3.22.17 \(\int \frac {4 x^3+4 x^2 \log (5)+(x-8 x^4+(1-8 x^2-8 x^3) \log (5)) \log (x) \log (\log (x))+(4 x^2+4 x \log (5)+(-12 x^3+(-8 x-12 x^2) \log (5)) \log (x) \log (\log (x))) \log (\frac {x^2}{(x^2+2 x \log (5)+\log ^2(5)) \log (\log (x))})+(-4 x^2-4 x \log (5)) \log (x) \log (\log (x)) \log ^2(\frac {x^2}{(x^2+2 x \log (5)+\log ^2(5)) \log (\log (x))})}{(2 x+2 \log (5)) \log (x) \log (\log (x))} \, dx\)

Optimal. Leaf size=31 \[ \frac {x}{2}-x^2 \left (x+\log \left (\frac {x^2}{(x+\log (5))^2 \log (\log (x))}\right )\right )^2 \]

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Rubi [F]  time = 1.98, 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 {4 x^3+4 x^2 \log (5)+\left (x-8 x^4+\left (1-8 x^2-8 x^3\right ) \log (5)\right ) \log (x) \log (\log (x))+\left (4 x^2+4 x \log (5)+\left (-12 x^3+\left (-8 x-12 x^2\right ) \log (5)\right ) \log (x) \log (\log (x))\right ) \log \left (\frac {x^2}{\left (x^2+2 x \log (5)+\log ^2(5)\right ) \log (\log (x))}\right )+\left (-4 x^2-4 x \log (5)\right ) \log (x) \log (\log (x)) \log ^2\left (\frac {x^2}{\left (x^2+2 x \log (5)+\log ^2(5)\right ) \log (\log (x))}\right )}{(2 x+2 \log (5)) \log (x) \log (\log (x))} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(4*x^3 + 4*x^2*Log[5] + (x - 8*x^4 + (1 - 8*x^2 - 8*x^3)*Log[5])*Log[x]*Log[Log[x]] + (4*x^2 + 4*x*Log[5]
+ (-12*x^3 + (-8*x - 12*x^2)*Log[5])*Log[x]*Log[Log[x]])*Log[x^2/((x^2 + 2*x*Log[5] + Log[5]^2)*Log[Log[x]])]
+ (-4*x^2 - 4*x*Log[5])*Log[x]*Log[Log[x]]*Log[x^2/((x^2 + 2*x*Log[5] + Log[5]^2)*Log[Log[x]])]^2)/((2*x + 2*L
og[5])*Log[x]*Log[Log[x]]),x]

[Out]

