Integrand size = 242, antiderivative size = 35 \[ \int \frac {-108 x^2+e^{\frac {e^x}{x}} \left (e^x (162-162 x)-162 x\right ) \log (x)+\left (108 x^2-486 x^3\right ) \log (x)+\left (36 x+\left (-36 x+216 x^2\right ) \log (x)\right ) \log \left (\frac {x}{2 \log (x)}\right )-18 x \log (x) \log ^2\left (\frac {x}{2 \log (x)}\right )}{81 e^{\frac {2 e^x}{x}} x^3 \log (x)+162 e^{\frac {e^x}{x}} x^5 \log (x)+81 x^7 \log (x)+\left (-108 e^{\frac {e^x}{x}} x^4 \log (x)-108 x^6 \log (x)\right ) \log \left (\frac {x}{2 \log (x)}\right )+\left (18 e^{\frac {e^x}{x}} x^3 \log (x)+54 x^5 \log (x)\right ) \log ^2\left (\frac {x}{2 \log (x)}\right )-12 x^4 \log (x) \log ^3\left (\frac {x}{2 \log (x)}\right )+x^3 \log (x) \log ^4\left (\frac {x}{2 \log (x)}\right )} \, dx=\frac {2}{x \left (e^{\frac {e^x}{x}}+\left (x-\frac {1}{3} \log \left (\frac {x}{2 \log (x)}\right )\right )^2\right )} \]
Time = 0.29 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.40 \[ \int \frac {-108 x^2+e^{\frac {e^x}{x}} \left (e^x (162-162 x)-162 x\right ) \log (x)+\left (108 x^2-486 x^3\right ) \log (x)+\left (36 x+\left (-36 x+216 x^2\right ) \log (x)\right ) \log \left (\frac {x}{2 \log (x)}\right )-18 x \log (x) \log ^2\left (\frac {x}{2 \log (x)}\right )}{81 e^{\frac {2 e^x}{x}} x^3 \log (x)+162 e^{\frac {e^x}{x}} x^5 \log (x)+81 x^7 \log (x)+\left (-108 e^{\frac {e^x}{x}} x^4 \log (x)-108 x^6 \log (x)\right ) \log \left (\frac {x}{2 \log (x)}\right )+\left (18 e^{\frac {e^x}{x}} x^3 \log (x)+54 x^5 \log (x)\right ) \log ^2\left (\frac {x}{2 \log (x)}\right )-12 x^4 \log (x) \log ^3\left (\frac {x}{2 \log (x)}\right )+x^3 \log (x) \log ^4\left (\frac {x}{2 \log (x)}\right )} \, dx=\frac {18}{x \left (9 e^{\frac {e^x}{x}}+9 x^2-6 x \log \left (\frac {x}{2 \log (x)}\right )+\log ^2\left (\frac {x}{2 \log (x)}\right )\right )} \]
Integrate[(-108*x^2 + E^(E^x/x)*(E^x*(162 - 162*x) - 162*x)*Log[x] + (108* x^2 - 486*x^3)*Log[x] + (36*x + (-36*x + 216*x^2)*Log[x])*Log[x/(2*Log[x]) ] - 18*x*Log[x]*Log[x/(2*Log[x])]^2)/(81*E^((2*E^x)/x)*x^3*Log[x] + 162*E^ (E^x/x)*x^5*Log[x] + 81*x^7*Log[x] + (-108*E^(E^x/x)*x^4*Log[x] - 108*x^6* Log[x])*Log[x/(2*Log[x])] + (18*E^(E^x/x)*x^3*Log[x] + 54*x^5*Log[x])*Log[ x/(2*Log[x])]^2 - 12*x^4*Log[x]*Log[x/(2*Log[x])]^3 + x^3*Log[x]*Log[x/(2* Log[x])]^4),x]
Time = 2.94 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.40, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.008, Rules used = {7292, 7238}
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.
