3.96.32 \(\int \frac {-2 x^6+e^x (-216 x^3+54 x^5)+(e^{3 x} (-46656+11664 x^2)+e^{2 x} (-216 x^3-216 x^4-54 x^5+54 x^6)+e^x (2 x^6-2 x^7)) \log (x)+(-216 x^3+54 x^5+(2 x^6+e^{2 x} (-139968+34992 x^2)+e^x (-432 x^3-216 x^4-108 x^5+54 x^6)) \log (x)) \log (\log (x))+(-216 x^3-54 x^5+e^x (-139968+34992 x^2)) \log (x) \log ^2(\log (x))+(-46656+11664 x^2) \log (x) \log ^3(\log (x))}{e^{3 x} x^5 \log (x)+3 e^{2 x} x^5 \log (x) \log (\log (x))+3 e^x x^5 \log (x) \log ^2(\log (x))+x^5 \log (x) \log ^3(\log (x))} \, dx\)

Optimal. Leaf size=27 \[ \left (\frac {27 \left (-\frac {4}{x}+x\right )}{x}-\frac {x}{e^x+\log (\log (x))}\right )^2 \]

________________________________________________________________________________________

Rubi [F]  time = 5.10, 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 {-2 x^6+e^x \left (-216 x^3+54 x^5\right )+\left (e^{3 x} \left (-46656+11664 x^2\right )+e^{2 x} \left (-216 x^3-216 x^4-54 x^5+54 x^6\right )+e^x \left (2 x^6-2 x^7\right )\right ) \log (x)+\left (-216 x^3+54 x^5+\left (2 x^6+e^{2 x} \left (-139968+34992 x^2\right )+e^x \left (-432 x^3-216 x^4-108 x^5+54 x^6\right )\right ) \log (x)\right ) \log (\log (x))+\left (-216 x^3-54 x^5+e^x \left (-139968+34992 x^2\right )\right ) \log (x) \log ^2(\log (x))+\left (-46656+11664 x^2\right ) \log (x) \log ^3(\log (x))}{e^{3 x} x^5 \log (x)+3 e^{2 x} x^5 \log (x) \log (\log (x))+3 e^x x^5 \log (x) \log ^2(\log (x))+x^5 \log (x) \log ^3(\log (x))} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-2*x^6 + E^x*(-216*x^3 + 54*x^5) + (E^(3*x)*(-46656 + 11664*x^2) + E^(2*x)*(-216*x^3 - 216*x^4 - 54*x^5 +
54*x^6) + E^x*(2*x^6 - 2*x^7))*Log[x] + (-216*x^3 + 54*x^5 + (2*x^6 + E^(2*x)*(-139968 + 34992*x^2) + E^x*(-4
32*x^3 - 216*x^4 - 108*x^5 + 54*x^6))*Log[x])*Log[Log[x]] + (-216*x^3 - 54*x^5 + E^x*(-139968 + 34992*x^2))*Lo
g[x]*Log[Log[x]]^2 + (-46656 + 11664*x^2)*Log[x]*Log[Log[x]]^3)/(E^(3*x)*x^5*Log[x] + 3*E^(2*x)*x^5*Log[x]*Log
[Log[x]] + 3*E^x*x^5*Log[x]*Log[Log[x]]^2 + x^5*Log[x]*Log[Log[x]]^3),x]

[Out]

