3.22.94 \(\int \frac {(-4+4 x^2-x^4+\log ^2(\frac {x^3}{3})+(4-2 x^2) \log (\log (x))-\log ^2(\log (x)))^x (-4+2 x^2+(-8 x^2+4 x^4) \log (x)-6 \log (x) \log (\frac {x^3}{3})+(2+4 x^2 \log (x)) \log (\log (x))+((4-4 x^2+x^4) \log (x)-\log (x) \log ^2(\frac {x^3}{3})+(-4+2 x^2) \log (x) \log (\log (x))+\log (x) \log ^2(\log (x))) \log (-4+4 x^2-x^4+\log ^2(\frac {x^3}{3})+(4-2 x^2) \log (\log (x))-\log ^2(\log (x))))}{(4-4 x^2+x^4) \log (x)-\log (x) \log ^2(\frac {x^3}{3})+(-4+2 x^2) \log (x) \log (\log (x))+\log (x) \log ^2(\log (x))} \, dx\)

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

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Rubi [F]  time = 4.17, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {\left (-4+4 x^2-x^4+\log ^2\left (\frac {x^3}{3}\right )+\left (4-2 x^2\right ) \log (\log (x))-\log ^2(\log (x))\right )^x \left (-4+2 x^2+\left (-8 x^2+4 x^4\right ) \log (x)-6 \log (x) \log \left (\frac {x^3}{3}\right )+\left (2+4 x^2 \log (x)\right ) \log (\log (x))+\left (\left (4-4 x^2+x^4\right ) \log (x)-\log (x) \log ^2\left (\frac {x^3}{3}\right )+\left (-4+2 x^2\right ) \log (x) \log (\log (x))+\log (x) \log ^2(\log (x))\right ) \log \left (-4+4 x^2-x^4+\log ^2\left (\frac {x^3}{3}\right )+\left (4-2 x^2\right ) \log (\log (x))-\log ^2(\log (x))\right )\right )}{\left (4-4 x^2+x^4\right ) \log (x)-\log (x) \log ^2\left (\frac {x^3}{3}\right )+\left (-4+2 x^2\right ) \log (x) \log (\log (x))+\log (x) \log ^2(\log (x))} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[((-4 + 4*x^2 - x^4 + Log[x^3/3]^2 + (4 - 2*x^2)*Log[Log[x]] - Log[Log[x]]^2)^x*(-4 + 2*x^2 + (-8*x^2 + 4*x
^4)*Log[x] - 6*Log[x]*Log[x^3/3] + (2 + 4*x^2*Log[x])*Log[Log[x]] + ((4 - 4*x^2 + x^4)*Log[x] - Log[x]*Log[x^3
/3]^2 + (-4 + 2*x^2)*Log[x]*Log[Log[x]] + Log[x]*Log[Log[x]]^2)*Log[-4 + 4*x^2 - x^4 + Log[x^3/3]^2 + (4 - 2*x
^2)*Log[Log[x]] - Log[Log[x]]^2]))/((4 - 4*x^2 + x^4)*Log[x] - Log[x]*Log[x^3/3]^2 + (-4 + 2*x^2)*Log[x]*Log[L
og[x]] + Log[x]*Log[Log[x]]^2),x]

[Out]