\(\displaystyle \int \frac {-108 x^2+\left (\left (216 x^2-36 x\right ) \log (x)+36 x\right ) \log \left (\frac {x}{2 \log (x)}\right )+\left (108 x^2-486 x^3\right ) \log (x)-18 x \log (x) \log ^2\left (\frac {x}{2 \log (x)}\right )+e^{\frac {e^x}{x}} \left (e^x (162-162 x)-162 x\right ) \log (x)}{81 x^7 \log (x)+162 e^{\frac {e^x}{x}} x^5 \log (x)-12 x^4 \log (x) \log ^3\left (\frac {x}{2 \log (x)}\right )+x^3 \log (x) \log ^4\left (\frac {x}{2 \log (x)}\right )+81 e^{\frac {2 e^x}{x}} x^3 \log (x)+\left (-108 x^6 \log (x)-108 e^{\frac {e^x}{x}} x^4 \log (x)\right ) \log \left (\frac {x}{2 \log (x)}\right )+\left (54 x^5 \log (x)+18 e^{\frac {e^x}{x}} x^3 \log (x)\right ) \log ^2\left (\frac {x}{2 \log (x)}\right )} \, dx\) |
\(\Big \downarrow \) 7292 |
\(\displaystyle \int \frac {-108 x^2+\left (\left (216 x^2-36 x\right ) \log (x)+36 x\right ) \log \left (\frac {x}{2 \log (x)}\right )+\left (108 x^2-486 x^3\right ) \log (x)-18 x \log (x) \log ^2\left (\frac {x}{2 \log (x)}\right )+e^{\frac {e^x}{x}} \left (e^x (162-162 x)-162 x\right ) \log (x)}{x^3 \log (x) \left (9 x^2+9 e^{\frac {e^x}{x}}+\log ^2\left (\frac {x}{2 \log (x)}\right )-6 x \log \left (\frac {x}{2 \log (x)}\right )\right )^2}dx\) |
\(\Big \downarrow \) 7238 |
\(\displaystyle \frac {18}{x \left (9 x^2+9 e^{\frac {e^x}{x}}+\log ^2\left (\frac {x}{2 \log (x)}\right )-6 x \log \left (\frac {x}{2 \log (x)}\right )\right )}\) |
Int[(-108*x^2 + E^(E^x/x)*(E^x*(162 - 162*x) - 162*x)*Log[x] + (108*x^2 - 486*x^3)*Log[x] + (36*x + (-36*x + 216*x^2)*Log[x])*Log[x/(2*Log[x])] - 18 *x*Log[x]*Log[x/(2*Log[x])]^2)/(81*E^((2*E^x)/x)*x^3*Log[x] + 162*E^(E^x/x )*x^5*Log[x] + 81*x^7*Log[x] + (-108*E^(E^x/x)*x^4*Log[x] - 108*x^6*Log[x] )*Log[x/(2*Log[x])] + (18*E^(E^x/x)*x^3*Log[x] + 54*x^5*Log[x])*Log[x/(2*L og[x])]^2 - 12*x^4*Log[x]*Log[x/(2*Log[x])]^3 + x^3*Log[x]*Log[x/(2*Log[x] )]^4),x]
3.7.35.3.1 Defintions of rubi rules used
Int[(u_)*(y_)^(m_.)*(z_)^(n_.), x_Symbol] :> With[{q = DerivativeDivides[y* z, u*z^(n - m), x]}, Simp[q*y^(m + 1)*(z^(m + 1)/(m + 1)), x] /; !FalseQ[q ]] /; FreeQ[{m, n}, x] && NeQ[m, -1]
Result contains higher order function than in optimal. Order 9 vs. order 3.