11664/x^4 - 5832/x^2 - 2*Defer[Int][x/(Log[x]*(E^x + Log[Log[x]])^3), x] + 2*Defer[Int][(x^2*Log[Log[x]])/(E^x
+ Log[Log[x]])^3, x] + 2*Defer[Int][x/(E^x + Log[Log[x]])^2, x] - 2*Defer[Int][x^2/(E^x + Log[Log[x]])^2, x]
+ 54*Defer[Int][1/(Log[x]*(E^x + Log[Log[x]])^2), x] - 216*Defer[Int][1/(x^2*Log[x]*(E^x + Log[Log[x]])^2), x]
+ 216*Defer[Int][Log[Log[x]]/(x*(E^x + Log[Log[x]])^2), x] - 54*Defer[Int][(x*Log[Log[x]])/(E^x + Log[Log[x]]
)^2, x] - 54*Defer[Int][(E^x + Log[Log[x]])^(-1), x] - 216*Defer[Int][1/(x^2*(E^x + Log[Log[x]])), x] - 216*De
fer[Int][1/(x*(E^x + Log[Log[x]])), x] + 54*Defer[Int][x/(E^x + Log[Log[x]]), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2 \left (x^3-27 e^x \left (-4+x^2\right )-27 \left (-4+x^2\right ) \log (\log (x))\right ) \left (-x^3-\log (x) \left (e^x \left (216 e^x+(-1+x) x^3\right )+\left (432 e^x-x^3\right ) \log (\log (x))+216 \log ^2(\log (x))\right )\right )}{x^5 \log (x) \left (e^x+\log (\log (x))\right )^3} \, dx\\ &=2 \int \frac {\left (x^3-27 e^x \left (-4+x^2\right )-27 \left (-4+x^2\right ) \log (\log (x))\right ) \left (-x^3-\log (x) \left (e^x \left (216 e^x+(-1+x) x^3\right )+\left (432 e^x-x^3\right ) \log (\log (x))+216 \log ^2(\log (x))\right )\right )}{x^5 \log (x) \left (e^x+\log (\log (x))\right )^3} \, dx\\ &=2 \int \left (\frac {5832 (-2+x) (2+x)}{x^5}+\frac {27 \left (-4-4 x-x^2+x^3\right )}{x^2 \left (e^x+\log (\log (x))\right )}+\frac {x (-1+x \log (x) \log (\log (x)))}{\log (x) \left (e^x+\log (\log (x))\right )^3}-\frac {108-27 x^2-x^3 \log (x)+x^4 \log (x)-108 x \log (x) \log (\log (x))+27 x^3 \log (x) \log (\log (x))}{x^2 \log (x) \left (e^x+\log (\log (x))\right )^2}\right ) \, dx\\ &=2 \int \frac {x (-1+x \log (x) \log (\log (x)))}{\log (x) \left (e^x+\log (\log (x))\right )^3} \, dx-2 \int \frac {108-27 x^2-x^3 \log (x)+x^4 \log (x)-108 x \log (x) \log (\log (x))+27 x^3 \log (x) \log (\log (x))}{x^2 \log (x) \left (e^x+\log (\log (x))\right )^2} \, dx+54 \int \frac {-4-4 x-x^2+x^3}{x^2 \left (e^x+\log (\log (x))\right )} \, dx+11664 \int \frac {(-2+x) (2+x)}{x^5} \, dx\\ &=2 \int \left (-\frac {x}{\log (x) \left (e^x+\log (\log (x))\right )^3}+\frac {x^2 \log (\log (x))}{\left (e^x+\log (\log (x))\right )^3}\right ) \, dx-2 \int \left (-\frac {x}{\left (e^x+\log (\log (x))\right )^2}+\frac {x^2}{\left (e^x+\log (\log (x))\right )^2}-\frac {27}{\log (x) \left (e^x+\log (\log (x))\right )^2}+\frac {108}{x^2 \log (x) \left (e^x+\log (\log (x))\right )^2}-\frac {108 \log (\log (x))}{x \left (e^x+\log (\log (x))\right )^2}+\frac {27 x \log (\log (x))}{\left (e^x+\log (\log (x))\right )^2}\right ) \, dx+54 \int \left (-\frac {1}{e^x+\log (\log (x))}-\frac {4}{x^2 \left (e^x+\log (\log (x))\right )}-\frac {4}{x \left (e^x+\log (\log (x))\right )}+\frac {x}{e^x+\log (\log (x))}\right ) \, dx+11664 \int \frac {-4+x^2}{x^5} \, dx\\ &=-\left (2 \int \frac {x}{\log (x) \left (e^x+\log (\log (x))\right )^3} \, dx\right )+2 \int \frac {x^2 \log (\log (x))}{\left (e^x+\log (\log (x))\right )^3} \, dx+2 \int \frac {x}{\left (e^x+\log (\log (x))\right )^2} \, dx-2 \int \frac {x^2}{\left (e^x+\log (\log (x))\right )^2} \, dx+54 \int \frac {1}{\log (x) \left (e^x+\log (\log (x))\right )^2} \, dx-54 \int \frac {x \log (\log (x))}{\left (e^x+\log (\log (x))\right )^2} \, dx-54 \int \frac {1}{e^x+\log (\log (x))} \, dx+54 \int \frac {x}{e^x+\log (\log (x))} \, dx-216 \int \frac {1}{x^2 \log (x) \left (e^x+\log (\log (x))\right )^2} \, dx+216 \int \frac {\log (\log (x))}{x \left (e^x+\log (\log (x))\right )^2} \, dx-216 \int \frac {1}{x^2 \left (e^x+\log (\log (x))\right )} \, dx-216 \int \frac {1}{x \left (e^x+\log (\log (x))\right )} \, dx+11664 \int \left (-\frac {4}{x^5}+\frac {1}{x^3}\right ) \, dx\\ &=\frac {11664}{x^4}-\frac {5832}{x^2}-2 \int \frac {x}{\log (x) \left (e^x+\log (\log (x))\right )^3} \, dx+2 \int \frac {x^2 \log (\log (x))}{\left (e^x+\log (\log (x))\right )^3} \, dx+2 \int \frac {x}{\left (e^x+\log (\log (x))\right )^2} \, dx-2 \int \frac {x^2}{\left (e^x+\log (\log (x))\right )^2} \, dx+54 \int \frac {1}{\log (x) \left (e^x+\log (\log (x))\right )^2} \, dx-54 \int \frac {x \log (\log (x))}{\left (e^x+\log (\log (x))\right )^2} \, dx-54 \int \frac {1}{e^x+\log (\log (x))} \, dx+54 \int \frac {x}{e^x+\log (\log (x))} \, dx-216 \int \frac {1}{x^2 \log (x) \left (e^x+\log (\log (x))\right )^2} \, dx+216 \int \frac {\log (\log (x))}{x \left (e^x+\log (\log (x))\right )^2} \, dx-216 \int \frac {1}{x^2 \left (e^x+\log (\log (x))\right )} \, dx-216 \int \frac {1}{x \left (e^x+\log (\log (x))\right )} \, dx\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]  time = 0.15, size = 48, normalized size = 1.78 \begin {gather*} 2 \left (\frac {5832}{x^4}-\frac {2916}{x^2}+\frac {x^2}{2 \left (e^x+\log (\log (x))\right )^2}-\frac {27 \left (-4+x^2\right )}{x \left (e^x+\log (\log (x))\right )}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-2*x^6 + E^x*(-216*x^3 + 54*x^5) + (E^(3*x)*(-46656 + 11664*x^2) + E^(2*x)*(-216*x^3 - 216*x^4 - 54
*x^5 + 54*x^6) + E^x*(2*x^6 - 2*x^7))*Log[x] + (-216*x^3 + 54*x^5 + (2*x^6 + E^(2*x)*(-139968 + 34992*x^2) + E
^x*(-432*x^3 - 216*x^4 - 108*x^5 + 54*x^6))*Log[x])*Log[Log[x]] + (-216*x^3 - 54*x^5 + E^x*(-139968 + 34992*x^
2))*Log[x]*Log[Log[x]]^2 + (-46656 + 11664*x^2)*Log[x]*Log[Log[x]]^3)/(E^(3*x)*x^5*Log[x] + 3*E^(2*x)*x^5*Log[
x]*Log[Log[x]] + 3*E^x*x^5*Log[x]*Log[Log[x]]^2 + x^5*Log[x]*Log[Log[x]]^3),x]