-2*Log[27]*Defer[Int][(Log[x^3/3]^2 - (-2 + x^2 + Log[Log[x]])^2)^(-1 + x), x] + 8*Defer[Int][x^2*(Log[x^3/3]^
2 - (-2 + x^2 + Log[Log[x]])^2)^(-1 + x), x] - 4*Defer[Int][x^4*(Log[x^3/3]^2 - (-2 + x^2 + Log[Log[x]])^2)^(-
1 + x), x] + 4*Defer[Int][(Log[x^3/3]^2 - (-2 + x^2 + Log[Log[x]])^2)^(-1 + x)/Log[x], x] - 2*Defer[Int][(x^2*
(Log[x^3/3]^2 - (-2 + x^2 + Log[Log[x]])^2)^(-1 + x))/Log[x], x] + 6*Defer[Int][Log[x^3]*(Log[x^3/3]^2 - (-2 +
x^2 + Log[Log[x]])^2)^(-1 + x), x] - 4*Defer[Int][x^2*Log[Log[x]]*(Log[x^3/3]^2 - (-2 + x^2 + Log[Log[x]])^2)
^(-1 + x), x] - 2*Defer[Int][(Log[Log[x]]*(Log[x^3/3]^2 - (-2 + x^2 + Log[Log[x]])^2)^(-1 + x))/Log[x], x] + D
efer[Int][(Log[x^3/3]^2 - (-2 + x^2 + Log[Log[x]])^2)^x*Log[Log[x^3/3]^2 - (-2 + x^2 + Log[Log[x]])^2], x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right )^{-1+x} \left (4-2 x^2-4 x^2 \left (-2+x^2\right ) \log (x)+6 \log (x) \log \left (\frac {x^3}{3}\right )-\left (2+4 x^2 \log (x)\right ) \log (\log (x))-\log (x) \left (-\log ^2\left (\frac {x^3}{3}\right )+\left (-2+x^2+\log (\log (x))\right )^2\right ) \log \left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right )\right )}{\log (x)} \, dx\\ &=\int \left (-\frac {2 \left (-2+x^2-4 x^2 \log (x)+2 x^4 \log (x)+\log (27) \log (x)-3 \log (x) \log \left (x^3\right )+\log (\log (x))+2 x^2 \log (x) \log (\log (x))\right ) \left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right )^{-1+x}}{\log (x)}+\left (2-x^2-\log \left (\frac {x^3}{3}\right )-\log (\log (x))\right ) \left (x^2-2 \left (1-\frac {\log (3)}{2}\right )-\log \left (x^3\right )+\log (\log (x))\right ) \left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right )^{-1+x} \log \left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right )\right ) \, dx\\ &=-\left (2 \int \frac {\left (-2+x^2-4 x^2 \log (x)+2 x^4 \log (x)+\log (27) \log (x)-3 \log (x) \log \left (x^3\right )+\log (\log (x))+2 x^2 \log (x) \log (\log (x))\right ) \left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right )^{-1+x}}{\log (x)} \, dx\right )+\int \left (2-x^2-\log \left (\frac {x^3}{3}\right )-\log (\log (x))\right ) \left (x^2-2 \left (1-\frac {\log (3)}{2}\right )-\log \left (x^3\right )+\log (\log (x))\right ) \left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right )^{-1+x} \log \left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right ) \, dx\\ &=-\left (2 \int \left (\frac {\left (-2+x^2-4 x^2 \log (x)+2 x^4 \log (x)+\log (27) \log (x)-3 \log (x) \log \left (x^3\right )\right ) \left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right )^{-1+x}}{\log (x)}+\frac {\left (1+2 x^2 \log (x)\right ) \log (\log (x)) \left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right )^{-1+x}}{\log (x)}\right ) \, dx\right )+\int \left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right )^x \log \left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right ) \, dx\\ &=-\left (2 \int \frac {\left (-2+x^2-4 x^2 \log (x)+2 x^4 \log (x)+\log (27) \log (x)-3 \log (x) \log \left (x^3\right )\right ) \left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right )^{-1+x}}{\log (x)} \, dx\right )-2 \int \frac {\left (1+2 x^2 \log (x)\right ) \log (\log (x)) \left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right )^{-1+x}}{\log (x)} \, dx+\int \left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right )^x \log \left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right ) \, dx\\ &=-\left (2 \int \left (\frac {\left (-2+x^2-4 x^2 \log (x)+2 x^4 \log (x)+\log (27) \log (x)\right ) \left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right )^{-1+x}}{\log (x)}-3 \log \left (x^3\right ) \left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right )^{-1+x}\right ) \, dx\right )-2 \int \left (2 x^2 \log (\log (x)) \left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right )^{-1+x}+\frac {\log (\log (x)) \left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right )^{-1+x}}{\log (x)}\right ) \, dx+\int \left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right )^x \log \left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right ) \, dx\\ &=-\left (2 \int \frac {\left (-2+x^2-4 x^2 \log (x)+2 x^4 \log (x)+\log (27) \log (x)\right ) \left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right )^{-1+x}}{\log (x)} \, dx\right )-2 \int \frac {\log (\log (x)) \left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right )^{-1+x}}{\log (x)} \, dx-4 \int x^2 \log (\log (x)) \left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right )^{-1+x} \, dx+6 \int \log \left (x^3\right ) \left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right )^{-1+x} \, dx+\int \left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right )^x \log \left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right ) \, dx\\ &=-\left (2 \int \frac {\log (\log (x)) \left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right )^{-1+x}}{\log (x)} \, dx\right )-2 \int \left (-4 x^2 \left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right )^{-1+x}+2 x^4 \left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right )^{-1+x}+\log (27) \left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right )^{-1+x}+\frac {\left (-2+x^2\right ) \left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right )^{-1+x}}{\log (x)}\right ) \, dx-4 \int x^2 \log (\log (x)) \left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right )^{-1+x} \, dx+6 \int \log \left (x^3\right ) \left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right )^{-1+x} \, dx+\int \left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right )^x \log \left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right ) \, dx\\ &=-\left (2 \int \frac {\left (-2+x^2\right ) \left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right )^{-1+x}}{\log (x)} \, dx\right )-2 \int \frac {\log (\log (x)) \left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right )^{-1+x}}{\log (x)} \, dx-4 \int x^4 \left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right )^{-1+x} \, dx-4 \int x^2 \log (\log (x)) \left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right )^{-1+x} \, dx+6 \int \log \left (x^3\right ) \left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right )^{-1+x} \, dx+8 \int x^2 \left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right )^{-1+x} \, dx-(2 \log (27)) \int \left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right )^{-1+x} \, dx+\int \left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right )^x \log \left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right ) \, dx\\ &=-\left (2 \int \frac {\log (\log (x)) \left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right )^{-1+x}}{\log (x)} \, dx\right )-2 \int \left (-\frac {2 \left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right )^{-1+x}}{\log (x)}+\frac {x^2 \left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right )^{-1+x}}{\log (x)}\right ) \, dx-4 \int x^4 \left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right )^{-1+x} \, dx-4 \int x^2 \log (\log (x)) \left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right )^{-1+x} \, dx+6 \int \log \left (x^3\right ) \left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right )^{-1+x} \, dx+8 \int x^2 \left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right )^{-1+x} \, dx-(2 \log (27)) \int \left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right )^{-1+x} \, dx+\int \left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right )^x \log \left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right ) \, dx\\ &=-\left (2 \int \frac {x^2 \left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right )^{-1+x}}{\log (x)} \, dx\right )-2 \int \frac {\log (\log (x)) \left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right )^{-1+x}}{\log (x)} \, dx-4 \int x^4 \left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right )^{-1+x} \, dx+4 \int \frac {\left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right )^{-1+x}}{\log (x)} \, dx-4 \int x^2 \log (\log (x)) \left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right )^{-1+x} \, dx+6 \int \log \left (x^3\right ) \left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right )^{-1+x} \, dx+8 \int x^2 \left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right )^{-1+x} \, dx-(2 \log (27)) \int \left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right )^{-1+x} \, dx+\int \left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right )^x \log \left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right ) \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.22, size = 25, normalized size = 1.00 \begin {gather*} \left (\log ^2\left (\frac {x^3}{3}\right )-\left (-2+x^2+\log (\log (x))\right )^2\right )^x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[((-4 + 4*x^2 - x^4 + Log[x^3/3]^2 + (4 - 2*x^2)*Log[Log[x]] - Log[Log[x]]^2)^x*(-4 + 2*x^2 + (-8*x^2
+ 4*x^4)*Log[x] - 6*Log[x]*Log[x^3/3] + (2 + 4*x^2*Log[x])*Log[Log[x]] + ((4 - 4*x^2 + x^4)*Log[x] - Log[x]*L
og[x^3/3]^2 + (-4 + 2*x^2)*Log[x]*Log[Log[x]] + Log[x]*Log[Log[x]]^2)*Log[-4 + 4*x^2 - x^4 + Log[x^3/3]^2 + (4
- 2*x^2)*Log[Log[x]] - Log[Log[x]]^2]))/((4 - 4*x^2 + x^4)*Log[x] - Log[x]*Log[x^3/3]^2 + (-4 + 2*x^2)*Log[x]
*Log[Log[x]] + Log[x]*Log[Log[x]]^2),x]