Time = 0.34 (sec) , antiderivative size = 676, normalized size of antiderivative = 19.31
\[\text {Expression too large to display}\]
int((-18*x*ln(x)*ln(1/2*x/ln(x))^2+((216*x^2-36*x)*ln(x)+36*x)*ln(1/2*x/ln (x))+((-162*x+162)*exp(x)-162*x)*ln(x)*exp(exp(x)/x)+(-486*x^3+108*x^2)*ln (x)-108*x^2)/(x^3*ln(x)*ln(1/2*x/ln(x))^4-12*x^4*ln(x)*ln(1/2*x/ln(x))^3+( 18*x^3*ln(x)*exp(exp(x)/x)+54*x^5*ln(x))*ln(1/2*x/ln(x))^2+(-108*x^4*ln(x) *exp(exp(x)/x)-108*x^6*ln(x))*ln(1/2*x/ln(x))+81*x^3*ln(x)*exp(exp(x)/x)^2 +162*x^5*ln(x)*exp(exp(x)/x)+81*x^7*ln(x)),x)
-72/x/(-8*ln(2)*ln(ln(x))+8*ln(2)*ln(x)+8*ln(x)*ln(ln(x))-24*x*ln(2)+24*x* ln(x)-36*exp(exp(x)/x)-24*x*ln(ln(x))-4*ln(2)^2-4*ln(ln(x))^2-4*ln(x)^2-36 *x^2+Pi^2*csgn(I*x)^2*csgn(I/ln(x))^2*csgn(I*x/ln(x))^2-2*Pi^2*csgn(I*x)^2 *csgn(I/ln(x))*csgn(I*x/ln(x))^3-2*Pi^2*csgn(I*x)*csgn(I/ln(x))^2*csgn(I*x /ln(x))^3-2*Pi^2*csgn(I*x)*csgn(I*x/ln(x))^5-2*Pi^2*csgn(I/ln(x))*csgn(I*x /ln(x))^5-12*I*Pi*x*csgn(I*x/ln(x))^3-4*I*ln(2)*Pi*csgn(I*x/ln(x))^3+4*I*l n(x)*Pi*csgn(I*x/ln(x))^3-4*I*ln(ln(x))*Pi*csgn(I*x/ln(x))^3+4*Pi^2*csgn(I *x)*csgn(I/ln(x))*csgn(I*x/ln(x))^4+Pi^2*csgn(I*x/ln(x))^6+Pi^2*csgn(I*x)^ 2*csgn(I*x/ln(x))^4+Pi^2*csgn(I/ln(x))^2*csgn(I*x/ln(x))^4-4*I*ln(2)*Pi*cs gn(I*x)*csgn(I/ln(x))*csgn(I*x/ln(x))-12*I*Pi*x*csgn(I*x)*csgn(I/ln(x))*cs gn(I*x/ln(x))+4*I*ln(x)*Pi*csgn(I*x)*csgn(I/ln(x))*csgn(I*x/ln(x))-4*I*ln( ln(x))*Pi*csgn(I*x)*csgn(I/ln(x))*csgn(I*x/ln(x))+12*I*Pi*x*csgn(I*x)*csgn (I*x/ln(x))^2+12*I*Pi*x*csgn(I/ln(x))*csgn(I*x/ln(x))^2+4*I*ln(2)*Pi*csgn( I*x)*csgn(I*x/ln(x))^2+4*I*ln(2)*Pi*csgn(I/ln(x))*csgn(I*x/ln(x))^2-4*I*ln (x)*Pi*csgn(I*x)*csgn(I*x/ln(x))^2-4*I*ln(x)*Pi*csgn(I/ln(x))*csgn(I*x/ln( x))^2+4*I*ln(ln(x))*Pi*csgn(I*x)*csgn(I*x/ln(x))^2+4*I*ln(ln(x))*Pi*csgn(I /ln(x))*csgn(I*x/ln(x))^2)
Time = 0.25 (sec) , antiderivative size = 45, normalized size of antiderivative = 1.29 \[ \int \frac {-108 x^2+e^{\frac {e^x}{x}} \left (e^x (162-162 x)-162 x\right ) \log (x)+\left (108 x^2-486 x^3\right ) \log (x)+\left (36 x+\left (-36 x+216 x^2\right ) \log (x)\right ) \log \left (\frac {x}{2 \log (x)}\right )-18 x \log (x) \log ^2\left (\frac {x}{2 \log (x)}\right )}{81 e^{\frac {2 e^x}{x}} x^3 \log (x)+162 e^{\frac {e^x}{x}} x^5 \log (x)+81 x^7 \log (x)+\left (-108 e^{\frac {e^x}{x}} x^4 \log (x)-108 x^6 \log (x)\right ) \log \left (\frac {x}{2 \log (x)}\right )+\left (18 e^{\frac {e^x}{x}} x^3 \log (x)+54 