[Out]

2*(5832/x^4 - 2916/x^2 + x^2/(2*(E^x + Log[Log[x]])^2) - (27*(-4 + x^2))/(x*(E^x + Log[Log[x]])))

________________________________________________________________________________________

fricas [B]  time = 0.60, size = 94, normalized size = 3.48 \begin {gather*} \frac {x^{6} - 5832 \, {\left (x^{2} - 2\right )} \log \left (\log \relax (x)\right )^{2} - 5832 \, {\left (x^{2} - 2\right )} e^{\left (2 \, x\right )} - 54 \, {\left (x^{5} - 4 \, x^{3}\right )} e^{x} - 54 \, {\left (x^{5} - 4 \, x^{3} + 216 \, {\left (x^{2} - 2\right )} e^{x}\right )} \log \left (\log \relax (x)\right )}{2 \, x^{4} e^{x} \log \left (\log \relax (x)\right ) + x^{4} \log \left (\log \relax (x)\right )^{2} + x^{4} e^{\left (2 \, x\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((11664*x^2-46656)*log(x)*log(log(x))^3+((34992*x^2-139968)*exp(x)-54*x^5-216*x^3)*log(x)*log(log(x)
)^2+(((34992*x^2-139968)*exp(x)^2+(54*x^6-108*x^5-216*x^4-432*x^3)*exp(x)+2*x^6)*log(x)+54*x^5-216*x^3)*log(lo
g(x))+((11664*x^2-46656)*exp(x)^3+(54*x^6-54*x^5-216*x^4-216*x^3)*exp(x)^2+(-2*x^7+2*x^6)*exp(x))*log(x)+(54*x
^5-216*x^3)*exp(x)-2*x^6)/(x^5*log(x)*log(log(x))^3+3*x^5*exp(x)*log(x)*log(log(x))^2+3*x^5*exp(x)^2*log(x)*lo
g(log(x))+x^5*exp(x)^3*log(x)),x, algorithm="fricas")