-x^4 - 2*x^2*Log[5] + (x*(1 + 8*Log[5]^2))/2 + x^2*Log[25] - 2*x*Log[5]*Log[25] - 4*Log[5]^3*Log[x + Log[5]] +
2*Log[5]^2*Log[25]*Log[x + Log[5]] + 2*Log[25]^2*Log[x + Log[5]] - 2*x^3*Log[x^2/((x + Log[5])^2*Log[Log[x]])
] - 2*x*Log[25]*Log[x^2/((x + Log[5])^2*Log[Log[x]])] - 2*Log[25]*Defer[Int][1/(Log[x]*Log[Log[x]]), x] + 2*Lo
g[5]*Log[25]*Defer[Int][Log[x^2/((x + Log[5])^2*Log[Log[x]])]/(x + Log[5]), x] + 2*Defer[Int][(x*Log[x^2/((x +
Log[5])^2*Log[Log[x]])])/(Log[x]*Log[Log[x]]), x] - 2*Defer[Int][x*Log[x^2/((x + Log[5])^2*Log[Log[x]])]^2, x
]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {2 x \left (x+\log \left (\frac {x^2}{(x+\log (5))^2 \log (\log (x))}\right )\right )}{\log (x) \log (\log (x))}+\frac {x-8 x^4+\log (5)-8 x^2 \log (5)-8 x^3 \log (5)-4 x \left (3 x^2+3 x \log (5)+\log (25)\right ) \log \left (\frac {x^2}{(x+\log (5))^2 \log (\log (x))}\right )-4 x (x+\log (5)) \log ^2\left (\frac {x^2}{(x+\log (5))^2 \log (\log (x))}\right )}{2 (x+\log (5))}\right ) \, dx\\ &=\frac {1}{2} \int \frac {x-8 x^4+\log (5)-8 x^2 \log (5)-8 x^3 \log (5)-4 x \left (3 x^2+3 x \log (5)+\log (25)\right ) \log \left (\frac {x^2}{(x+\log (5))^2 \log (\log (x))}\right )-4 x (x+\log (5)) \log ^2\left (\frac {x^2}{(x+\log (5))^2 \log (\log (x))}\right )}{x+\log (5)} \, dx+2 \int \frac {x \left (x+\log \left (\frac {x^2}{(x+\log (5))^2 \log (\log (x))}\right )\right )}{\log (x) \log (\log (x))} \, dx\\ &=\frac {1}{2} \int \left (\frac {x-8 x^4+\log (5)-8 x^2 \log (5)-8 x^3 \log (5)}{x+\log (5)}-\frac {4 x \left (3 x^2+3 x \log (5)+\log (25)\right ) \log \left (\frac {x^2}{(x+\log (5))^2 \log (\log (x))}\right )}{x+\log (5)}-4 x \log ^2\left (\frac {x^2}{(x+\log (5))^2 \log (\log (x))}\right )\right ) \, dx+2 \int \left (\frac {x^2}{\log (x) \log (\log (x))}+\frac {x \log \left (\frac {x^2}{(x+\log (5))^2 \log (\log (x))}\right )}{\log (x) \log (\log (x))}\right ) \, dx\\ &=\frac {1}{2} \int \frac {x-8 x^4+\log (5)-8 x^2 \log (5)-8 x^3 \log (5)}{x+\log (5)} \, dx+2 \int \frac {x^2}{\log (x) \log (\log (x))} \, dx-2 \int \frac {x \left (3 x^2+3 x \log (5)+\log (25)\right ) \log \left (\frac {x^2}{(x+\log (5))^2 \log (\log (x))}\right )}{x+\log (5)} \, dx+2 \int \frac {x \log \left (\frac {x^2}{(x+\log (5))^2 \log (\log (x))}\right )}{\log (x) \log (\log (x))} \, dx-2 \int x \log ^2\left (\frac {x^2}{(x+\log (5))^2 \log (\log (x))}\right ) \, dx\\ &=\frac {1}{2} \int \left (1-8 x^3-8 x \log (5)+8 \log ^2(5)-\frac {8 \log ^3(5)}{x+\log (5)}\right ) \, dx+2 \int \frac {x^2}{\log (x) \log (\log (x))} \, dx+2 \int \frac {x \log \left (\frac {x^2}{(x+\log (5))^2 \log (\log (x))}\right )}{\log (x) \log (\log (x))} \, dx-2 \int x \log ^2\left (\frac {x^2}{(x+\log (5))^2 \log (\log (x))}\right ) \, dx-2 \int \left (3 x^2 \log \left (\frac {x^2}{(x+\log (5))^2 \log (\log (x))}\right )+\log (25) \log \left (\frac {x^2}{(x+\log (5))^2 \log (\log (x))}\right )-\frac {\log (5) \log (25) \log \left (\frac {x^2}{(x+\log (5))^2 \log (\log (x))}\right )}{x+\log (5)}\right ) \, dx\\ &=-x^4-2 x^2 \log (5)+\frac {1}{2} x \left (1+8 \log ^2(5)\right )-4 \log ^3(5) \log (x+\log (5))+2 \int \frac {x^2}{\log (x) \log (\log (x))} \, dx+2 \int \frac {x \log \left (\frac {x^2}{(x+\log (5))^2 \log (\log (x))}\right )}{\log (x) \log (\log (x))} \, dx-2 \int x \log ^2\left (\frac {x^2}{(x+\log (5))^2 \log (\log (x))}\right ) \, dx-6 \int x^2 \log \left (\frac {x^2}{(x+\log (5))^2 \log (\log (x))}\right ) \, dx-(2 \log (25)) \int \log \left (\frac {x^2}{(x+\log (5))^2 \log (\log (x))}\right ) \, dx+(2 \log (5) \log (25)) \int \frac {\log \left (\frac {x^2}{(x+\log (5))^2 \log (\log (x))}\right )}{x+\log (5)} \, dx\\ &=-x^4-2 x^2 \log (5)+\frac {1}{2} x \left (1+8 \log ^2(5)\right )-4 \log ^3(5) \log (x+\log (5))-2 x^3 \log \left (\frac {x^2}{(x+\log (5))^2 \log (\log (x))}\right )-2 x \log (25) \log \left (\frac {x^2}{(x+\log (5))^2 \log (\log (x))}\right )+2 \int \frac {x^2}{\log (x) \log (\log (x))} \, dx+2 \int \frac {x \log \left (\frac {x^2}{(x+\log (5))^2 \log (\log (x))}\right )}{\log (x) \log (\log (x))} \, dx-2 \int x \log ^2\left (\frac {x^2}{(x+\log (5))^2 \log (\log (x))}\right ) \, dx+6 \int \frac {x^2 (-x-\log (5)+\log (25) \log (x) \log (\log (x)))}{3 (x+\log (5)) \log (x) \log (\log (x))} \, dx+(2 \log (25)) \int \frac {-x-\log (5)+\log (25) \log (x) \log (\log (x))}{(x+\log (5)) \log (x) \log (\log (x))} \, dx+(2 \log (5) \log (25)) \int \frac {\log \left (\frac {x^2}{(x+\log (5))^2 \log (\log (x))}\right )}{x+\log (5)} \, dx\\ &=-x^4-2 x^2 \log (5)+\frac {1}{2} x \left (1+8 \log ^2(5)\right )-4 \log ^3(5) \log (x+\log (5))-2 x^3 \log \left (\frac {x^2}{(x+\log (5))^2 \log (\log (x))}\right )-2 x \log (25) \log \left (\frac {x^2}{(x+\log (5))^2 \log (\log (x))}\right )+2 \int \frac {x^2}{\log (x) \log (\log (x))} \, dx+2 \int \frac {x^2 (-x-\log (5)+\log (25) \log (x) \log (\log (x)))}{(x+\log (5)) \log (x) \log (\log (x))} \, dx+2 \int \frac {x \log \left (\frac {x^2}{(x+\log (5))^2 \log (\log (x))}\right )}{\log (x) \log (\log (x))} \, dx-2 \int x \log ^2\left (\frac {x^2}{(x+\log (5))^2 \log (\log (x))}\right ) \, dx+(2 \log (25)) \int \left (\frac {\log (25)}{x+\log (5)}-\frac {1}{\log (x) \log (\log (x))}\right ) \, dx+(2 \log (5) \log (25)) \int \frac {\log \left (\frac {x^2}{(x+\log (5))^2 \log (\log (x))}\right )}{x+\log (5)} \, dx\\ &=-x^4-2 x^2 \log (5)+\frac {1}{2} x \left (1+8 \log ^2(5)\right )-4 \log ^3(5) \log (x+\log (5))+2 \log ^2(25) \log (x+\log (5))-2 x^3 \log \left (\frac {x^2}{(x+\log (5))^2 \log (\log (x))}\right )-2 x \log (25) \log \left (\frac {x^2}{(x+\log (5))^2 \log (\log (x))}\right )+2 \int \left (\frac {x^2 \log (25)}{x+\log (5)}-\frac {x^2}{\log (x) \log (\log (x))}\right ) \, dx+2 \int \frac {x^2}{\log (x) \log (\log (x))} \, dx+2 \int \frac {x \log \left (\frac {x^2}{(x+\log (5))^2 \log (\log (x))}\right )}{\log (x) \log (\log (x))} \, dx-2 \int x \log ^2\left (\frac {x^2}{(x+\log (5))^2 \log (\log (x))}\right ) \, dx-(2 \log (25)) \int \frac {1}{\log (x) \log (\log (x))} \, dx+(2 \log (5) \log (25)) \int \frac {\log \left (\frac {x^2}{(x+\log (5))^2 \log (\log (x))}\right )}{x+\log (5)} \, dx\\ &=-x^4-2 x^2 \log (5)+\frac {1}{2} x \left (1+8 \log ^2(5)\right )-4 \log ^3(5) \log (x+\log (5))+2 \log ^2(25) \log (x+\log (5))-2 x^3 \log \left (\frac {x^2}{(x+\log (5))^2 \log (\log (x))}\right )-2 x \log (25) \log \left (\frac {x^2}{(x+\log (5))^2 \log (\log (x))}\right )+2 \int \frac {x \log \left (\frac {x^2}{(x+\log (5))^2 \log (\log (x))}\right )}{\log (x) \log (\log (x))} \, dx-2 \int x \log ^2\left (\frac {x^2}{(x+\log (5))^2 \log (\log (x))}\right ) \, dx+(2 \log (25)) \int \frac {x^2}{x+\log (5)} \, dx-(2 \log (25)) \int \frac {1}{\log (x) \log (\log (x))} \, dx+(2 \log (5) \log (25)) \int \frac {\log \left (\frac {x^2}{(x+\log (5))^2 \log (\log (x))}\right )}{x+\log (5)} \, dx\\ &=-x^4-2 x^2 \log (5)+\frac {1}{2} x \left (1+8 \log ^2(5)\right )-4 \log ^3(5) \log (x+\log (5))+2 \log ^2(25) \log (x+\log (5))-2 x^3 \log \left (\frac {x^2}{(x+\log (5))^2 \log (\log (x))}\right )-2 x \log (25) \log \left (\frac {x^2}{(x+\log (5))^2 \log (\log (x))}\right )+2 \int \frac {x \log \left (\frac {x^2}{(x+\log (5))^2 \log (\log (x))}\right )}{\log (x) \log (\log (x))} \, dx-2 \int x \log ^2\left (\frac {x^2}{(x+\log (5))^2 \log (\log (x))}\right ) \, dx+(2 \log (25)) \int \left (x-\log (5)+\frac {\log ^2(5)}{x+\log (5)}\right ) \, dx-(2 \log (25)) \int \frac {1}{\log (x) \log (\log (x))} \, dx+(2 \log (5) \log (25)) \int \frac {\log \left (\frac {x^2}{(x+\log (5))^2 \log (\log (x))}\right )}{x+\log (5)} \, dx\\ &=-x^4-2 x^2 \log (5)+\frac {1}{2} x \left (1+8 \log ^2(5)\right )+x^2 \log (25)-2 x \log (5) \log (25)-4 \log ^3(5) \log (x+\log (5))+2 \log ^2(5) \log (25) \log (x+\log (5))+2 \log ^2(25) \log (x+\log (5))-2 x^3 \log \left (\frac {x^2}{(x+\log (5))^2 \log (\log (x))}\right )-2 x \log (25) \log \left (\frac {x^2}{(x+\log (5))^2 \log (\log (x))}\right )+2 \int \frac {x \log \left (\frac {x^2}{(x+\log (5))^2 \log (\log (x))}\right )}{\log (x) \log (\log (x))} \, dx-2 \int x \log ^2\left (\frac {x^2}{(x+\log (5))^2 \log (\log (x))}\right ) \, dx-(2 \log (25)) \int \frac {1}{\log (x) \log (\log (x))} \, dx+(2 \log (5) \log (25)) \int \frac {\log \left (\frac {x^2}{(x+\log (5))^2 \log (\log (x))}\right )}{x+\log (5)} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.26, size = 55, normalized size = 1.77 \begin {gather*} \frac {x}{2}-x^4-2 x^3 \log \left (\frac {x^2}{(x+\log (5))^2 \log (\log (x))}\right )-x^2 \log ^2\left (\frac {x^2}{(x+\log (5))^2 \log (\log (x))}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(4*x^3 + 4*x^2*Log[5] + (x - 8*x^4 + (1 - 8*x^2 - 8*x^3)*Log[5])*Log[x]*Log[Log[x]] + (4*x^2 + 4*x*L
og[5] + (-12*x^3 + (-8*x - 12*x^2)*Log[5])*Log[x]*Log[Log[x]])*Log[x^2/((x^2 + 2*x*Log[5] + Log[5]^2)*Log[Log[
x]])] + (-4*x^2 - 4*x*Log[5])*Log[x]*Log[Log[x]]*Log[x^2/((x^2 + 2*x*Log[5] + Log[5]^2)*Log[Log[x]])]^2)/((2*x
+ 2*Log[5])*Log[x]*Log[Log[x]]),x]

