
^2*(-1 + x/Log[Log[2]])]^5), x] + 28*Log[Log[2]]*Defer[Int][1/((4 - x)^4*(-x^2 + x*Log[Log[2]] + Log[x]*Log[Lo
g[2]])*Log[-(x*Log[x]) + x^2*(-1 + x/Log[Log[2]])]^5), x] + 12*Defer[Int][1/((4 - x)^2*(-x^2 + x*Log[Log[2]] +
Log[x]*Log[Log[2]])*Log[-(x*Log[x]) + x^2*(-1 + x/Log[Log[2]])]^5), x] + 192*Defer[Int][1/((4 - x)^5*(x^2 - x
*Log[Log[2]] - Log[x]*Log[Log[2]])*Log[-(x*Log[x]) + x^2*(-1 + x/Log[Log[2]])]^4), x] + 16*(4 - 3*Log[Log[2]])
*Defer[Int][1/((4 - x)^5*(x^2 - x*Log[Log[2]] - Log[x]*Log[Log[2]])*Log[-(x*Log[x]) + x^2*(-1 + x/Log[Log[2]])
]^4), x] + 4*Log[Log[2]]*Defer[Int][1/((4 - x)^4*(x^2 - x*Log[Log[2]] - Log[x]*Log[Log[2]])*Log[-(x*Log[x]) +
x^2*(-1 + x/Log[Log[2]])]^4), x] + 36*Defer[Int][1/((4 - x)^3*(x^2 - x*Log[Log[2]] - Log[x]*Log[Log[2]])*Log[-
(x*Log[x]) + x^2*(-1 + x/Log[Log[2]])]^4), x] + (4 - 3*Log[Log[2]])*Defer[Int][1/((4 - x)^3*(x^2 - x*Log[Log[2
]] - Log[x]*Log[Log[2]])*Log[-(x*Log[x]) + x^2*(-1 + x/Log[Log[2]])]^4), x] + 16*Log[Log[2]]*Defer[Int][1/((-4
+ x)^5*(x^2 - x*Log[Log[2]] - Log[x]*Log[Log[2]])*Log[-(x*Log[x]) + x^2*(-1 + x/Log[Log[2]])]^4), x] + 3*Log[
Log[2]]*Defer[Int][Log[x]/((4 - x)^4*(x^2 - x*Log[Log[2]] - Log[x]*Log[Log[2]])*Log[-(x*Log[x]) + x^2*(-1 + x/
Log[Log[2]])]^4), x] + 16*Log[Log[2]]*Defer[Int][Log[x]/((-4 + x)^5*(x^2 - x*Log[Log[2]] - Log[x]*Log[Log[2]])
*Log[-(x*Log[x]) + x^2*(-1 + x/Log[Log[2]])]^4), x] + 144*Defer[Int][1/((4 - x)^4*(-x^2 + x*Log[Log[2]] + Log[
x]*Log[Log[2]])*Log[-(x*Log[x]) + x^2*(-1 + x/Log[Log[2]])]^4), x] + 8*(4 - 3*Log[Log[2]])*Defer[Int][1/((4 -
x)^4*(-x^2 + x*Log[Log[2]] + Log[x]*Log[Log[2]])*Log[-(x*Log[x]) + x^2*(-1 + x/Log[Log[2]])]^4), x] + 3*Defer[
Int][1/((4 - x)^2*(-x^2 + x*Log[Log[2]] + Log[x]*Log[Log[2]])*Log[-(x*Log[x]) + x^2*(-1 + x/Log[Log[2]])]^4),
x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {4 (-4+x) \left (3 x^2-\log (\log (2))-2 x \log (\log (2))\right )+x (4+3 x) (x-\log (\log (2))) \log \left (x \left (-\log (x)+x \left (-1+\frac {x}{\log (\log (2))}\right )\right )\right )-\log (x) \log (\log (2)) \left (4 (-4+x)+(4+3 x) \log \left (x \left (-\log (x)+x \left (-1+\frac {x}{\log (\log (2))}\right )\right )\right )\right )}{(4-x)^5 (x (x-\log (\log (2)))-\log (x) \log (\log (2))) \log ^5\left (-x \log (x)+x^2 \left (-1+\frac {x}{\log (\log (2))}\right )\right )} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.12, size = 28, normalized size = 0.97 \begin {gather*} \frac {x}{(-4+x)^4 \log ^4\left (x \left (-\log (x)+x \left (-1+\frac {x}{\log (\log (2))}\right )\right )\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-48*x^2 + 12*x^3 + (16 + 28*x - 8*x^2 + (16 - 4*x)*Log[x])*Log[Log[2]] + (4*x^2 + 3*x^3 + (-4*x - 3
*x^2 + (-4 - 3*x)*Log[x])*Log[Log[2]])*Log[(x^3 + (-x^2 - x*Log[x])*Log[Log[2]])/Log[Log[2]]])/((1024*x^2 - 12
80*x^3 + 640*x^4 - 160*x^5 + 20*x^6 - x^7 + (-1024*x + 1280*x^2 - 640*x^3 + 160*x^4 - 20*x^5 + x^6 + (-1024 +
1280*x - 640*x^2 + 160*x^3 - 20*x^4 + x^5)*Log[x])*Log[Log[2]])*Log[(x^3 + (-x^2 - x*Log[x])*Log[Log[2]])/Log[
Log[2]]]^5),x]

