Integrand size = 243, antiderivative size = 27 \begin {dmath*} \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=\left (\frac {27 \left (-\frac {4}{x}+x\right )}{x}-\frac {x}{e^x+\log (\log (x))}\right )^2 \end {dmath*}
Time = 0.17 (sec) , antiderivative size = 48, normalized size of antiderivative = 1.78 \begin {dmath*} \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=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 {dmath*}
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 + 116 64*x^2)*Log[x]*Log[Log[x]]^3)/(E^(3*x)*x^5*Log[x] + 3*E^(2*x)*x^5*Log[x]*L og[Log[x]] + 3*E^x*x^5*Log[x]*Log[Log[x]]^2 + x^5*Log[x]*Log[Log[x]]^3),x]
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]])))
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {-2 x^6+\left (11664 x^2-46656\right ) \log (x) \log ^3(\log (x))+e^x \left (54 x^5-216 x^3\right )+\left (-54 x^5-216 x^3+e^x \left (34992 x^2-139968\right )\right ) \log (x) \log ^2(\log (x))+\left (54 x^5-216 x^3+\left (2 x^6+e^{2 x} \left (34992 x^2-139968\right )+e^x \left (54 x^6-108 x^5-216 x^4-432 x^3\right )\right ) \log (x)\right ) \log (\log (x))+\left (e^{3 x} \left (11664 x^2-46656\right )+e^x \left (2 x^6-2 x^7\right )+e^{2 x} \left (54 x^6-54 x^5-216 x^4-216 x^3\right )\right ) \log (x)}{x^5 \log (x) \log ^3(\log (x))+3 e^x x^5 \log (x) \log ^2(\log (x))+e^{3 x} x^5 \log (x)+3 e^{2 x} x^5 \log (x) \log (\log (x))} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 \left (x^3-27 e^x \left (x^2-4\right )-27 \left (x^2-4\right ) \log (\log (x))\right ) \left (-x^3-\log (x) \left (e^x \left ((x-1) x^3+216 e^x\right )+\left (432 e^x-x^3\right ) \log (\log (x))+216 \log ^2(\log (x))\right )\right )}{x^5 \log (x) \left (e^x+\log (\log (x))\right )^3}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 2 \int -\frac {\left (x^3+27 e^x \left (4-x^2\right )+27 \left (4-x^2\right ) \log (\log (x))\right ) \left (x^3+\log (x) \left (216 \log ^2(\log (x))+\left (432 e^x-x^3\right ) \log (\log (x))+e^x \left (216 e^x-(1-x) x^3\right )\right )\right )}{x^5 \log (x) \left (\log (\log (x))+e^x\right )^3}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -2 \int \frac {\left (x^3+27 e^x \left (4-x^2\right )+27 \left (4-x^2\right ) \log (\log (x))\right ) \left (x^3+\log (x) \left (216 \log ^2(\log (x))+\left (432 e^x-x^3\right ) \log (\log (x))+e^x \left (216 e^x-(1-x) x^3\right )\right )\right )}{x^5 \log (x) \left (\log (\log (x))+e^x\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (-\frac {5832 (x-2) (x+2)}{x^5}-\frac {x (x \log (x) \log (\log (x))-1)}{\log (x) \left (\log (\log (x))+e^x\right )^3}+\frac {\log (x) x^4-\log (x) x^3+27 \log (x) \log (\log (x)) x^3-27 x^2-108 \log (x) \log (\log (x)) x+108}{x^2 \log (x) \left (\log (\log (x))+e^x\right )^2}-\frac {27 \left (x^3-x^2-4 x-4\right )}{x^2 \left (\log (\log (x))+e^x\right )}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -2 \left (-\int \frac {x^2 \log (\log (x))}{\left (\log (\log (x))+e^x\right )^3}dx+\int \frac {x^2}{\left (\log (\log (x))+e^x\right )^2}dx+108 \int \frac {1}{x^2 \log (x) \left (\log (\log (x))+e^x\right )^2}dx+108 \int \frac {1}{x^2 \left (\log (\log (x))+e^x\right )}dx+\int \frac {x}{\log (x) \left (\log (\log (x))+e^x\right )^3}dx-\int \frac {x}{\left (\log (\log (x))+e^x\right )^2}dx-27 \int \frac {1}{\log (x) \left (\log (\log (x))+e^x\right )^2}dx-108 \int \frac {\log (\log (x))}{x \left (\log (\log (x))+e^x\right )^2}dx+27 \int \frac {x \log (\log (x))}{\left (\log (\log (x))+e^x\right )^2}dx+27 \int \frac {1}{\log (\log (x))+e^x}dx+108 \int \frac {1}{x \left (\log (\log (x))+e^x\right )}dx-27 \int \frac {x}{\log (\log (x))+e^x}dx-\frac {5832}{x^4}+\frac {2916}{x^2}\right )\) |
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*(-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]
3.6.32.3.1 Defintions of rubi rules used
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Time = 17.84 (sec) , antiderivative size = 52, normalized size of antiderivative = 1.93
| method | result | size |
| risch | \(-\frac {5832 \left (x^{2}-2\right )}{x^{4}}+\frac {x^{3}-54 \,{\mathrm e}^{x} x^{2}-54 x^{2} \ln \left (\ln \left (x \right )\right )+216 \,{\mathrm e}^{x}+216 \ln \left (\ln \left (x \right )\right )}{\left (\ln \left (\ln \left (x \right )\right )+{\mathrm e}^{x}\right )^{2} x}\) | \(52\) |
| parallelrisch | \(-\frac {23328 \,{\mathrm e}^{x} \ln \left (\ln \left (x \right )\right ) x^{2}+11664 \,{\mathrm e}^{2 x} x^{2}-432 \,{\mathrm e}^{x} x^{3}+11664 x^{2} \ln \left (\ln \left (x \right )\right )^{2}-46656 \,{\mathrm e}^{x} \ln \left (\ln \left (x \right )\right )+108 x^{5} {\mathrm e}^{x}-23328 \ln \left (\ln \left (x \right )\right )^{2}-2 x^{6}-23328 \,{\mathrm e}^{2 x}-432 \ln \left (\ln \left (x \right )\right ) x^{3}+108 \ln \left (\ln \left (x \right )\right ) x^{5}}{2 x^{4} \left ({\mathrm e}^{2 x}+2 \,{\mathrm e}^{x} \ln \left (\ln \left (x \right )\right )+\ln \left (\ln \left (x \right )\right )^{2}\right )}\) | \(110\) |
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)*e xp(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*e xp(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)
-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
Leaf count of result is larger than twice the leaf count of optimal. 94 vs. \(2 (26) = 52\).
Time = 0.27 (sec) , antiderivative size = 94, normalized size of antiderivative = 3.48 \begin {dmath*} \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=\frac {x^{6} - 5832 \, {\left (x^{2} - 2\right )} \log \left (\log \left (x\right )\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 \left (x\right )\right )}{2 \, x^{4} e^{x} \log \left (\log \left (x\right )\right ) + x^{4} \log \left (\log \left (x\right )\right )^{2} + x^{4} e^{\left (2 \, x\right )}} \end {dmath*}
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(log( 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)*lo g(log(x))^3+3*x^5*exp(x)*log(x)*log(log(x))^2+3*x^5*exp(x)^2*log(x)*log(lo g(x))+x^5*exp(x)^3*log(x)),x, algorithm=\
(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*l og(log(x)) + x^4*log(log(x))^2 + x^4*e^(2*x))
Leaf count of result is larger than twice the leaf count of optimal. 66 vs. \(2 (19) = 38\).