[Out]

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

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fricas [B]  time = 0.88, size = 47, normalized size = 1.88 \begin {gather*} {\left (-x^{4} + 4 \, x^{2} + \log \relax (3)^{2} - 6 \, \log \relax (3) \log \relax (x) + 9 \, \log \relax (x)^{2} - 2 \, {\left (x^{2} - 2\right )} \log \left (\log \relax (x)\right ) - \log \left (\log \relax (x)\right )^{2} - 4\right )}^{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((log(x)*log(log(x))^2+(2*x^2-4)*log(x)*log(log(x))-log(x)*log(1/3*x^3)^2+(x^4-4*x^2+4)*log(x))*log(
-log(log(x))^2+(-2*x^2+4)*log(log(x))+log(1/3*x^3)^2-x^4+4*x^2-4)+(4*x^2*log(x)+2)*log(log(x))-6*log(x)*log(1/
3*x^3)+(4*x^4-8*x^2)*log(x)+2*x^2-4)*exp(x*log(-log(log(x))^2+(-2*x^2+4)*log(log(x))+log(1/3*x^3)^2-x^4+4*x^2-
4))/(log(x)*log(log(x))^2+(2*x^2-4)*log(x)*log(log(x))-log(x)*log(1/3*x^3)^2+(x^4-4*x^2+4)*log(x)),x, algorith
m="fricas")

[Out]

(-x^4 + 4*x^2 + log(3)^2 - 6*log(3)*log(x) + 9*log(x)^2 - 2*(x^2 - 2)*log(log(x)) - log(log(x))^2 - 4)^x

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giac [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((log(x)*log(log(x))^2+(2*x^2-4)*log(x)*log(log(x))-log(x)*log(1/3*x^3)^2+(x^4-4*x^2+4)*log(x))*log(
-log(log(x))^2+(-2*x^2+4)*log(log(x))+log(1/3*x^3)^2-x^4+4*x^2-4)+(4*x^2*log(x)+2)*log(log(x))-6*log(x)*log(1/
3*x^3)+(4*x^4-8*x^2)*log(x)+2*x^2-4)*exp(x*log(-log(log(x))^2+(-2*x^2+4)*log(log(x))+log(1/3*x^3)^2-x^4+4*x^2-
4))/(log(x)*log(log(x))^2+(2*x^2-4)*log(x)*log(log(x))-log(x)*log(1/3*x^3)^2+(x^4-4*x^2+4)*log(x)),x, algorith
m="giac")

[Out]

Timed out

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maple [C]  time = 0.30, size = 115, normalized size = 4.60

method	result	size
risch	\(\left (-\ln \left (\ln \relax (x )\right )^{2}+\left (-2 x^{2}+4\right ) \ln \left (\ln \relax (x )\right )+\left (-\ln \relax (3)+3 \ln \relax (x )-\frac {i \pi \,\mathrm {csgn}\left (i x^{2}\right ) \left (-\mathrm {csgn}\left (i x^{2}\right )+\mathrm {csgn}\left (i x \right )\right )^{2}}{2}-\frac {i \pi \,\mathrm {csgn}\left (i x^{3}\right ) \left (-\mathrm {csgn}\left (i x^{3}\right )+\mathrm {csgn}\left (i x^{2}\right )\right ) \left (-\mathrm {csgn}\left (i x^{3}\right )+\mathrm {csgn}\left (i x \right )\right )}{2}\right )^{2}-x^{4}+4 x^{2}-4\right )^{x}\)	\(115\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((ln(x)*ln(ln(x))^2+(2*x^2-4)*ln(x)*ln(ln(x))-ln(x)*ln(1/3*x^3)^2+(x^4-4*x^2+4)*ln(x))*ln(-ln(ln(x))^2+(-2
*x^2+4)*ln(ln(x))+ln(1/3*x^3)^2-x^4+4*x^2-4)+(4*x^2*ln(x)+2)*ln(ln(x))-6*ln(x)*ln(1/3*x^3)+(4*x^4-8*x^2)*ln(x)
+2*x^2-4)*exp(x*ln(-ln(ln(x))^2+(-2*x^2+4)*ln(ln(x))+ln(1/3*x^3)^2-x^4+4*x^2-4))/(ln(x)*ln(ln(x))^2+(2*x^2-4)*
ln(x)*ln(ln(x))-ln(x)*ln(1/3*x^3)^2+(x^4-4*x^2+4)*ln(x)),x,method=_RETURNVERBOSE)

[Out]