[Out]

(x^6 - 5832*(x^2 - 2)*log(log(x))^2 - 5832*(x^2 - 2)*e^(2*x) - 54*(x^5 - 4*x^3)*e^x - 54*(x^5 - 4*x^3 + 216*(x
^2 - 2)*e^x)*log(log(x)))/(2*x^4*e^x*log(log(x)) + x^4*log(log(x))^2 + x^4*e^(2*x))

________________________________________________________________________________________

giac [B]  time = 0.24, size = 114, normalized size = 4.22 \begin {gather*} \frac {x^{6} - 54 \, x^{5} e^{x} - 54 \, x^{5} \log \left (\log \relax (x)\right ) + 216 \, x^{3} e^{x} + 216 \, x^{3} \log \left (\log \relax (x)\right ) - 11664 \, x^{2} e^{x} \log \left (\log \relax (x)\right ) - 5832 \, x^{2} \log \left (\log \relax (x)\right )^{2} - 5832 \, x^{2} e^{\left (2 \, x\right )} + 23328 \, e^{x} \log \left (\log \relax (x)\right ) + 11664 \, \log \left (\log \relax (x)\right )^{2} + 11664 \, e^{\left (2 \, x\right )}}{2 \, x^{4} e^{x} \log \left (\log \relax (x)\right ) + x^{4} \log \left (\log \relax (x)\right )^{2} + x^{4} e^{\left (2 \, x\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((11664*x^2-46656)*log(x)*log(log(x))^3+((34992*x^2-139968)*exp(x)-54*x^5-216*x^3)*log(x)*log(log(x)
)^2+(((34992*x^2-139968)*exp(x)^2+(54*x^6-108*x^5-216*x^4-432*x^3)*exp(x)+2*x^6)*log(x)+54*x^5-216*x^3)*log(lo
g(x))+((11664*x^2-46656)*exp(x)^3+(54*x^6-54*x^5-216*x^4-216*x^3)*exp(x)^2+(-2*x^7+2*x^6)*exp(x))*log(x)+(54*x
^5-216*x^3)*exp(x)-2*x^6)/(x^5*log(x)*log(log(x))^3+3*x^5*exp(x)*log(x)*log(log(x))^2+3*x^5*exp(x)^2*log(x)*lo
g(log(x))+x^5*exp(x)^3*log(x)),x, algorithm="giac")

[Out]

(x^6 - 54*x^5*e^x - 54*x^5*log(log(x)) + 216*x^3*e^x + 216*x^3*log(log(x)) - 11664*x^2*e^x*log(log(x)) - 5832*
x^2*log(log(x))^2 - 5832*x^2*e^(2*x) + 23328*e^x*log(log(x)) + 11664*log(log(x))^2 + 11664*e^(2*x))/(2*x^4*e^x
*log(log(x)) + x^4*log(log(x))^2 + x^4*e^(2*x))

