3.9.35 \(\int \frac {4^{\frac {-16-8 x-x^2}{-2-2 x+2 \log (\log (x^2))}} ((32+48 x+18 x^2+2 x^3) \log (4)+(2+8 x+10 x^2+4 x^3+(-8 x-6 x^2+3 x^3+x^4) \log (4)) \log (x^2)+(-4-12 x-8 x^2+(-8 x-10 x^2-2 x^3) \log (4)) \log (x^2) \log (\log (x^2))+(2+4 x) \log (x^2) \log ^2(\log (x^2)))}{(2+4 x+2 x^2) \log (x^2)+(-4-4 x) \log (x^2) \log (\log (x^2))+2 \log (x^2) \log ^2(\log (x^2))} \, dx\)

Optimal. Leaf size=26 \[ 2^{\frac {(4+x)^2}{1+x-\log \left (\log \left (x^2\right )\right )}} \left (x+x^2\right ) \]

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Rubi [F]  time = 21.49, 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^{\frac {-16-8 x-x^2}{-2-2 x+2 \log \left (\log \left (x^2\right )\right )}} \left (\left (32+48 x+18 x^2+2 x^3\right ) \log (4)+\left (2+8 x+10 x^2+4 x^3+\left (-8 x-6 x^2+3 x^3+x^4\right ) \log (4)\right ) \log \left (x^2\right )+\left (-4-12 x-8 x^2+\left (-8 x-10 x^2-2 x^3\right ) \log (4)\right ) \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )+(2+4 x) \log \left (x^2\right ) \log ^2\left (\log \left (x^2\right )\right )\right )}{\left (2+4 x+2 x^2\right ) \log \left (x^2\right )+(-4-4 x) \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )+2 \log \left (x^2\right ) \log ^2\left (\log \left (x^2\right )\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(4^((-16 - 8*x - x^2)/(-2 - 2*x + 2*Log[Log[x^2]]))*((32 + 48*x + 18*x^2 + 2*x^3)*Log[4] + (2 + 8*x + 10*x
^2 + 4*x^3 + (-8*x - 6*x^2 + 3*x^3 + x^4)*Log[4])*Log[x^2] + (-4 - 12*x - 8*x^2 + (-8*x - 10*x^2 - 2*x^3)*Log[
4])*Log[x^2]*Log[Log[x^2]] + (2 + 4*x)*Log[x^2]*Log[Log[x^2]]^2))/((2 + 4*x + 2*x^2)*Log[x^2] + (-4 - 4*x)*Log
[x^2]*Log[Log[x^2]] + 2*Log[x^2]*Log[Log[x^2]]^2),x]

[Out]