(-ln(ln(x))^2+(-2*x^2+4)*ln(ln(x))+(-ln(3)+3*ln(x)-1/2*I*Pi*csgn(I*x^2)*(-csgn(I*x^2)+csgn(I*x))^2-1/2*I*Pi*cs
gn(I*x^3)*(-csgn(I*x^3)+csgn(I*x^2))*(-csgn(I*x^3)+csgn(I*x)))^2-x^4+4*x^2-4)^x

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maxima [A]  time = 0.80, size = 44, normalized size = 1.76 \begin {gather*} e^{\left (x \log \left (x^{2} - \log \relax (3) + 3 \, \log \relax (x) + \log \left (\log \relax (x)\right ) - 2\right ) + x \log \left (-x^{2} - \log \relax (3) + 3 \, \log \relax (x) - \log \left (\log \relax (x)\right ) + 2\right )\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((log(x)*log(log(x))^2+(2*x^2-4)*log(x)*log(log(x))-log(x)*log(1/3*x^3)^2+(x^4-4*x^2+4)*log(x))*log(
-log(log(x))^2+(-2*x^2+4)*log(log(x))+log(1/3*x^3)^2-x^4+4*x^2-4)+(4*x^2*log(x)+2)*log(log(x))-6*log(x)*log(1/
3*x^3)+(4*x^4-8*x^2)*log(x)+2*x^2-4)*exp(x*log(-log(log(x))^2+(-2*x^2+4)*log(log(x))+log(1/3*x^3)^2-x^4+4*x^2-
4))/(log(x)*log(log(x))^2+(2*x^2-4)*log(x)*log(log(x))-log(x)*log(1/3*x^3)^2+(x^4-4*x^2+4)*log(x)),x, algorith
m="maxima")

[Out]

e^(x*log(x^2 - log(3) + 3*log(x) + log(log(x)) - 2) + x*log(-x^2 - log(3) + 3*log(x) - log(log(x)) + 2))

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mupad [B]  time = 2.09, size = 52, normalized size = 2.08 \begin {gather*} {\left (-x^4-2\,x^2\,\ln \left (\ln \relax (x)\right )+4\,x^2+{\ln \left (x^3\right )}^2-2\,\ln \relax (3)\,\ln \left (x^3\right )-{\ln \left (\ln \relax (x)\right )}^2+4\,\ln \left (\ln \relax (x)\right )+{\ln \relax (3)}^2-4\right )}^x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(x*log(log(x^3/3)^2 - log(log(x))*(2*x^2 - 4) - log(log(x))^2 + 4*x^2 - x^4 - 4))*(log(x)*(8*x^2 - 4*
x^4) - log(log(x))*(4*x^2*log(x) + 2) - log(log(x^3/3)^2 - log(log(x))*(2*x^2 - 4) - log(log(x))^2 + 4*x^2 - x
^4 - 4)*(log(x)*(x^4 - 4*x^2 + 4) - log(x^3/3)^2*log(x) + log(log(x))^2*log(x) + log(log(x))*log(x)*(2*x^2 - 4
)) - 2*x^2 + 6*log(x^3/3)*log(x) + 4))/(log(x)*(x^4 - 4*x^2 + 4) - log(x^3/3)^2*log(x) + log(log(x))^2*log(x)
+ log(log(x))*log(x)*(2*x^2 - 4)),x)

[Out]

(4*log(log(x)) - 2*log(x^3)*log(3) - 2*x^2*log(log(x)) + log(x^3)^2 - log(log(x))^2 + log(3)^2 + 4*x^2 - x^4 -
4)^x

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sympy [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((ln(x)*ln(ln(x))**2+(2*x**2-4)*ln(x)*ln(ln(x))-ln(x)*ln(1/3*x**3)**2+(x**4-4*x**2+4)*ln(x))*ln(-ln(
ln(x))**2+(-2*x**2+4)*ln(ln(x))+ln(1/3*x**3)**2-x**4+4*x**2-4)+(4*x**2*ln(x)+2)*ln(ln(x))-6*ln(x)*ln(1/3*x**3)
+(4*x**4-8*x**2)*ln(x)+2*x**2-4)*exp(x*ln(-ln(ln(x))**2+(-2*x**2+4)*ln(ln(x))+ln(1/3*x**3)**2-x**4+4*x**2-4))/
(ln(x)*ln(ln(x))**2+(2*x**2-4)*ln(x)*ln(ln(x))-ln(x)*ln(1/3*x**3)**2+(x**4-4*x**2+4)*ln(x)),x)

[Out]

Timed out

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