x^5 \log (x)\right ) \log ^2\left (\frac {x}{2 \log (x)}\right )-12 x^4 \log (x) \log ^3\left (\frac {x}{2 \log (x)}\right )+x^3 \log (x) \log ^4\left (\frac {x}{2 \log (x)}\right )} \, dx=\frac {18}{9 \, x^{3} - 6 \, x^{2} \log \left (\frac {x}{2 \, \log \left (x\right )}\right ) + x \log \left (\frac {x}{2 \, \log \left (x\right )}\right )^{2} + 9 \, x e^{\left (\frac {e^{x}}{x}\right )}} \]
integrate((-18*x*log(x)*log(1/2*x/log(x))^2+((216*x^2-36*x)*log(x)+36*x)*l og(1/2*x/log(x))+((-162*x+162)*exp(x)-162*x)*log(x)*exp(exp(x)/x)+(-486*x^ 3+108*x^2)*log(x)-108*x^2)/(x^3*log(x)*log(1/2*x/log(x))^4-12*x^4*log(x)*l og(1/2*x/log(x))^3+(18*x^3*log(x)*exp(exp(x)/x)+54*x^5*log(x))*log(1/2*x/l og(x))^2+(-108*x^4*log(x)*exp(exp(x)/x)-108*x^6*log(x))*log(1/2*x/log(x))+ 81*x^3*log(x)*exp(exp(x)/x)^2+162*x^5*log(x)*exp(exp(x)/x)+81*x^7*log(x)), x, algorithm=\
Time = 0.36 (sec) , antiderivative size = 41, normalized size of antiderivative = 1.17 \[ \int \frac {-108 x^2+e^{\frac {e^x}{x}} \left (e^x (162-162 x)-162 x\right ) \log (x)+\left (108 x^2-486 x^3\right ) \log (x)+\left (36 x+\left (-36 x+216 x^2\right ) \log (x)\right ) \log \left (\frac {x}{2 \log (x)}\right )-18 x \log (x) \log ^2\left (\frac {x}{2 \log (x)}\right )}{81 e^{\frac {2 e^x}{x}} x^3 \log (x)+162 e^{\frac {e^x}{x}} x^5 \log (x)+81 x^7 \log (x)+\left (-108 e^{\frac {e^x}{x}} x^4 \log (x)-108 x^6 \log (x)\right ) \log \left (\frac {x}{2 \log (x)}\right )+\left (18 e^{\frac {e^x}{x}} x^3 \log (x)+54 x^5 \log (x)\right ) \log ^2\left (\frac {x}{2 \log (x)}\right )-12 x^4 \log (x) \log ^3\left (\frac {x}{2 \log (x)}\right )+x^3 \log (x) \log ^4\left (\frac {x}{2 \log (x)}\right )} \, dx=\frac {18}{9 x^{3} - 6 x^{2} \log {\left (\frac {x}{2 \log {\left (x \right )}} \right )} + 9 x e^{\frac {e^{x}}{x}} + x \log {\left (\frac {x}{2 \log {\left (x \right )}} \right )}^{2}} \]
integrate((-18*x*ln(x)*ln(1/2*x/ln(x))**2+((216*x**2-36*x)*ln(x)+36*x)*ln( 1/2*x/ln(x))+((-162*x+162)*exp(x)-162*x)*ln(x)*exp(exp(x)/x)+(-486*x**3+10 8*x**2)*ln(x)-108*x**2)/(x**3*ln(x)*ln(1/2*x/ln(x))**4-12*x**4*ln(x)*ln(1/ 2*x/ln(x))**3+(18*x**3*ln(x)*exp(exp(x)/x)+54*x**5*ln(x))*ln(1/2*x/ln(x))* *2+(-108*x**4*ln(x)*exp(exp(x)/x)-108*x**6*ln(x))*ln(1/2*x/ln(x))+81*x**3* ln(x)*exp(exp(x)/x)**2+162*x**5*ln(x)*exp(exp(x)/x)+81*x**7*ln(x)),x)
Leaf count of result is larger than twice the leaf count of optimal. 80 vs. \(2 (33) = 66\).