Defer[Int][2^((4 + x)^2/(1 + x - Log[Log[x^2]])), x] + Defer[Int][2^(1 + (4 + x)^2/(1 + x - Log[Log[x^2]]))*x,
x] - Log[4]*Defer[Int][(2^((19 + 11*x + x^2 - 3*Log[Log[x^2]])/(1 + x - Log[Log[x^2]]))*x)/(1 + x - Log[Log[x
^2]])^2, x] - Log[4]*Defer[Int][(2^((19 + 11*x + x^2 - 3*Log[Log[x^2]])/(1 + x - Log[Log[x^2]]))*x^2)/(1 + x -
Log[Log[x^2]])^2, x] - Log[65536]*Defer[Int][(2^((15 + 7*x + x^2 + Log[Log[x^2]])/(1 + x - Log[Log[x^2]]))*x^
2)/(1 + x - Log[Log[x^2]])^2, x] - Log[4]*Defer[Int][(2^((15 + 7*x + x^2 + Log[Log[x^2]])/(1 + x - Log[Log[x^2
]]))*x^3)/(1 + x - Log[Log[x^2]])^2, x] - Log[65536]*Defer[Int][(2^((15 + 7*x + x^2 + Log[Log[x^2]])/(1 + x -
Log[Log[x^2]]))*x^3)/(1 + x - Log[Log[x^2]])^2, x] - Log[4]*Defer[Int][(2^((15 + 7*x + x^2 + Log[Log[x^2]])/(1
+ x - Log[Log[x^2]]))*x^4)/(1 + x - Log[Log[x^2]])^2, x] + Log[4]*Defer[Int][2^((20 + 12*x + x^2 - 4*Log[Log[
x^2]])/(1 + x - Log[Log[x^2]]))/(Log[x^2]*(1 + x - Log[Log[x^2]])^2), x] + Log[4]*Defer[Int][(2^((20 + 12*x +
x^2 - 4*Log[Log[x^2]])/(1 + x - Log[Log[x^2]]))*x)/(Log[x^2]*(1 + x - Log[Log[x^2]])^2), x] + Log[4]*Defer[Int
][(2^((19 + 11*x + x^2 - 3*Log[Log[x^2]])/(1 + x - Log[Log[x^2]]))*x)/(Log[x^2]*(1 + x - Log[Log[x^2]])^2), x]
+ Log[4]*Defer[Int][(2^((4 + x)^2/(1 + x - Log[Log[x^2]]))*x^2)/(Log[x^2]*(1 + x - Log[Log[x^2]])^2), x] + Lo
g[4]*Defer[Int][(2^((19 + 11*x + x^2 - 3*Log[Log[x^2]])/(1 + x - Log[Log[x^2]]))*x^2)/(Log[x^2]*(1 + x - Log[L
og[x^2]])^2), x] + Log[4]*Defer[Int][(2^((4 + x)^2/(1 + x - Log[Log[x^2]]))*x^3)/(Log[x^2]*(1 + x - Log[Log[x^
2]])^2), x] + Log[4]*Defer[Int][(2^(2 + (4 + x)^2/(1 + x - Log[Log[x^2]]))*x)/(1 + x - Log[Log[x^2]]), x] + 5*
Log[4]*Defer[Int][(2^((4 + x)^2/(1 + x - Log[Log[x^2]]))*x^2)/(1 + x - Log[Log[x^2]]), x] + Log[4]*Defer[Int][
(2^((4 + x)^2/(1 + x - Log[Log[x^2]]))*x^3)/(1 + x - Log[Log[x^2]]), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2^{\frac {15+7 x+x^2+\log \left (\log \left (x^2\right )\right )}{1+x-\log \left (\log \left (x^2\right )\right )}} \left (2 (1+x) (4+x)^2 \log (4)+\log \left (x^2\right ) \left ((1+x) \left (2+x (6-8 \log (4))+x^3 \log (4)+x^2 (4+\log (16))\right )-2 (1+x) \left (2+x^2 \log (4)+4 x (1+\log (4))\right ) \log \left (\log \left (x^2\right )\right )+(2+4 x) \log ^2\left (\log \left (x^2\right )\right )\right )\right )}{\log \left (x^2\right ) \left (1+x-\log \left (\log \left (x^2\right )\right )\right )^2} \, dx\\ &=\int \left (2^{1+\frac {15+7 x+x^2+\log \left (\log \left (x^2\right )\right )}{1+x-\log \left (\log \left (x^2\right )\right )}} (1+2 x)-\frac {2^{\frac {15+7 x+x^2+\log \left (\log \left (x^2\right )\right )}{1+x-\log \left (\log \left (x^2\right )\right )}} (1+x) \left (-32 \log (4)-16 x \log (4)-2 x^2 \log (4)+16 x \log (4) \log \left (x^2\right )+x^3 \log (4) \log \left (x^2\right )+x^2 \log (65536) \log \left (x^2\right )\right )}{\log \left (x^2\right ) \left (1+x-\log \left (\log \left (x^2\right )\right )\right )^2}+\frac {2^{1+\frac {15+7 x+x^2+\log \left (\log \left (x^2\right )\right )}{1+x-\log \left (\log \left (x^2\right )\right )}} x \left (4+5 x+x^2\right ) \log (4)}{1+x-\log \left (\log \left (x^2\right )\right )}\right ) \, dx\\ &=\log (4) \int \frac {2^{1+\frac {15+7 x+x^2+\log \left (\log \left (x^2\right )\right )}{1+x-\log \left (\log \left (x^2\right )\right )}} x \left (4+5 x+x^2\right )}{1+x-\log \left (\log \left (x^2\right )\right )} \, dx+\int 2^{1+\frac {15+7 x+x^2+\log \left (\log \left (x^2\right )\right )}{1+x-\log \left (\log \left (x^2\right )\right )}} (1+2 x) \, dx-\int \frac {2^{\frac {15+7 x+x^2+\log \left (\log \left (x^2\right )\right )}{1+x-\log \left (\log \left (x^2\right )\right )}} (1+x) \left (-32 \log (4)-16 x \log (4)-2 x^2 \log (4)+16 x \log (4) \log \left (x^2\right )+x^3 \log (4) \log \left (x^2\right )+x^2 \log (65536) \log \left (x^2\right )\right )}{\log \left (x^2\right ) \left (1+x-\log \left (\log \left (x^2\right )\right )\right )^2} \, dx\\ &=\log (4) \int \frac {2^{\frac {(4+x)^2}{1+x-\log \left (\log \left (x^2\right )\right )}} x \left (4+5 x+x^2\right )}{1+x-\log \left (\log \left (x^2\right )\right )} \, dx+\int 2^{\frac {(4+x)^2}{1+x-\log \left (\log \left (x^2\right )\right )}} (1+2 x) \, dx-\int \frac {2^{\frac {15+7 x+x^2+\log \left (\log \left (x^2\right )\right )}{1+x-\log \left (\log \left (x^2\right )\right )}} (1+x) \left (-2 (4+x)^2 \log (4)+x \left (16 \log (4)+x^2 \log (4)+x \log (65536)\right ) \log \left (x^2\right )\right )}{\log \left (x^2\right ) \left (1+x-\log \left (\log \left (x^2\right )\right )\right )^2} \, dx\\ &=\log (4) \int \left (\frac {2^{2+\frac {(4+x)^2}{1+x-\log \left (\log \left (x^2\right )\right )}} x}{1+x-\log \left (\log \left (x^2\right )\right )}+\frac {5\ 2^{\frac {(4+x)^2}{1+x-\log \left (\log \left (x^2\right )\right )}} x^2}{1+x-\log \left (\log \left (x^2\right )\right )}+\frac {2^{\frac {(4+x)^2}{1+x-\log \left (\log \left (x^2\right )\right )}} x^3}{1+x-\log \left (\log \left (x^2\right )\right )}\right ) \, dx+\int \left (2^{\frac {(4+x)^2}{1+x-\log \left (\log \left (x^2\right )\right )}}+2^{1+\frac {(4+x)^2}{1+x-\log \left (\log \left (x^2\right )\right )}} x\right ) \, dx-\int \left (\frac {2^{\frac {15+7 x+x^2+\log \left (\log \left (x^2\right )\right )}{1+x-\log \left (\log \left (x^2\right )\right )}} \left (-32 \log (4)-16 x \log (4)-2 x^2 \log (4)+16 x \log (4) \log \left (x^2\right )+x^3 \log (4) \log \left (x^2\right )+x^2 \log (65536) \log \left (x^2\right )\right )}{\log \left (x^2\right ) \left (1+x-\log \left (\log \left (x^2\right )\right )\right )^2}+\frac {2^{\frac {15+7 x+x^2+\log \left (\log \left (x^2\right )\right )}{1+x-\log \left (\log \left (x^2\right )\right )}} x \left (-32 \log (4)-16 x \log (4)-2 x^2 \log (4)+16 x \log (4) \log \left (x^2\right )+x^3 \log (4) \log \left (x^2\right )+x^2 \log (65536) \log \left (x^2\right )\right )}{\log \left (x^2\right ) \left (1+x-\log \left (\log \left (x^2\right )\right )\right )^2}\right ) \, dx\\ &=\log (4) \int \frac {2^{2+\frac {(4+x)^2}{1+x-\log \left (\log \left (x^2\right )\right )}} x}{1+x-\log \left (\log \left (x^2\right )\right )} \, dx+\log (4) \int \frac {2^{\frac {(4+x)^2}{1+x-\log \left (\log \left (x^2\right )\right )}} x^3}{1+x-\log \left (\log \left (x^2\right )\right )} \, dx+(5 \log (4)) \int \frac {2^{\frac {(4+x)^2}{1+x-\log \left (\log \left (x^2\right )\right )}} x^2}{1+x-\log \left (\log \left (x^2\right )\right )} \, dx+\int 2^{\frac {(4+x)^2}{1+x-\log \left (\log \left (x^2\right )\right )}} \, dx+\int 2^{1+\frac {(4+x)^2}{1+x-\log \left (\log \left (x^2\right )\right )}} x \, dx-\int \frac {2^{\frac {15+7 x+x^2+\log \left (\log \left (x^2\right )\right )}{1+x-\log \left (\log \left (x^2\right )\right )}} \left (-32 \log (4)-16 x \log (4)-2 x^2 \log (4)+16 x \log (4) \log \left (x^2\right )+x^3 \log (4) \log \left (x^2\right )+x^2 \log (65536) \log \left (x^2\right )\right )}{\log \left (x^2\right ) \left (1+x-\log \left (\log \left (x^2\right )\right )\right )^2} \, dx-\int \frac {2^{\frac {15+7 x+x^2+\log \left (\log \left (x^2\right )\right )}{1+x-\log \left (\log \left (x^2\right )\right )}} x \left (-32 \log (4)-16 x \log (4)-2 x^2 \log (4)+16 x \log (4) \log \left (x^2\right )+x^3 \log (4) \log \left (x^2\right )+x^2 \log (65536) \log \left (x^2\right )\right )}{\log \left (x^2\right ) \left (1+x-\log \left (\log \left (x^2\right )\right )\right )^2} \, dx\\ &=\log (4) \int \frac {2^{2+\frac {(4+x)^2}{1+x-\log \left (\log \left (x^2\right )\right )}} x}{1+x-\log \left (\log \left (x^2\right )\right )} \, dx+\log (4) \int \frac {2^{\frac {(4+x)^2}{1+x-\log \left (\log \left (x^2\right )\right )}} x^3}{1+x-\log \left (\log \left (x^2\right )\right )} \, dx+(5 \log (4)) \int \frac {2^{\frac {(4+x)^2}{1+x-\log \left (\log \left (x^2\right )\right )}} x^2}{1+x-\log \left (\log \left (x^2\right )\right )} \, dx+\int 2^{\frac {(4+x)^2}{1+x-\log \left (\log \left (x^2\right )\right )}} \, dx+\int 2^{1+\frac {(4+x)^2}{1+x-\log \left (\log \left (x^2\right )\right )}} x \, dx-\int \frac {2^{\frac {15+7 x+x^2+\log \left (\log \left (x^2\right )\right )}{1+x-\log \left (\log \left (x^2\right )\right )}} \left (-2 (4+x)^2 \log (4)+x \left (16 \log (4)+x^2 \log (4)+x \log (65536)\right ) \log \left (x^2\right )\right )}{\log \left (x^2\right ) \left (1+x-\log \left (\log \left (x^2\right )\right )\right )^2} \, dx-\int \frac {2^{\frac {15+7 x+x^2+\log \left (\log \left (x^2\right )\right )}{1+x-\log \left (\log \left (x^2\right )\right )}} x \left (-2 (4+x)^2 \log (4)+x \left (16 \log (4)+x^2 \log (4)+x \log (65536)\right ) \log \left (x^2\right )\right )}{\log \left (x^2\right ) \left (1+x-\log \left (\log \left (x^2\right )\right )\right )^2} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}