________________________________________________________________________________________

maple [A]  time = 0.07, size = 52, normalized size = 1.93

method	result	size
risch	\(-\frac {5832 \left (x^{2}-2\right )}{x^{4}}+\frac {x^{3}-54 \,{\mathrm e}^{x} x^{2}-54 x^{2} \ln \left (\ln \relax (x )\right )+216 \,{\mathrm e}^{x}+216 \ln \left (\ln \relax (x )\right )}{\left (\ln \left (\ln \relax (x )\right )+{\mathrm e}^{x}\right )^{2} x}\)	\(52\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((11664*x^2-46656)*ln(x)*ln(ln(x))^3+((34992*x^2-139968)*exp(x)-54*x^5-216*x^3)*ln(x)*ln(ln(x))^2+(((34992
*x^2-139968)*exp(x)^2+(54*x^6-108*x^5-216*x^4-432*x^3)*exp(x)+2*x^6)*ln(x)+54*x^5-216*x^3)*ln(ln(x))+((11664*x
^2-46656)*exp(x)^3+(54*x^6-54*x^5-216*x^4-216*x^3)*exp(x)^2+(-2*x^7+2*x^6)*exp(x))*ln(x)+(54*x^5-216*x^3)*exp(
x)-2*x^6)/(x^5*ln(x)*ln(ln(x))^3+3*x^5*exp(x)*ln(x)*ln(ln(x))^2+3*x^5*exp(x)^2*ln(x)*ln(ln(x))+x^5*exp(x)^3*ln
(x)),x,method=_RETURNVERBOSE)

[Out]

-5832*(x^2-2)/x^4+(x^3-54*exp(x)*x^2-54*x^2*ln(ln(x))+216*exp(x)+216*ln(ln(x)))/(ln(ln(x))+exp(x))^2/x

________________________________________________________________________________________

maxima [B]  time = 0.44, size = 94, normalized size = 3.48 \begin {gather*} \frac {x^{6} - 5832 \, {\left (x^{2} - 2\right )} \log \left (\log \relax (x)\right )^{2} - 5832 \, {\left (x^{2} - 2\right )} e^{\left (2 \, x\right )} - 54 \, {\left (x^{5} - 4 \, x^{3}\right )} e^{x} - 54 \, {\left (x^{5} - 4 \, x^{3} + 216 \, {\left (x^{2} - 2\right )} e^{x}\right )} \log \left (\log \relax (x)\right )}{2 \, x^{4} e^{x} \log \left (\log \relax (x)\right ) + x^{4} \log \left (\log \relax (x)\right )^{2} + x^{4} e^{\left (2 \, x\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((11664*x^2-46656)*log(x)*log(log(x))^3+((34992*x^2-139968)*exp(x)-54*x^5-216*x^3)*log(x)*log(log(x)
)^2+(((34992*x^2-139968)*exp(x)^2+(54*x^6-108*x^5-216*x^4-432*x^3)*exp(x)+2*x^6)*log(x)+54*x^5-216*x^3)*log(lo
g(x))+((11664*x^2-46656)*exp(x)^3+(54*x^6-54*x^5-216*x^4-216*x^3)*exp(x)^2+(-2*x^7+2*x^6)*exp(x))*log(x)+(54*x
^5-216*x^3)*exp(x)-2*x^6)/(x^5*log(x)*log(log(x))^3+3*x^5*exp(x)*log(x)*log(log(x))^2+3*x^5*exp(x)^2*log(x)*lo
g(log(x))+x^5*exp(x)^3*log(x)),x, algorithm="maxima")

[Out]

(x^6 - 5832*(x^2 - 2)*log(log(x))^2 - 5832*(x^2 - 2)*e^(2*x) - 54*(x^5 - 4*x^3)*e^x - 54*(x^5 - 4*x^3 + 216*(x
^2 - 2)*e^x)*log(log(x)))/(2*x^4*e^x*log(log(x)) + x^4*log(log(x))^2 + x^4*e^(2*x))