[Out]

x/((-4 + x)^4*Log[x*(-Log[x] + x*(-1 + x/Log[Log[2]]))]^4)

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fricas [A]  time = 0.65, size = 48, normalized size = 1.66 \begin {gather*} \frac {x}{{\left (x^{4} - 16 \, x^{3} + 96 \, x^{2} - 256 \, x + 256\right )} \log \left (\frac {x^{3} - {\left (x^{2} + x \log \relax (x)\right )} \log \left (\log \relax (2)\right )}{\log \left (\log \relax (2)\right )}\right )^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((-3*x-4)*log(x)-3*x^2-4*x)*log(log(2))+3*x^3+4*x^2)*log(((-x*log(x)-x^2)*log(log(2))+x^3)/log(log
(2)))+((-4*x+16)*log(x)-8*x^2+28*x+16)*log(log(2))+12*x^3-48*x^2)/(((x^5-20*x^4+160*x^3-640*x^2+1280*x-1024)*l
og(x)+x^6-20*x^5+160*x^4-640*x^3+1280*x^2-1024*x)*log(log(2))-x^7+20*x^6-160*x^5+640*x^4-1280*x^3+1024*x^2)/lo
g(((-x*log(x)-x^2)*log(log(2))+x^3)/log(log(2)))^5,x, algorithm="fricas")

[Out]

x/((x^4 - 16*x^3 + 96*x^2 - 256*x + 256)*log((x^3 - (x^2 + x*log(x))*log(log(2)))/log(log(2)))^4)

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giac [B]  time = 3.28, size = 6083, normalized size = 209.76 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((-3*x-4)*log(x)-3*x^2-4*x)*log(log(2))+3*x^3+4*x^2)*log(((-x*log(x)-x^2)*log(log(2))+x^3)/log(log
(2)))+((-4*x+16)*log(x)-8*x^2+28*x+16)*log(log(2))+12*x^3-48*x^2)/(((x^5-20*x^4+160*x^3-640*x^2+1280*x-1024)*l
og(x)+x^6-20*x^5+160*x^4-640*x^3+1280*x^2-1024*x)*log(log(2))-x^7+20*x^6-160*x^5+640*x^4-1280*x^3+1024*x^2)/lo
g(((-x*log(x)-x^2)*log(log(2))+x^3)/log(log(2)))^5,x, algorithm="giac")

[Out]