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Mathematica [F]  time = 3.62, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {4^{\frac {-16-8 x-x^2}{-2-2 x+2 \log \left (\log \left (x^2\right )\right )}} \left (\left (32+48 x+18 x^2+2 x^3\right ) \log (4)+\left (2+8 x+10 x^2+4 x^3+\left (-8 x-6 x^2+3 x^3+x^4\right ) \log (4)\right ) \log \left (x^2\right )+\left (-4-12 x-8 x^2+\left (-8 x-10 x^2-2 x^3\right ) \log (4)\right ) \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )+(2+4 x) \log \left (x^2\right ) \log ^2\left (\log \left (x^2\right )\right )\right )}{\left (2+4 x+2 x^2\right ) \log \left (x^2\right )+(-4-4 x) \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )+2 \log \left (x^2\right ) \log ^2\left (\log \left (x^2\right )\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Integrate[(4^((-16 - 8*x - x^2)/(-2 - 2*x + 2*Log[Log[x^2]]))*((32 + 48*x + 18*x^2 + 2*x^3)*Log[4] + (2 + 8*x
+ 10*x^2 + 4*x^3 + (-8*x - 6*x^2 + 3*x^3 + x^4)*Log[4])*Log[x^2] + (-4 - 12*x - 8*x^2 + (-8*x - 10*x^2 - 2*x^3
)*Log[4])*Log[x^2]*Log[Log[x^2]] + (2 + 4*x)*Log[x^2]*Log[Log[x^2]]^2))/((2 + 4*x + 2*x^2)*Log[x^2] + (-4 - 4*
x)*Log[x^2]*Log[Log[x^2]] + 2*Log[x^2]*Log[Log[x^2]]^2),x]