Time = 0.20 (sec) , antiderivative size = 66, normalized size of antiderivative = 2.44 \begin {dmath*} \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=\frac {x^{3} - 54 x^{2} \log {\left (\log {\left (x \right )} \right )} + \left (216 - 54 x^{2}\right ) e^{x} + 216 \log {\left (\log {\left (x \right )} \right )}}{x e^{2 x} + 2 x e^{x} \log {\left (\log {\left (x \right )} \right )} + x \log {\left (\log {\left (x \right )} \right )}^{2}} + \frac {11664 - 5832 x^{2}}{x^{4}} \end {dmath*}
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+(5 4*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)
(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
Leaf count of result is larger than twice the leaf count of optimal. 94 vs. \(2 (26) = 52\).
Time = 0.31 (sec) , antiderivative size = 94, normalized size of antiderivative = 3.48 \begin {dmath*} \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=\frac {x^{6} - 5832 \, {\left (x^{2} - 2\right )} \log \left (\log \left (x\right )\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 \left (x\right )\right )}{2 \, x^{4} e^{x} \log \left (\log \left (x\right )\right ) + x^{4} \log \left (\log \left (x\right )\right )^{2} + x^{4} e^{\left (2 \, x\right )}} \end {dmath*}
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(log( 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)*lo g(log(x))^3+3*x^5*exp(x)*log(x)*log(log(x))^2+3*x^5*exp(x)^2*log(x)*log(lo g(x))+x^5*exp(x)^3*log(x)),x, algorithm=\
(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*l og(log(x)) + x^4*log(log(x))^2 + x^4*e^(2*x))
Leaf count of result is larger than twice the leaf count of optimal. 114 vs. \(2 (26) = 52\).
Time = 0.45 (sec) , antiderivative size = 114, normalized size of antiderivative = 4.22 \begin {dmath*} \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=\frac {x^{6} - 54 \, x^{5} e^{x} - 54 \, x^{5} \log \left (\log \left (x\right )\right ) + 216 \, x^{3} e^{x} + 216 \, x^{3} \log \left (\log \left (x\right )\right ) - 11664 \, x^{2} e^{x} \log \left (\log \left (x\right )\right ) - 5832 \, x^{2} \log \left (\log \left (x\right )\right )^{2} - 5832 \, x^{2} e^{\left (2 \, x\right )} + 23328 \, e^{x} \log \left (\log \left (x\right )\right ) + 11664 \, \log \left (\log \left (x\right )\right )^{2} + 11664 \, e^{\left (2 \, x\right )}}{2 \, x^{4} e^{x} \log \left (\log \left (x\right )\right ) + x^{4} \log \left (\log \left (x\right )\right )^{2} + x^{4} e^{\left (2 \, x\right )}} \end {dmath*}
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(log( 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)*lo g(log(x))^3+3*x^5*exp(x)*log(x)*log(log(x))^2+3*x^5*exp(x)^2*log(x)*log(lo g(x))+x^5*exp(x)^3*log(x)),x, algorithm=\
(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*l og(log(x)) + x^4*log(log(x))^2 + x^4*e^(2*x))
Timed out. \begin {dmath*} \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=\int \frac {\ln \left (\ln \left (x\right )\right )\,\left (\ln \left (x\right )\,\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 \left (x\right )\,\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 \left (x\right )\right )}^3\,\ln \left (x\right )\,\left (11664\,x^2-46656\right )-{\ln \left (\ln \left (x\right )\right )}^2\,\ln \left (x\right )\,\left (216\,x^3-{\mathrm {e}}^x\,\left (34992\,x^2-139968\right )+54\,x^5\right )}{x^5\,{\mathrm {e}}^{3\,x}\,\ln \left (x\right )+x^5\,{\ln \left (\ln \left (x\right )\right )}^3\,\ln \left (x\right )+3\,x^5\,\ln \left (\ln \left (x\right )\right )\,{\mathrm {e}}^{2\,x}\,\ln \left (x\right )+3\,x^5\,{\ln \left (\ln \left (x\right )\right )}^2\,{\mathrm {e}}^x\,\ln \left (x\right )} \,d x \end {dmath*}
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 - 4665 6) - 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) - log(log(x))^2*log(x)*(216*x^3 - exp(x)*(34 992*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)
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 - 4665 6) - 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) - log(log(x))^2*log(x)*(216*x^3 - exp(x)*(34 992*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)