________________________________________________________________________________________

mupad [F]  time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {\ln \left (\ln \relax (x)\right )\,\left (\ln \relax (x)\,\left ({\mathrm {e}}^{2\,x}\,\left (34992\,x^2-139968\right )-{\mathrm {e}}^x\,\left (-54\,x^6+108\,x^5+216\,x^4+432\,x^3\right )+2\,x^6\right )-216\,x^3+54\,x^5\right )-{\mathrm {e}}^x\,\left (216\,x^3-54\,x^5\right )+\ln \relax (x)\,\left ({\mathrm {e}}^x\,\left (2\,x^6-2\,x^7\right )+{\mathrm {e}}^{3\,x}\,\left (11664\,x^2-46656\right )-{\mathrm {e}}^{2\,x}\,\left (-54\,x^6+54\,x^5+216\,x^4+216\,x^3\right )\right )-2\,x^6+{\ln \left (\ln \relax (x)\right )}^3\,\ln \relax (x)\,\left (11664\,x^2-46656\right )-{\ln \left (\ln \relax (x)\right )}^2\,\ln \relax (x)\,\left (216\,x^3-{\mathrm {e}}^x\,\left (34992\,x^2-139968\right )+54\,x^5\right )}{x^5\,{\mathrm {e}}^{3\,x}\,\ln \relax (x)+x^5\,{\ln \left (\ln \relax (x)\right )}^3\,\ln \relax (x)+3\,x^5\,\ln \left (\ln \relax (x)\right )\,{\mathrm {e}}^{2\,x}\,\ln \relax (x)+3\,x^5\,{\ln \left (\ln \relax (x)\right )}^2\,{\mathrm {e}}^x\,\ln \relax (x)} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((log(log(x))*(log(x)*(exp(2*x)*(34992*x^2 - 139968) - exp(x)*(432*x^3 + 216*x^4 + 108*x^5 - 54*x^6) + 2*x^
6) - 216*x^3 + 54*x^5) - exp(x)*(216*x^3 - 54*x^5) + log(x)*(exp(x)*(2*x^6 - 2*x^7) + exp(3*x)*(11664*x^2 - 46
656) - exp(2*x)*(216*x^3 + 216*x^4 + 54*x^5 - 54*x^6)) - 2*x^6 + log(log(x))^3*log(x)*(11664*x^2 - 46656) - lo
g(log(x))^2*log(x)*(216*x^3 - exp(x)*(34992*x^2 - 139968) + 54*x^5))/(x^5*exp(3*x)*log(x) + x^5*log(log(x))^3*
log(x) + 3*x^5*log(log(x))*exp(2*x)*log(x) + 3*x^5*log(log(x))^2*exp(x)*log(x)),x)

[Out]

int((log(log(x))*(log(x)*(exp(2*x)*(34992*x^2 - 139968) - exp(x)*(432*x^3 + 216*x^4 + 108*x^5 - 54*x^6) + 2*x^
6) - 216*x^3 + 54*x^5) - exp(x)*(216*x^3 - 54*x^5) + log(x)*(exp(x)*(2*x^6 - 2*x^7) + exp(3*x)*(11664*x^2 - 46
656) - exp(2*x)*(216*x^3 + 216*x^4 + 54*x^5 - 54*x^6)) - 2*x^6 + log(log(x))^3*log(x)*(11664*x^2 - 46656) - lo
g(log(x))^2*log(x)*(216*x^3 - exp(x)*(34992*x^2 - 139968) + 54*x^5))/(x^5*exp(3*x)*log(x) + x^5*log(log(x))^3*
log(x) + 3*x^5*log(log(x))*exp(2*x)*log(x) + 3*x^5*log(log(x))^2*exp(x)*log(x)), x)

________________________________________________________________________________________

sympy [B]  time = 0.44, size = 66, normalized size = 2.44 \begin {gather*} \frac {x^{3} - 54 x^{2} \log {\left (\log {\relax (x )} \right )} + \left (216 - 54 x^{2}\right ) e^{x} + 216 \log {\left (\log {\relax (x )} \right )}}{x e^{2 x} + 2 x e^{x} \log {\left (\log {\relax (x )} \right )} + x \log {\left (\log {\relax (x )} \right )}^{2}} + \frac {11664 - 5832 x^{2}}{x^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((11664*x**2-46656)*ln(x)*ln(ln(x))**3+((34992*x**2-139968)*exp(x)-54*x**5-216*x**3)*ln(x)*ln(ln(x))
**2+(((34992*x**2-139968)*exp(x)**2+(54*x**6-108*x**5-216*x**4-432*x**3)*exp(x)+2*x**6)*ln(x)+54*x**5-216*x**3
)*ln(ln(x))+((11664*x**2-46656)*exp(x)**3+(54*x**6-54*x**5-216*x**4-216*x**3)*exp(x)**2+(-2*x**7+2*x**6)*exp(x
))*ln(x)+(54*x**5-216*x**3)*exp(x)-2*x**6)/(x**5*ln(x)*ln(ln(x))**3+3*x**5*exp(x)*ln(x)*ln(ln(x))**2+3*x**5*ex
p(x)**2*ln(x)*ln(ln(x))+x**5*exp(x)**3*ln(x)),x)

[Out]

(x**3 - 54*x**2*log(log(x)) + (216 - 54*x**2)*exp(x) + 216*log(log(x)))/(x*exp(2*x) + 2*x*exp(x)*log(log(x)) +
x*log(log(x))**2) + (11664 - 5832*x**2)/x**4

________________________________________________________________________________________