[Out]

Integrate[(4^((-16 - 8*x - x^2)/(-2 - 2*x + 2*Log[Log[x^2]]))*((32 + 48*x + 18*x^2 + 2*x^3)*Log[4] + (2 + 8*x
+ 10*x^2 + 4*x^3 + (-8*x - 6*x^2 + 3*x^3 + x^4)*Log[4])*Log[x^2] + (-4 - 12*x - 8*x^2 + (-8*x - 10*x^2 - 2*x^3
)*Log[4])*Log[x^2]*Log[Log[x^2]] + (2 + 4*x)*Log[x^2]*Log[Log[x^2]]^2))/((2 + 4*x + 2*x^2)*Log[x^2] + (-4 - 4*
x)*Log[x^2]*Log[Log[x^2]] + 2*Log[x^2]*Log[Log[x^2]]^2), x]

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fricas [A]  time = 1.04, size = 29, normalized size = 1.12 \begin {gather*} {\left (x^{2} + x\right )} 2^{\frac {x^{2} + 8 \, x + 16}{x - \log \left (\log \left (x^{2}\right )\right ) + 1}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x+2)*log(x^2)*log(log(x^2))^2+(2*(-2*x^3-10*x^2-8*x)*log(2)-8*x^2-12*x-4)*log(x^2)*log(log(x^2))
+(2*(x^4+3*x^3-6*x^2-8*x)*log(2)+4*x^3+10*x^2+8*x+2)*log(x^2)+2*(2*x^3+18*x^2+48*x+32)*log(2))*exp(2*(-x^2-8*x
-16)*log(2)/(2*log(log(x^2))-2*x-2))/(2*log(x^2)*log(log(x^2))^2+(-4*x-4)*log(x^2)*log(log(x^2))+(2*x^2+4*x+2)
*log(x^2)),x, algorithm="fricas")

[Out]

(x^2 + x)*2^((x^2 + 8*x + 16)/(x - log(log(x^2)) + 1))

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int -\frac {{\left ({\left (2 \, x + 1\right )} \log \left (x^{2}\right ) \log \left (\log \left (x^{2}\right )\right )^{2} - 2 \, {\left (2 \, x^{2} + {\left (x^{3} + 5 \, x^{2} + 4 \, x\right )} \log \relax (2) + 3 \, x + 1\right )} \log \left (x^{2}\right ) \log \left (\log \left (x^{2}\right )\right ) + 2 \, {\left (x^{3} + 9 \, x^{2} + 24 \, x + 16\right )} \log \relax (2) + {\left (2 \, x^{3} + 5 \, x^{2} + {\left (x^{4} + 3 \, x^{3} - 6 \, x^{2} - 8 \, x\right )} \log \relax (2) + 4 \, x + 1\right )} \log \left (x^{2}\right )\right )} 2^{\frac {x^{2} + 8 \, x + 16}{x - \log \left (\log \left (x^{2}\right )\right ) + 1}}}{2 \, {\left (x + 1\right )} \log \left (x^{2}\right ) \log \left (\log \left (x^{2}\right )\right ) - \log \left (x^{2}\right ) \log \left (\log \left (x^{2}\right )\right )^{2} - {\left (x^{2} + 2 \, x + 1\right )} \log \left (x^{2}\right )}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x+2)*log(x^2)*log(log(x^2))^2+(2*(-2*x^3-10*x^2-8*x)*log(2)-8*x^2-12*x-4)*log(x^2)*log(log(x^2))
+(2*(x^4+3*x^3-6*x^2-8*x)*log(2)+4*x^3+10*x^2+8*x+2)*log(x^2)+2*(2*x^3+18*x^2+48*x+32)*log(2))*exp(2*(-x^2-8*x
-16)*log(2)/(2*log(log(x^2))-2*x-2))/(2*log(x^2)*log(log(x^2))^2+(-4*x-4)*log(x^2)*log(log(x^2))+(2*x^2+4*x+2)
*log(x^2)),x, algorithm="giac")