(3*x^3 - 2*x^2*log(log(2)) - x*log(x)*log(log(2)) - x*log(log(2)))/(3*x^6*log(x^2 - x*log(log(2)) - log(x)*log
(log(2)))^4 + 12*x^6*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))^3*log(x) + 18*x^6*log(x^2 - x*log(log(2)) -
log(x)*log(log(2)))^2*log(x)^2 + 12*x^6*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))*log(x)^3 + 3*x^6*log(x)
^4 - 2*x^5*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))^4*log(log(2)) - 8*x^5*log(x^2 - x*log(log(2)) - log(x
)*log(log(2)))^3*log(x)*log(log(2)) - x^4*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))^4*log(x)*log(log(2)) -
12*x^5*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))^2*log(x)^2*log(log(2)) - 4*x^4*log(x^2 - x*log(log(2)) -
log(x)*log(log(2)))^3*log(x)^2*log(log(2)) - 8*x^5*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))*log(x)^3*log
(log(2)) - 6*x^4*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))^2*log(x)^3*log(log(2)) - 2*x^5*log(x)^4*log(log
(2)) - 4*x^4*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))*log(x)^4*log(log(2)) - x^4*log(x)^5*log(log(2)) - 1
2*x^6*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))^3*log(log(log(2))) - 36*x^6*log(x^2 - x*log(log(2)) - log(
x)*log(log(2)))^2*log(x)*log(log(log(2))) - 36*x^6*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))*log(x)^2*log(
log(log(2))) - 12*x^6*log(x)^3*log(log(log(2))) + 8*x^5*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))^3*log(lo
g(2))*log(log(log(2))) + 24*x^5*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))^2*log(x)*log(log(2))*log(log(log
(2))) + 4*x^4*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))^3*log(x)*log(log(2))*log(log(log(2))) + 24*x^5*log
(x^2 - x*log(log(2)) - log(x)*log(log(2)))*log(x)^2*log(log(2))*log(log(log(2))) + 12*x^4*log(x^2 - x*log(log(
2)) - log(x)*log(log(2)))^2*log(x)^2*log(log(2))*log(log(log(2))) + 8*x^5*log(x)^3*log(log(2))*log(log(log(2))
) + 12*x^4*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))*log(x)^3*log(log(2))*log(log(log(2))) + 4*x^4*log(x)^
4*log(log(2))*log(log(log(2))) + 18*x^6*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))^2*log(log(log(2)))^2 + 3
6*x^6*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))*log(x)*log(log(log(2)))^2 + 18*x^6*log(x)^2*log(log(log(2)
))^2 - 12*x^5*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))^2*log(log(2))*log(log(log(2)))^2 - 24*x^5*log(x^2
- x*log(log(2)) - log(x)*log(log(2)))*log(x)*log(log(2))*log(log(log(2)))^2 - 6*x^4*log(x^2 - x*log(log(2)) -
log(x)*log(log(2)))^2*log(x)*log(log(2))*log(log(log(2)))^2 - 12*x^5*log(x)^2*log(log(2))*log(log(log(2)))^2 -
12*x^4*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))*log(x)^2*log(log(2))*log(log(log(2)))^2 - 6*x^4*log(x)^3
*log(log(2))*log(log(log(2)))^2 - 12*x^6*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))*log(log(log(2)))^3 - 12
*x^6*log(x)*log(log(log(2)))^3 + 8*x^5*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))*log(log(2))*log(log(log(2
)))^3 + 8*x^5*log(x)*log(log(2))*log(log(log(2)))^3 + 4*x^4*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))*log(
x)*log(log(2))*log(log(log(2)))^3 + 4*x^4*log(x)^2*log(log(2))*log(log(log(2)))^3 + 3*x^6*log(log(log(2)))^4 -
2*x^5*log(log(2))*log(log(log(2)))^4 - x^4*log(x)*log(log(2))*log(log(log(2)))^4 - 48*x^5*log(x^2 - x*log(log
(2)) - log(x)*log(log(2)))^4 - 192*x^5*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))^3*log(x) - 288*x^5*log(x^
2 - x*log(log(2)) - log(x)*log(log(2)))^2*log(x)^2 - 192*x^5*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))*log
(x)^3 - 48*x^5*log(x)^4 + 31*x^4*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))^4*log(log(2)) + 124*x^4*log(x^2
- x*log(log(2)) - log(x)*log(log(2)))^3*log(x)*log(log(2)) + 16*x^3*log(x^2 - x*log(log(2)) - log(x)*log(log(
2)))^4*log(x)*log(log(2)) + 186*x^4*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))^2*log(x)^2*log(log(2)) + 64*
x^3*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))^3*log(x)^2*log(log(2)) + 124*x^4*log(x^2 - x*log(log(2)) - l
og(x)*log(log(2)))*log(x)^3*log(log(2)) + 96*x^3*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))^2*log(x)^3*log(
log(2)) + 31*x^4*log(x)^4*log(log(2)) + 64*x^3*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))*log(x)^4*log(log(
2)) + 16*x^3*log(x)^5*log(log(2)) + 192*x^5*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))^3*log(log(log(2))) +
576*x^5*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))^2*log(x)*log(log(log(2))) + 576*x^5*log(x^2 - x*log(log
(2)) - log(x)*log(log(2)))*log(x)^2*log(log(log(2))) + 192*x^5*log(x)^3*log(log(log(2))) - 124*x^4*log(x^2 - x
*log(log(2)) - log(x)*log(log(2)))^3*log(log(2))*log(log(log(2))) - 372*x^4*log(x^2 - x*log(log(2)) - log(x)*l
og(log(2)))^2*log(x)*log(log(2))*log(log(log(2))) - 64*x^3*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))^3*log
(x)*log(log(2))*log(log(log(2))) - 372*x^4*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))*log(x)^2*log(log(2))*
log(log(log(2))) - 192*x^3*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))^2*log(x)^2*log(log(2))*log(log(log(2)
)) - 124*x^4*log(x)^3*log(log(2))*log(log(log(2))) - 192*x^3*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))*log
(x)^3*log(log(2))*log(log(log(2))) - 64*x^3*log(x)^4*log(log(2))*log(log(log(2))) - 288*x^5*log(x^2 - x*log(lo
g(2)) - log(x)*log(log(2)))^2*log(log(log(2)))^2 - 576*x^5*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))*log(x
)*log(log(log(2)))^2 - 288*x^5*log(x)^2*log(log(log(2)))^2 + 186*x^4*log(x^2 - x*log(log(2)) - log(x)*log(log(
2)))^2*log(log(2))*log(log(log(2)))^2 + 372*x^4*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))*log(x)*log(log(2
))*log(log(log(2)))^2 + 96*x^3*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))^2*log(x)*log(log(2))*log(log(log(