Time = 0.56 (sec) , antiderivative size = 80, normalized size of antiderivative = 2.29 \[ \int \frac {-108 x^2+e^{\frac {e^x}{x}} \left (e^x (162-162 x)-162 x\right ) \log (x)+\left (108 x^2-486 x^3\right ) \log (x)+\left (36 x+\left (-36 x+216 x^2\right ) \log (x)\right ) \log \left (\frac {x}{2 \log (x)}\right )-18 x \log (x) \log ^2\left (\frac {x}{2 \log (x)}\right )}{81 e^{\frac {2 e^x}{x}} x^3 \log (x)+162 e^{\frac {e^x}{x}} x^5 \log (x)+81 x^7 \log (x)+\left (-108 e^{\frac {e^x}{x}} x^4 \log (x)-108 x^6 \log (x)\right ) \log \left (\frac {x}{2 \log (x)}\right )+\left (18 e^{\frac {e^x}{x}} x^3 \log (x)+54 x^5 \log (x)\right ) \log ^2\left (\frac {x}{2 \log (x)}\right )-12 x^4 \log (x) \log ^3\left (\frac {x}{2 \log (x)}\right )+x^3 \log (x) \log ^4\left (\frac {x}{2 \log (x)}\right )} \, dx=\frac {18}{9 \, x^{3} + 6 \, x^{2} \log \left (2\right ) + x \log \left (2\right )^{2} + x \log \left (x\right )^{2} + x \log \left (\log \left (x\right )\right )^{2} + 9 \, x e^{\left (\frac {e^{x}}{x}\right )} - 2 \, {\left (3 \, x^{2} + x \log \left (2\right )\right )} \log \left (x\right ) + 2 \, {\left (3 \, x^{2} + x \log \left (2\right ) - x \log \left (x\right )\right )} \log \left (\log \left (x\right )\right )} \]
integrate((-18*x*log(x)*log(1/2*x/log(x))^2+((216*x^2-36*x)*log(x)+36*x)*l og(1/2*x/log(x))+((-162*x+162)*exp(x)-162*x)*log(x)*exp(exp(x)/x)+(-486*x^ 3+108*x^2)*log(x)-108*x^2)/(x^3*log(x)*log(1/2*x/log(x))^4-12*x^4*log(x)*l og(1/2*x/log(x))^3+(18*x^3*log(x)*exp(exp(x)/x)+54*x^5*log(x))*log(1/2*x/l og(x))^2+(-108*x^4*log(x)*exp(exp(x)/x)-108*x^6*log(x))*log(1/2*x/log(x))+ 81*x^3*log(x)*exp(exp(x)/x)^2+162*x^5*log(x)*exp(exp(x)/x)+81*x^7*log(x)), x, algorithm=\
18/(9*x^3 + 6*x^2*log(2) + x*log(2)^2 + x*log(x)^2 + x*log(log(x))^2 + 9*x *e^(e^x/x) - 2*(3*x^2 + x*log(2))*log(x) + 2*(3*x^2 + x*log(2) - x*log(x)) *log(log(x)))
Leaf count of result is larger than twice the leaf count of optimal. 7627 vs. \(2 (33) = 66\).