[Out]

integrate(-((2*x + 1)*log(x^2)*log(log(x^2))^2 - 2*(2*x^2 + (x^3 + 5*x^2 + 4*x)*log(2) + 3*x + 1)*log(x^2)*log
(log(x^2)) + 2*(x^3 + 9*x^2 + 24*x + 16)*log(2) + (2*x^3 + 5*x^2 + (x^4 + 3*x^3 - 6*x^2 - 8*x)*log(2) + 4*x +
1)*log(x^2))*2^((x^2 + 8*x + 16)/(x - log(log(x^2)) + 1))/(2*(x + 1)*log(x^2)*log(log(x^2)) - log(x^2)*log(log
(x^2))^2 - (x^2 + 2*x + 1)*log(x^2)), x)

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maple [F]  time = 0.12, size = 0, normalized size = 0.00 \[\int \frac {\left (\left (4 x +2\right ) \ln \left (x^{2}\right ) \ln \left (\ln \left (x^{2}\right )\right )^{2}+\left (2 \left (-2 x^{3}-10 x^{2}-8 x \right ) \ln \relax (2)-8 x^{2}-12 x -4\right ) \ln \left (x^{2}\right ) \ln \left (\ln \left (x^{2}\right )\right )+\left (2 \left (x^{4}+3 x^{3}-6 x^{2}-8 x \right ) \ln \relax (2)+4 x^{3}+10 x^{2}+8 x +2\right ) \ln \left (x^{2}\right )+2 \left (2 x^{3}+18 x^{2}+48 x +32\right ) \ln \relax (2)\right ) {\mathrm e}^{\frac {2 \left (-x^{2}-8 x -16\right ) \ln \relax (2)}{2 \ln \left (\ln \left (x^{2}\right )\right )-2 x -2}}}{2 \ln \left (x^{2}\right ) \ln \left (\ln \left (x^{2}\right )\right )^{2}+\left (-4 x -4\right ) \ln \left (x^{2}\right ) \ln \left (\ln \left (x^{2}\right )\right )+\left (2 x^{2}+4 x +2\right ) \ln \left (x^{2}\right )}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((4*x+2)*ln(x^2)*ln(ln(x^2))^2+(2*(-2*x^3-10*x^2-8*x)*ln(2)-8*x^2-12*x-4)*ln(x^2)*ln(ln(x^2))+(2*(x^4+3*x^
3-6*x^2-8*x)*ln(2)+4*x^3+10*x^2+8*x+2)*ln(x^2)+2*(2*x^3+18*x^2+48*x+32)*ln(2))*exp(2*(-x^2-8*x-16)*ln(2)/(2*ln
(ln(x^2))-2*x-2))/(2*ln(x^2)*ln(ln(x^2))^2+(-4*x-4)*ln(x^2)*ln(ln(x^2))+(2*x^2+4*x+2)*ln(x^2)),x)

[Out]

int(((4*x+2)*ln(x^2)*ln(ln(x^2))^2+(2*(-2*x^3-10*x^2-8*x)*ln(2)-8*x^2-12*x-4)*ln(x^2)*ln(ln(x^2))+(2*(x^4+3*x^
3-6*x^2-8*x)*ln(2)+4*x^3+10*x^2+8*x+2)*ln(x^2)+2*(2*x^3+18*x^2+48*x+32)*ln(2))*exp(2*(-x^2-8*x-16)*ln(2)/(2*ln
(ln(x^2))-2*x-2))/(2*ln(x^2)*ln(ln(x^2))^2+(-4*x-4)*ln(x^2)*ln(ln(x^2))+(2*x^2+4*x+2)*ln(x^2)),x)

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maxima [F(-2)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: RuntimeError} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x+2)*log(x^2)*log(log(x^2))^2+(2*(-2*x^3-10*x^2-8*x)*log(2)-8*x^2-12*x-4)*log(x^2)*log(log(x^2))
+(2*(x^4+3*x^3-6*x^2-8*x)*log(2)+4*x^3+10*x^2+8*x+2)*log(x^2)+2*(2*x^3+18*x^2+48*x+32)*log(2))*exp(2*(-x^2-8*x
-16)*log(2)/(2*log(log(x^2))-2*x-2))/(2*log(x^2)*log(log(x^2))^2+(-4*x-4)*log(x^2)*log(log(x^2))+(2*x^2+4*x+2)
*log(x^2)),x, algorithm="maxima")