2)))^2 + 186*x^4*log(x)^2*log(log(2))*log(log(log(2)))^2 + 192*x^3*log(x^2 - x*log(log(2)) - log(x)*log(log(2)
))*log(x)^2*log(log(2))*log(log(log(2)))^2 + 96*x^3*log(x)^3*log(log(2))*log(log(log(2)))^2 + 192*x^5*log(x^2
- x*log(log(2)) - log(x)*log(log(2)))*log(log(log(2)))^3 + 192*x^5*log(x)*log(log(log(2)))^3 - 124*x^4*log(x^2
- x*log(log(2)) - log(x)*log(log(2)))*log(log(2))*log(log(log(2)))^3 - 124*x^4*log(x)*log(log(2))*log(log(log
(2)))^3 - 64*x^3*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))*log(x)*log(log(2))*log(log(log(2)))^3 - 64*x^3*
log(x)^2*log(log(2))*log(log(log(2)))^3 - 48*x^5*log(log(log(2)))^4 + 31*x^4*log(log(2))*log(log(log(2)))^4 +
16*x^3*log(x)*log(log(2))*log(log(log(2)))^4 + 288*x^4*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))^4 + 1152*
x^4*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))^3*log(x) + 1728*x^4*log(x^2 - x*log(log(2)) - log(x)*log(log
(2)))^2*log(x)^2 + 1152*x^4*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))*log(x)^3 + 288*x^4*log(x)^4 - 176*x^
3*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))^4*log(log(2)) - 704*x^3*log(x^2 - x*log(log(2)) - log(x)*log(l
og(2)))^3*log(x)*log(log(2)) - 96*x^2*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))^4*log(x)*log(log(2)) - 105
6*x^3*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))^2*log(x)^2*log(log(2)) - 384*x^2*log(x^2 - x*log(log(2)) -
log(x)*log(log(2)))^3*log(x)^2*log(log(2)) - 704*x^3*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))*log(x)^3*l
og(log(2)) - 576*x^2*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))^2*log(x)^3*log(log(2)) - 176*x^3*log(x)^4*l
og(log(2)) - 384*x^2*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))*log(x)^4*log(log(2)) - 96*x^2*log(x)^5*log(
log(2)) - 1152*x^4*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))^3*log(log(log(2))) - 3456*x^4*log(x^2 - x*log
(log(2)) - log(x)*log(log(2)))^2*log(x)*log(log(log(2))) - 3456*x^4*log(x^2 - x*log(log(2)) - log(x)*log(log(2
)))*log(x)^2*log(log(log(2))) - 1152*x^4*log(x)^3*log(log(log(2))) + 704*x^3*log(x^2 - x*log(log(2)) - log(x)*
log(log(2)))^3*log(log(2))*log(log(log(2))) + 2112*x^3*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))^2*log(x)*
log(log(2))*log(log(log(2))) + 384*x^2*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))^3*log(x)*log(log(2))*log(
log(log(2))) + 2112*x^3*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))*log(x)^2*log(log(2))*log(log(log(2))) +
1152*x^2*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))^2*log(x)^2*log(log(2))*log(log(log(2))) + 704*x^3*log(x
)^3*log(log(2))*log(log(log(2))) + 1152*x^2*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))*log(x)^3*log(log(2))
*log(log(log(2))) + 384*x^2*log(x)^4*log(log(2))*log(log(log(2))) + 1728*x^4*log(x^2 - x*log(log(2)) - log(x)*
log(log(2)))^2*log(log(log(2)))^2 + 3456*x^4*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))*log(x)*log(log(log(
2)))^2 + 1728*x^4*log(x)^2*log(log(log(2)))^2 - 1056*x^3*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))^2*log(l
og(2))*log(log(log(2)))^2 - 2112*x^3*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))*log(x)*log(log(2))*log(log(
log(2)))^2 - 576*x^2*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))^2*log(x)*log(log(2))*log(log(log(2)))^2 - 1
056*x^3*log(x)^2*log(log(2))*log(log(log(2)))^2 - 1152*x^2*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))*log(x
)^2*log(log(2))*log(log(log(2)))^2 - 576*x^2*log(x)^3*log(log(2))*log(log(log(2)))^2 - 1152*x^4*log(x^2 - x*lo
g(log(2)) - log(x)*log(log(2)))*log(log(log(2)))^3 - 1152*x^4*log(x)*log(log(log(2)))^3 + 704*x^3*log(x^2 - x*
log(log(2)) - log(x)*log(log(2)))*log(log(2))*log(log(log(2)))^3 + 704*x^3*log(x)*log(log(2))*log(log(log(2)))
^3 + 384*x^2*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))*log(x)*log(log(2))*log(log(log(2)))^3 + 384*x^2*log
(x)^2*log(log(2))*log(log(log(2)))^3 + 288*x^4*log(log(log(2)))^4 - 176*x^3*log(log(2))*log(log(log(2)))^4 - 9
6*x^2*log(x)*log(log(2))*log(log(log(2)))^4 - 768*x^3*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))^4 - 3072*x
^3*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))^3*log(x) - 4608*x^3*log(x^2 - x*log(log(2)) - log(x)*log(log(
2)))^2*log(x)^2 - 3072*x^3*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))*log(x)^3 - 768*x^3*log(x)^4 + 416*x^2
*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))^4*log(log(2)) + 1664*x^2*log(x^2 - x*log(log(2)) - log(x)*log(l
og(2)))^3*log(x)*log(log(2)) + 256*x*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))^4*log(x)*log(log(2)) + 2496
*x^2*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))^2*log(x)^2*log(log(2)) + 1024*x*log(x^2 - x*log(log(2)) - l
og(x)*log(log(2)))^3*log(x)^2*log(log(2)) + 1664*x^2*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))*log(x)^3*lo
g(log(2)) + 1536*x*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))^2*log(x)^3*log(log(2)) + 416*x^2*log(x)^4*log
(log(2)) + 1024*x*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))*log(x)^4*log(log(2)) + 256*x*log(x)^5*log(log(
2)) + 3072*x^3*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))^3*log(log(log(2))) + 9216*x^3*log(x^2 - x*log(log
(2)) - log(x)*log(log(2)))^2*log(x)*log(log(log(2))) + 9216*x^3*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))*
log(x)^2*log(log(log(2))) + 3072*x^3*log(x)^3*log(log(log(2))) - 1664*x^2*log(x^2 - x*log(log(2)) - log(x)*log
(log(2)))^3*log(log(2))*log(log(log(2))) - 4992*x^2*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))^2*log(x)*log
(log(2))*log(log(log(2))) - 1024*x*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))^3*log(x)*log(log(2))*log(log(
log(2))) - 4992*x^2*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))*log(x)^2*log(log(2))*log(log(log(2))) - 3072