Time = 0.78 (sec) , antiderivative size = 7627, normalized size of antiderivative = 217.91 \[ \int \frac {-108 x^2+e^{\frac {e^x}{x}} \left (e^x (162-162 x)-162 x\right ) \log (x)+\left (108 x^2-486 x^3\right ) \log (x)+\left (36 x+\left (-36 x+216 x^2\right ) \log (x)\right ) \log \left (\frac {x}{2 \log (x)}\right )-18 x \log (x) \log ^2\left (\frac {x}{2 \log (x)}\right )}{81 e^{\frac {2 e^x}{x}} x^3 \log (x)+162 e^{\frac {e^x}{x}} x^5 \log (x)+81 x^7 \log (x)+\left (-108 e^{\frac {e^x}{x}} x^4 \log (x)-108 x^6 \log (x)\right ) \log \left (\frac {x}{2 \log (x)}\right )+\left (18 e^{\frac {e^x}{x}} x^3 \log (x)+54 x^5 \log (x)\right ) \log ^2\left (\frac {x}{2 \log (x)}\right )-12 x^4 \log (x) \log ^3\left (\frac {x}{2 \log (x)}\right )+x^3 \log (x) \log ^4\left (\frac {x}{2 \log (x)}\right )} \, dx=\text {Too large to display} \]
integrate((-18*x*log(x)*log(1/2*x/log(x))^2+((216*x^2-36*x)*log(x)+36*x)*l og(1/2*x/log(x))+((-162*x+162)*exp(x)-162*x)*log(x)*exp(exp(x)/x)+(-486*x^ 3+108*x^2)*log(x)-108*x^2)/(x^3*log(x)*log(1/2*x/log(x))^4-12*x^4*log(x)*l og(1/2*x/log(x))^3+(18*x^3*log(x)*exp(exp(x)/x)+54*x^5*log(x))*log(1/2*x/l og(x))^2+(-108*x^4*log(x)*exp(exp(x)/x)-108*x^6*log(x))*log(1/2*x/log(x))+ 81*x^3*log(x)*exp(exp(x)/x)^2+162*x^5*log(x)*exp(exp(x)/x)+81*x^7*log(x)), x, algorithm=\
18*(27*x^4*e^(2*x)*log(x) - 54*x^4*e^x*log(x) + 27*x^3*e^(2*x)*log(2)*log( x) - 36*x^3*e^x*log(2)*log(x) + 9*x^2*e^(2*x)*log(2)^2*log(x) - 6*x^2*e^x* log(2)^2*log(x) + x*e^(2*x)*log(2)^3*log(x) - 27*x^3*e^(2*x)*log(x)^2 + 36 *x^3*e^x*log(x)^2 - 18*x^2*e^(2*x)*log(2)*log(x)^2 + 12*x^2*e^x*log(2)*log (x)^2 - 3*x*e^(2*x)*log(2)^2*log(x)^2 + 9*x^2*e^(2*x)*log(x)^3 - 6*x^2*e^x *log(x)^3 + 3*x*e^(2*x)*log(2)*log(x)^3 - x*e^(2*x)*log(x)^4 + 27*x^3*e^(2 *x)*log(x)*log(log(x)) - 36*x^3*e^x*log(x)*log(log(x)) + 18*x^2*e^(2*x)*lo g(2)*log(x)*log(log(x)) - 12*x^2*e^x*log(2)*log(x)*log(log(x)) + 3*x*e^(2* x)*log(2)^2*log(x)*log(log(x)) - 18*x^2*e^(2*x)*log(x)^2*log(log(x)) + 12* x^2*e^x*log(x)^2*log(log(x)) - 6*x*e^(2*x)*log(2)*log(x)^2*log(log(x)) + 3 *x*e^(2*x)*log(x)^3*log(log(x)) + 9*x^2*e^(2*x)*log(x)*log(log(x))^2 - 6*x ^2*e^x*log(x)*log(log(x))^2 + 3*x*e^(2*x)*log(2)*log(x)*log(log(x))^2 - 3* x*e^(2*x)*log(x)^2*log(log(x))^2 + x*e^(2*x)*log(x)*log(log(x))^3 - 27*x^3 *e^(2*x)*log(x) + 18*x^3*e^x*log(x) - 27*x^2*e^(2*x)*log(2)*log(x) + 12*x^ 2*e^x*log(2)*log(x) - 9*x*e^(2*x)*log(2)^2*log(x) + 2*x*e^x*log(2)^2*log(x ) - e^(2*x)*log(2)^3*log(x) + 27*x^2*e^(2*x)*log(x)^2 - 12*x^2*e^x*log(x)^ 2 + 18*x*e^(2*x)*log(2)*log(x)^2 - 4*x*e^x*log(2)*log(x)^2 + 3*e^(2*x)*log (2)^2*log(x)^2 - 9*x*e^(2*x)*log(x)^3 + 2*x*e^x*log(x)^3 - 3*e^(2*x)*log(2 )*log(x)^3 + e^(2*x)*log(x)^4 - 27*x^2*e^(2*x)*log(x)*log(log(x)) + 12*x^2 *e^x*log(x)*log(log(x)) - 18*x*e^(2*x)*log(2)*log(x)*log(log(x)) + 4*x*...