[Out]

x/2 - x^4 - 2*x^3*Log[x^2/((x + Log[5])^2*Log[Log[x]])] - x^2*Log[x^2/((x + Log[5])^2*Log[Log[x]])]^2

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fricas [B]  time = 1.07, size = 71, normalized size = 2.29 \begin {gather*} -x^{4} - 2 \, x^{3} \log \left (\frac {x^{2}}{{\left (x^{2} + 2 \, x \log \relax (5) + \log \relax (5)^{2}\right )} \log \left (\log \relax (x)\right )}\right ) - x^{2} \log \left (\frac {x^{2}}{{\left (x^{2} + 2 \, x \log \relax (5) + \log \relax (5)^{2}\right )} \log \left (\log \relax (x)\right )}\right )^{2} + \frac {1}{2} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-4*x*log(5)-4*x^2)*log(x)*log(log(x))*log(x^2/(log(5)^2+2*x*log(5)+x^2)/log(log(x)))^2+(((-12*x^2-
8*x)*log(5)-12*x^3)*log(x)*log(log(x))+4*x*log(5)+4*x^2)*log(x^2/(log(5)^2+2*x*log(5)+x^2)/log(log(x)))+((-8*x
^3-8*x^2+1)*log(5)-8*x^4+x)*log(x)*log(log(x))+4*x^2*log(5)+4*x^3)/(2*log(5)+2*x)/log(x)/log(log(x)),x, algori
thm="fricas")

[Out]

-x^4 - 2*x^3*log(x^2/((x^2 + 2*x*log(5) + log(5)^2)*log(log(x)))) - x^2*log(x^2/((x^2 + 2*x*log(5) + log(5)^2)
*log(log(x))))^2 + 1/2*x

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giac [B]  time = 3.81, size = 95, normalized size = 3.06 \begin {gather*} -x^{4} - x^{2} \log \left (x^{2} \log \left (\log \relax (x)\right ) + 2 \, x \log \relax (5) \log \left (\log \relax (x)\right ) + \log \relax (5)^{2} \log \left (\log \relax (x)\right )\right )^{2} - 4 \, x^{3} \log \relax (x) - 4 \, x^{2} \log \relax (x)^{2} + 2 \, {\left (x^{3} + 2 \, x^{2} \log \relax (x)\right )} \log \left (x^{2} \log \left (\log \relax (x)\right ) + 2 \, x \log \relax (5) \log \left (\log \relax (x)\right ) + \log \relax (5)^{2} \log \left (\log \relax (x)\right )\right ) + \frac {1}{2} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-4*x*log(5)-4*x^2)*log(x)*log(log(x))*log(x^2/(log(5)^2+2*x*log(5)+x^2)/log(log(x)))^2+(((-12*x^2-
8*x)*log(5)-12*x^3)*log(x)*log(log(x))+4*x*log(5)+4*x^2)*log(x^2/(log(5)^2+2*x*log(5)+x^2)/log(log(x)))+((-8*x
^3-8*x^2+1)*log(5)-8*x^4+x)*log(x)*log(log(x))+4*x^2*log(5)+4*x^3)/(2*log(5)+2*x)/log(x)/log(log(x)),x, algori
thm="giac")