*x*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))^2*log(x)^2*log(log(2))*log(log(log(2))) - 1664*x^2*log(x)^3*l
og(log(2))*log(log(log(2))) - 3072*x*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))*log(x)^3*log(log(2))*log(lo
g(log(2))) - 1024*x*log(x)^4*log(log(2))*log(log(log(2))) - 4608*x^3*log(x^2 - x*log(log(2)) - log(x)*log(log(
2)))^2*log(log(log(2)))^2 - 9216*x^3*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))*log(x)*log(log(log(2)))^2 -
4608*x^3*log(x)^2*log(log(log(2)))^2 + 2496*x^2*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))^2*log(log(2))*l
og(log(log(2)))^2 + 4992*x^2*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))*log(x)*log(log(2))*log(log(log(2)))
^2 + 1536*x*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))^2*log(x)*log(log(2))*log(log(log(2)))^2 + 2496*x^2*l
og(x)^2*log(log(2))*log(log(log(2)))^2 + 3072*x*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))*log(x)^2*log(log
(2))*log(log(log(2)))^2 + 1536*x*log(x)^3*log(log(2))*log(log(log(2)))^2 + 3072*x^3*log(x^2 - x*log(log(2)) -
log(x)*log(log(2)))*log(log(log(2)))^3 + 3072*x^3*log(x)*log(log(log(2)))^3 - 1664*x^2*log(x^2 - x*log(log(2))
- log(x)*log(log(2)))*log(log(2))*log(log(log(2)))^3 - 1664*x^2*log(x)*log(log(2))*log(log(log(2)))^3 - 1024*
x*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))*log(x)*log(log(2))*log(log(log(2)))^3 - 1024*x*log(x)^2*log(lo
g(2))*log(log(log(2)))^3 - 768*x^3*log(log(log(2)))^4 + 416*x^2*log(log(2))*log(log(log(2)))^4 + 256*x*log(x)*
log(log(2))*log(log(log(2)))^4 + 768*x^2*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))^4 + 3072*x^2*log(x^2 -
x*log(log(2)) - log(x)*log(log(2)))^3*log(x) + 4608*x^2*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))^2*log(x)
^2 + 3072*x^2*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))*log(x)^3 + 768*x^2*log(x)^4 - 256*x*log(x^2 - x*lo
g(log(2)) - log(x)*log(log(2)))^4*log(log(2)) - 1024*x*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))^3*log(x)*
log(log(2)) - 256*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))^4*log(x)*log(log(2)) - 1536*x*log(x^2 - x*log(
log(2)) - log(x)*log(log(2)))^2*log(x)^2*log(log(2)) - 1024*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))^3*lo
g(x)^2*log(log(2)) - 1024*x*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))*log(x)^3*log(log(2)) - 1536*log(x^2
- x*log(log(2)) - log(x)*log(log(2)))^2*log(x)^3*log(log(2)) - 256*x*log(x)^4*log(log(2)) - 1024*log(x^2 - x*l
og(log(2)) - log(x)*log(log(2)))*log(x)^4*log(log(2)) - 256*log(x)^5*log(log(2)) - 3072*x^2*log(x^2 - x*log(lo
g(2)) - log(x)*log(log(2)))^3*log(log(log(2))) - 9216*x^2*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))^2*log(
x)*log(log(log(2))) - 9216*x^2*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))*log(x)^2*log(log(log(2))) - 3072*
x^2*log(x)^3*log(log(log(2))) + 1024*x*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))^3*log(log(2))*log(log(log
(2))) + 3072*x*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))^2*log(x)*log(log(2))*log(log(log(2))) + 1024*log(
x^2 - x*log(log(2)) - log(x)*log(log(2)))^3*log(x)*log(log(2))*log(log(log(2))) + 3072*x*log(x^2 - x*log(log(2
)) - log(x)*log(log(2)))*log(x)^2*log(log(2))*log(log(log(2))) + 3072*log(x^2 - x*log(log(2)) - log(x)*log(log
(2)))^2*log(x)^2*log(log(2))*log(log(log(2))) + 1024*x*log(x)^3*log(log(2))*log(log(log(2))) + 3072*log(x^2 -
x*log(log(2)) - log(x)*log(log(2)))*log(x)^3*log(log(2))*log(log(log(2))) + 1024*log(x)^4*log(log(2))*log(log(
log(2))) + 4608*x^2*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))^2*log(log(log(2)))^2 + 9216*x^2*log(x^2 - x*
log(log(2)) - log(x)*log(log(2)))*log(x)*log(log(log(2)))^2 + 4608*x^2*log(x)^2*log(log(log(2)))^2 - 1536*x*lo
g(x^2 - x*log(log(2)) - log(x)*log(log(2)))^2*log(log(2))*log(log(log(2)))^2 - 3072*x*log(x^2 - x*log(log(2))
- log(x)*log(log(2)))*log(x)*log(log(2))*log(log(log(2)))^2 - 1536*log(x^2 - x*log(log(2)) - log(x)*log(log(2)
))^2*log(x)*log(log(2))*log(log(log(2)))^2 - 1536*x*log(x)^2*log(log(2))*log(log(log(2)))^2 - 3072*log(x^2 - x
*log(log(2)) - log(x)*log(log(2)))*log(x)^2*log(log(2))*log(log(log(2)))^2 - 1536*log(x)^3*log(log(2))*log(log
(log(2)))^2 - 3072*x^2*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))*log(log(log(2)))^3 - 3072*x^2*log(x)*log(
log(log(2)))^3 + 1024*x*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))*log(log(2))*log(log(log(2)))^3 + 1024*x*
log(x)*log(log(2))*log(log(log(2)))^3 + 1024*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))*log(x)*log(log(2))*
log(log(log(2)))^3 + 1024*log(x)^2*log(log(2))*log(log(log(2)))^3 + 768*x^2*log(log(log(2)))^4 - 256*x*log(log
(2))*log(log(log(2)))^4 - 256*log(x)*log(log(2))*log(log(log(2)))^4 - 256*log(x^2 - x*log(log(2)) - log(x)*log
(log(2)))^4*log(log(2)) - 1024*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))^3*log(x)*log(log(2)) - 1536*log(x
^2 - x*log(log(2)) - log(x)*log(log(2)))^2*log(x)^2*log(log(2)) - 1024*log(x^2 - x*log(log(2)) - log(x)*log(lo
g(2)))*log(x)^3*log(log(2)) - 256*log(x)^4*log(log(2)) + 1024*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))^3*
log(log(2))*log(log(log(2))) + 3072*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))^2*log(x)*log(log(2))*log(log
(log(2))) + 3072*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))*log(x)^2*log(log(2))*log(log(log(2))) + 1024*lo
g(x)^3*log(log(2))*log(log(log(2))) - 1536*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))^2*log(log(2))*log(log
(log(2)))^2 - 3072*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))*log(x)*log(log(2))*log(log(log(2)))^2 - 1536*
log(x)^2*log(log(2))*log(log(log(2)))^2 + 1024*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))*log(log(2))*log(l
og(log(2)))^3 + 1024*log(x)*log(log(2))*log(log(log(2)))^3 - 256*log(log(2))*log(log(log(2)))^4)