[Out]

Exception raised: RuntimeError >> ECL says: In function CAR, the value of the first argument is  0which is not
of the expected type LIST

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mupad [F]  time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {{\mathrm {e}}^{\frac {2\,\ln \relax (2)\,\left (x^2+8\,x+16\right )}{2\,x-2\,\ln \left (\ln \left (x^2\right )\right )+2}}\,\left (\ln \left (x^2\right )\,\left (4\,x+2\right )\,{\ln \left (\ln \left (x^2\right )\right )}^2-\ln \left (x^2\right )\,\left (12\,x+2\,\ln \relax (2)\,\left (2\,x^3+10\,x^2+8\,x\right )+8\,x^2+4\right )\,\ln \left (\ln \left (x^2\right )\right )+2\,\ln \relax (2)\,\left (2\,x^3+18\,x^2+48\,x+32\right )+\ln \left (x^2\right )\,\left (8\,x-2\,\ln \relax (2)\,\left (-x^4-3\,x^3+6\,x^2+8\,x\right )+10\,x^2+4\,x^3+2\right )\right )}{2\,\ln \left (x^2\right )\,{\ln \left (\ln \left (x^2\right )\right )}^2-\ln \left (x^2\right )\,\left (4\,x+4\right )\,\ln \left (\ln \left (x^2\right )\right )+\ln \left (x^2\right )\,\left (2\,x^2+4\,x+2\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp((2*log(2)*(8*x + x^2 + 16))/(2*x - 2*log(log(x^2)) + 2))*(2*log(2)*(48*x + 18*x^2 + 2*x^3 + 32) + log
(x^2)*(8*x - 2*log(2)*(8*x + 6*x^2 - 3*x^3 - x^4) + 10*x^2 + 4*x^3 + 2) - log(x^2)*log(log(x^2))*(12*x + 2*log
(2)*(8*x + 10*x^2 + 2*x^3) + 8*x^2 + 4) + log(x^2)*log(log(x^2))^2*(4*x + 2)))/(log(x^2)*(4*x + 2*x^2 + 2) + 2
*log(x^2)*log(log(x^2))^2 - log(x^2)*log(log(x^2))*(4*x + 4)),x)

[Out]

int((exp((2*log(2)*(8*x + x^2 + 16))/(2*x - 2*log(log(x^2)) + 2))*(2*log(2)*(48*x + 18*x^2 + 2*x^3 + 32) + log
(x^2)*(8*x - 2*log(2)*(8*x + 6*x^2 - 3*x^3 - x^4) + 10*x^2 + 4*x^3 + 2) - log(x^2)*log(log(x^2))*(12*x + 2*log
(2)*(8*x + 10*x^2 + 2*x^3) + 8*x^2 + 4) + log(x^2)*log(log(x^2))^2*(4*x + 2)))/(log(x^2)*(4*x + 2*x^2 + 2) + 2
*log(x^2)*log(log(x^2))^2 - log(x^2)*log(log(x^2))*(4*x + 4)), x)

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sympy [A]  time = 9.68, size = 34, normalized size = 1.31 \begin {gather*} \left (x^{2} + x\right ) e^{\frac {\left (- 2 x^{2} - 16 x - 32\right ) \log {\relax (2 )}}{- 2 x + 2 \log {\left (\log {\left (x^{2} \right )} \right )} - 2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((4*x+2)*ln(x**2)*ln(ln(x**2))**2+(2*(-2*x**3-10*x**2-8*x)*ln(2)-8*x**2-12*x-4)*ln(x**2)*ln(ln(x**2)
)+(2*(x**4+3*x**3-6*x**2-8*x)*ln(2)+4*x**3+10*x**2+8*x+2)*ln(x**2)+2*(2*x**3+18*x**2+48*x+32)*ln(2))*exp(2*(-x
**2-8*x-16)*ln(2)/(2*ln(ln(x**2))-2*x-2))/(2*ln(x**2)*ln(ln(x**2))**2+(-4*x-4)*ln(x**2)*ln(ln(x**2))+(2*x**2+4
*x+2)*ln(x**2)),x)

[Out]

(x**2 + x)*exp((-2*x**2 - 16*x - 32)*log(2)/(-2*x + 2*log(log(x**2)) - 2))

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