[Out]

-x^4 - x^2*log(x^2*log(log(x)) + 2*x*log(5)*log(log(x)) + log(5)^2*log(log(x)))^2 - 4*x^3*log(x) - 4*x^2*log(x
)^2 + 2*(x^3 + 2*x^2*log(x))*log(x^2*log(log(x)) + 2*x*log(5)*log(log(x)) + log(5)^2*log(log(x))) + 1/2*x

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maple [C]  time = 0.90, size = 6484, normalized size = 209.16

method	result	size
risch	\(\text {Expression too large to display}\)	\(6484\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((-4*x*ln(5)-4*x^2)*ln(x)*ln(ln(x))*ln(x^2/(ln(5)^2+2*x*ln(5)+x^2)/ln(ln(x)))^2+(((-12*x^2-8*x)*ln(5)-12*x
^3)*ln(x)*ln(ln(x))+4*x*ln(5)+4*x^2)*ln(x^2/(ln(5)^2+2*x*ln(5)+x^2)/ln(ln(x)))+((-8*x^3-8*x^2+1)*ln(5)-8*x^4+x
)*ln(x)*ln(ln(x))+4*x^2*ln(5)+4*x^3)/(2*ln(5)+2*x)/ln(x)/ln(ln(x)),x,method=_RETURNVERBOSE)

[Out]

result too large to display

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maxima [B]  time = 0.69, size = 92, normalized size = 2.97 \begin {gather*} -x^{4} - 4 \, x^{2} \log \left (x + \log \relax (5)\right )^{2} - 4 \, x^{3} \log \relax (x) - 4 \, x^{2} \log \relax (x)^{2} - x^{2} \log \left (\log \left (\log \relax (x)\right )\right )^{2} + 4 \, {\left (x^{3} + 2 \, x^{2} \log \relax (x) - x^{2} \log \left (\log \left (\log \relax (x)\right )\right )\right )} \log \left (x + \log \relax (5)\right ) + 2 \, {\left (x^{3} + 2 \, x^{2} \log \relax (x)\right )} \log \left (\log \left (\log \relax (x)\right )\right ) + \frac {1}{2} \, x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-4*x*log(5)-4*x^2)*log(x)*log(log(x))*log(x^2/(log(5)^2+2*x*log(5)+x^2)/log(log(x)))^2+(((-12*x^2-
8*x)*log(5)-12*x^3)*log(x)*log(log(x))+4*x*log(5)+4*x^2)*log(x^2/(log(5)^2+2*x*log(5)+x^2)/log(log(x)))+((-8*x
^3-8*x^2+1)*log(5)-8*x^4+x)*log(x)*log(log(x))+4*x^2*log(5)+4*x^3)/(2*log(5)+2*x)/log(x)/log(log(x)),x, algori
thm="maxima")

[Out]

-x^4 - 4*x^2*log(x + log(5))^2 - 4*x^3*log(x) - 4*x^2*log(x)^2 - x^2*log(log(log(x)))^2 + 4*(x^3 + 2*x^2*log(x
) - x^2*log(log(log(x))))*log(x + log(5)) + 2*(x^3 + 2*x^2*log(x))*log(log(log(x))) + 1/2*x