________________________________________________________________________________________

maple [C]  time = 12.52, size = 192, normalized size = 6.62

method	result	size
risch	\(\frac {16 x}{\left (\pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i \left (\left (x +\ln \relax (x )\right ) \ln \left (\ln \relax (2)\right )-x^{2}\right )\right ) \mathrm {csgn}\left (i x \left (\left (x +\ln \relax (x )\right ) \ln \left (\ln \relax (2)\right )-x^{2}\right )\right )-\pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x \left (\left (x +\ln \relax (x )\right ) \ln \left (\ln \relax (2)\right )-x^{2}\right )\right )^{2}-\pi \,\mathrm {csgn}\left (i \left (\left (x +\ln \relax (x )\right ) \ln \left (\ln \relax (2)\right )-x^{2}\right )\right ) \mathrm {csgn}\left (i x \left (\left (x +\ln \relax (x )\right ) \ln \left (\ln \relax (2)\right )-x^{2}\right )\right )^{2}+\pi \mathrm {csgn}\left (i x \left (\left (x +\ln \relax (x )\right ) \ln \left (\ln \relax (2)\right )-x^{2}\right )\right )^{3}-2 i \ln \left (-\ln \left (\ln \relax (2)\right )\right )+2 i \ln \relax (x )+2 i \ln \left (\left (x +\ln \relax (x )\right ) \ln \left (\ln \relax (2)\right )-x^{2}\right )\right )^{4} \left (x -4\right )^{2} \left (x^{2}-8 x +16\right )}\)	\(192\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((((-3*x-4)*ln(x)-3*x^2-4*x)*ln(ln(2))+3*x^3+4*x^2)*ln(((-x*ln(x)-x^2)*ln(ln(2))+x^3)/ln(ln(2)))+((-4*x+16
)*ln(x)-8*x^2+28*x+16)*ln(ln(2))+12*x^3-48*x^2)/(((x^5-20*x^4+160*x^3-640*x^2+1280*x-1024)*ln(x)+x^6-20*x^5+16
0*x^4-640*x^3+1280*x^2-1024*x)*ln(ln(2))-x^7+20*x^6-160*x^5+640*x^4-1280*x^3+1024*x^2)/ln(((-x*ln(x)-x^2)*ln(l
n(2))+x^3)/ln(ln(2)))^5,x,method=_RETURNVERBOSE)