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mupad [F]  time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int \frac {\ln \left (\frac {x^2}{\ln \left (\ln \relax (x)\right )\,\left (x^2+2\,\ln \relax (5)\,x+{\ln \relax (5)}^2\right )}\right )\,\left (4\,x\,\ln \relax (5)+4\,x^2-\ln \left (\ln \relax (x)\right )\,\ln \relax (x)\,\left (\ln \relax (5)\,\left (12\,x^2+8\,x\right )+12\,x^3\right )\right )+4\,x^2\,\ln \relax (5)+4\,x^3-\ln \left (\ln \relax (x)\right )\,\ln \relax (x)\,\left (\ln \relax (5)\,\left (8\,x^3+8\,x^2-1\right )-x+8\,x^4\right )-\ln \left (\ln \relax (x)\right )\,\ln \relax (x)\,{\ln \left (\frac {x^2}{\ln \left (\ln \relax (x)\right )\,\left (x^2+2\,\ln \relax (5)\,x+{\ln \relax (5)}^2\right )}\right )}^2\,\left (4\,x^2+4\,\ln \relax (5)\,x\right )}{\ln \left (\ln \relax (x)\right )\,\ln \relax (x)\,\left (2\,x+2\,\ln \relax (5)\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log(x^2/(log(log(x))*(2*x*log(5) + log(5)^2 + x^2)))*(4*x*log(5) + 4*x^2 - log(log(x))*log(x)*(log(5)*(8*
x + 12*x^2) + 12*x^3)) + 4*x^2*log(5) + 4*x^3 - log(log(x))*log(x)*(log(5)*(8*x^2 + 8*x^3 - 1) - x + 8*x^4) -
log(log(x))*log(x)*log(x^2/(log(log(x))*(2*x*log(5) + log(5)^2 + x^2)))^2*(4*x*log(5) + 4*x^2))/(log(log(x))*l
og(x)*(2*x + 2*log(5))),x)

[Out]

int((log(x^2/(log(log(x))*(2*x*log(5) + log(5)^2 + x^2)))*(4*x*log(5) + 4*x^2 - log(log(x))*log(x)*(log(5)*(8*
x + 12*x^2) + 12*x^3)) + 4*x^2*log(5) + 4*x^3 - log(log(x))*log(x)*(log(5)*(8*x^2 + 8*x^3 - 1) - x + 8*x^4) -
log(log(x))*log(x)*log(x^2/(log(log(x))*(2*x*log(5) + log(5)^2 + x^2)))^2*(4*x*log(5) + 4*x^2))/(log(log(x))*l
og(x)*(2*x + 2*log(5))), x)

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sympy [B]  time = 1.96, size = 66, normalized size = 2.13 \begin {gather*} - x^{4} - 2 x^{3} \log {\left (\frac {x^{2}}{\left (x^{2} + 2 x \log {\relax (5 )} + \log {\relax (5 )}^{2}\right ) \log {\left (\log {\relax (x )} \right )}} \right )} - x^{2} \log {\left (\frac {x^{2}}{\left (x^{2} + 2 x \log {\relax (5 )} + \log {\relax (5 )}^{2}\right ) \log {\left (\log {\relax (x )} \right )}} \right )}^{2} + \frac {x}{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((-4*x*ln(5)-4*x**2)*ln(x)*ln(ln(x))*ln(x**2/(ln(5)**2+2*x*ln(5)+x**2)/ln(ln(x)))**2+(((-12*x**2-8*x
)*ln(5)-12*x**3)*ln(x)*ln(ln(x))+4*x*ln(5)+4*x**2)*ln(x**2/(ln(5)**2+2*x*ln(5)+x**2)/ln(ln(x)))+((-8*x**3-8*x*
*2+1)*ln(5)-8*x**4+x)*ln(x)*ln(ln(x))+4*x**2*ln(5)+4*x**3)/(2*ln(5)+2*x)/ln(x)/ln(ln(x)),x)

[Out]

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

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