[Out]

16*x/(Pi*csgn(I*x)*csgn(I*((x+ln(x))*ln(ln(2))-x^2))*csgn(I*x*((x+ln(x))*ln(ln(2))-x^2))-Pi*csgn(I*x)*csgn(I*x
*((x+ln(x))*ln(ln(2))-x^2))^2-Pi*csgn(I*((x+ln(x))*ln(ln(2))-x^2))*csgn(I*x*((x+ln(x))*ln(ln(2))-x^2))^2+Pi*cs
gn(I*x*((x+ln(x))*ln(ln(2))-x^2))^3-2*I*ln(-ln(ln(2)))+2*I*ln(x)+2*I*ln((x+ln(x))*ln(ln(2))-x^2))^4/(x-4)^2/(x
^2-8*x+16)

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maxima [B]  time = 3.99, size = 689, normalized size = 23.76 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((-3*x-4)*log(x)-3*x^2-4*x)*log(log(2))+3*x^3+4*x^2)*log(((-x*log(x)-x^2)*log(log(2))+x^3)/log(log
(2)))+((-4*x+16)*log(x)-8*x^2+28*x+16)*log(log(2))+12*x^3-48*x^2)/(((x^5-20*x^4+160*x^3-640*x^2+1280*x-1024)*l
og(x)+x^6-20*x^5+160*x^4-640*x^3+1280*x^2-1024*x)*log(log(2))-x^7+20*x^6-160*x^5+640*x^4-1280*x^3+1024*x^2)/lo
g(((-x*log(x)-x^2)*log(log(2))+x^3)/log(log(2)))^5,x, algorithm="maxima")

[Out]

x/(x^4*log(log(log(2)))^4 - 16*x^3*log(log(log(2)))^4 + 96*x^2*log(log(log(2)))^4 + (x^4 - 16*x^3 + 96*x^2 - 2
56*x + 256)*log(x^2 - x*log(log(2)) - log(x)*log(log(2)))^4 + (x^4 - 16*x^3 + 96*x^2 - 256*x + 256)*log(x)^4 -
256*x*log(log(log(2)))^4 - 4*(x^4*log(log(log(2))) - 16*x^3*log(log(log(2))) + 96*x^2*log(log(log(2))) - (x^4
- 16*x^3 + 96*x^2 - 256*x + 256)*log(x) - 256*x*log(log(log(2))) + 256*log(log(log(2))))*log(x^2 - x*log(log(
2)) - log(x)*log(log(2)))^3 - 4*(x^4*log(log(log(2))) - 16*x^3*log(log(log(2))) + 96*x^2*log(log(log(2))) - 25
6*x*log(log(log(2))) + 256*log(log(log(2))))*log(x)^3 + 256*log(log(log(2)))^4 + 6*(x^4*log(log(log(2)))^2 - 1
6*x^3*log(log(log(2)))^2 + 96*x^2*log(log(log(2)))^2 + (x^4 - 16*x^3 + 96*x^2 - 256*x + 256)*log(x)^2 - 256*x*
log(log(log(2)))^2 - 2*(x^4*log(log(log(2))) - 16*x^3*log(log(log(2))) + 96*x^2*log(log(log(2))) - 256*x*log(l
og(log(2))) + 256*log(log(log(2))))*log(x) + 256*log(log(log(2)))^2)*log(x^2 - x*log(log(2)) - log(x)*log(log(
2)))^2 + 6*(x^4*log(log(log(2)))^2 - 16*x^3*log(log(log(2)))^2 + 96*x^2*log(log(log(2)))^2 - 256*x*log(log(log
(2)))^2 + 256*log(log(log(2)))^2)*log(x)^2 - 4*(x^4*log(log(log(2)))^3 - 16*x^3*log(log(log(2)))^3 + 96*x^2*lo
g(log(log(2)))^3 - (x^4 - 16*x^3 + 96*x^2 - 256*x + 256)*log(x)^3 - 256*x*log(log(log(2)))^3 + 3*(x^4*log(log(
log(2))) - 16*x^3*log(log(log(2))) + 96*x^2*log(log(log(2))) - 256*x*log(log(log(2))) + 256*log(log(log(2))))*
log(x)^2 + 256*log(log(log(2)))^3 - 3*(x^4*log(log(log(2)))^2 - 16*x^3*log(log(log(2)))^2 + 96*x^2*log(log(log
(2)))^2 - 256*x*log(log(log(2)))^2 + 256*log(log(log(2)))^2)*log(x))*log(x^2 - x*log(log(2)) - log(x)*log(log(
2))) - 4*(x^4*log(log(log(2)))^3 - 16*x^3*log(log(log(2)))^3 + 96*x^2*log(log(log(2)))^3 - 256*x*log(log(log(2
)))^3 + 256*log(log(log(2)))^3)*log(x))

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mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int \frac {\ln \left (-\frac {\ln \left (\ln \relax (2)\right )\,\left (x\,\ln \relax (x)+x^2\right )-x^3}{\ln \left (\ln \relax (2)\right )}\right )\,\left (4\,x^2-\ln \left (\ln \relax (2)\right )\,\left (4\,x+\ln \relax (x)\,\left (3\,x+4\right )+3\,x^2\right )+3\,x^3\right )+\ln \left (\ln \relax (2)\right )\,\left (28\,x-\ln \relax (x)\,\left (4\,x-16\right )-8\,x^2+16\right )-48\,x^2+12\,x^3}{{\ln \left (-\frac {\ln \left (\ln \relax (2)\right )\,\left (x\,\ln \relax (x)+x^2\right )-x^3}{\ln \left (\ln \relax (2)\right )}\right )}^5\,\left (\ln \left (\ln \relax (2)\right )\,\left (1280\,x^2-1024\,x-640\,x^3+160\,x^4-20\,x^5+x^6+\ln \relax (x)\,\left (x^5-20\,x^4+160\,x^3-640\,x^2+1280\,x-1024\right )\right )+1024\,x^2-1280\,x^3+640\,x^4-160\,x^5+20\,x^6-x^7\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log(-(log(log(2))*(x*log(x) + x^2) - x^3)/log(log(2)))*(4*x^2 - log(log(2))*(4*x + log(x)*(3*x + 4) + 3*x
^2) + 3*x^3) + log(log(2))*(28*x - log(x)*(4*x - 16) - 8*x^2 + 16) - 48*x^2 + 12*x^3)/(log(-(log(log(2))*(x*lo
g(x) + x^2) - x^3)/log(log(2)))^5*(log(log(2))*(1280*x^2 - 1024*x - 640*x^3 + 160*x^4 - 20*x^5 + x^6 + log(x)*
(1280*x - 640*x^2 + 160*x^3 - 20*x^4 + x^5 - 1024)) + 1024*x^2 - 1280*x^3 + 640*x^4 - 160*x^5 + 20*x^6 - x^7))
,x)

[Out]

int((log(-(log(log(2))*(x*log(x) + x^2) - x^3)/log(log(2)))*(4*x^2 - log(log(2))*(4*x + log(x)*(3*x + 4) + 3*x
^2) + 3*x^3) + log(log(2))*(28*x - log(x)*(4*x - 16) - 8*x^2 + 16) - 48*x^2 + 12*x^3)/(log(-(log(log(2))*(x*lo
g(x) + x^2) - x^3)/log(log(2)))^5*(log(log(2))*(1280*x^2 - 1024*x - 640*x^3 + 160*x^4 - 20*x^5 + x^6 + log(x)*
(1280*x - 640*x^2 + 160*x^3 - 20*x^4 + x^5 - 1024)) + 1024*x^2 - 1280*x^3 + 640*x^4 - 160*x^5 + 20*x^6 - x^7))
, x)

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sympy [A]  time = 1.30, size = 46, normalized size = 1.59 \begin {gather*} \frac {x}{\left (x^{4} - 16 x^{3} + 96 x^{2} - 256 x + 256\right ) \log {\left (\frac {x^{3} + \left (- x^{2} - x \log {\relax (x )}\right ) \log {\left (\log {\relax (2 )} \right )}}{\log {\left (\log {\relax (2 )} \right )}} \right )}^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((-3*x-4)*ln(x)-3*x**2-4*x)*ln(ln(2))+3*x**3+4*x**2)*ln(((-x*ln(x)-x**2)*ln(ln(2))+x**3)/ln(ln(2))
)+((-4*x+16)*ln(x)-8*x**2+28*x+16)*ln(ln(2))+12*x**3-48*x**2)/(((x**5-20*x**4+160*x**3-640*x**2+1280*x-1024)*l
n(x)+x**6-20*x**5+160*x**4-640*x**3+1280*x**2-1024*x)*ln(ln(2))-x**7+20*x**6-160*x**5+640*x**4-1280*x**3+1024*
x**2)/ln(((-x*ln(x)-x**2)*ln(ln(2))+x**3)/ln(ln(2)))**5,x)

[Out]

x/((x**4 - 16*x**3 + 96*x**2 - 256*x + 256)*log((x**3 + (-x**2 - x*log(x))*log(log(2)))/log(log(2)))**4)

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