Timed out. \[ \int \frac {-108 x^2+e^{\frac {e^x}{x}} \left (e^x (162-162 x)-162 x\right ) \log (x)+\left (108 x^2-486 x^3\right ) \log (x)+\left (36 x+\left (-36 x+216 x^2\right ) \log (x)\right ) \log \left (\frac {x}{2 \log (x)}\right )-18 x \log (x) \log ^2\left (\frac {x}{2 \log (x)}\right )}{81 e^{\frac {2 e^x}{x}} x^3 \log (x)+162 e^{\frac {e^x}{x}} x^5 \log (x)+81 x^7 \log (x)+\left (-108 e^{\frac {e^x}{x}} x^4 \log (x)-108 x^6 \log (x)\right ) \log \left (\frac {x}{2 \log (x)}\right )+\left (18 e^{\frac {e^x}{x}} x^3 \log (x)+54 x^5 \log (x)\right ) \log ^2\left (\frac {x}{2 \log (x)}\right )-12 x^4 \log (x) \log ^3\left (\frac {x}{2 \log (x)}\right )+x^3 \log (x) \log ^4\left (\frac {x}{2 \log (x)}\right )} \, dx=\int -\frac {108\,x^2-\ln \left (\frac {x}{2\,\ln \left (x\right )}\right )\,\left (36\,x-\ln \left (x\right )\,\left (36\,x-216\,x^2\right )\right )-\ln \left (x\right )\,\left (108\,x^2-486\,x^3\right )+{\mathrm {e}}^{\frac {{\mathrm {e}}^x}{x}}\,\ln \left (x\right )\,\left (162\,x+{\mathrm {e}}^x\,\left (162\,x-162\right )\right )+18\,x\,{\ln \left (\frac {x}{2\,\ln \left (x\right )}\right )}^2\,\ln \left (x\right )}{81\,x^7\,\ln \left (x\right )+{\ln \left (\frac {x}{2\,\ln \left (x\right )}\right )}^2\,\left (54\,x^5\,\ln \left (x\right )+18\,x^3\,{\mathrm {e}}^{\frac {{\mathrm {e}}^x}{x}}\,\ln \left (x\right )\right )-\ln \left (\frac {x}{2\,\ln \left (x\right )}\right )\,\left (108\,x^6\,\ln \left (x\right )+108\,x^4\,{\mathrm {e}}^{\frac {{\mathrm {e}}^x}{x}}\,\ln \left (x\right )\right )+x^3\,{\ln \left (\frac {x}{2\,\ln \left (x\right )}\right )}^4\,\ln \left (x\right )-12\,x^4\,{\ln \left (\frac {x}{2\,\ln \left (x\right )}\right )}^3\,\ln \left (x\right )+81\,x^3\,{\mathrm {e}}^{\frac {2\,{\mathrm {e}}^x}{x}}\,\ln \left (x\right )+162\,x^5\,{\mathrm {e}}^{\frac {{\mathrm {e}}^x}{x}}\,\ln \left (x\right )} \,d x \]
int(-(108*x^2 - log(x/(2*log(x)))*(36*x - log(x)*(36*x - 216*x^2)) - log(x )*(108*x^2 - 486*x^3) + exp(exp(x)/x)*log(x)*(162*x + exp(x)*(162*x - 162) ) + 18*x*log(x/(2*log(x)))^2*log(x))/(81*x^7*log(x) + log(x/(2*log(x)))^2* (54*x^5*log(x) + 18*x^3*exp(exp(x)/x)*log(x)) - log(x/(2*log(x)))*(108*x^6 *log(x) + 108*x^4*exp(exp(x)/x)*log(x)) + x^3*log(x/(2*log(x)))^4*log(x) - 12*x^4*log(x/(2*log(x)))^3*log(x) + 81*x^3*exp((2*exp(x))/x)*log(x) + 162 *x^5*exp(exp(x)/x)*log(x)),x)
int(-(108*x^2 - log(x/(2*log(x)))*(36*x - log(x)*(36*x - 216*x^2)) - log(x )*(108*x^2 - 486*x^3) + exp(exp(x)/x)*log(x)*(162*x + exp(x)*(162*x - 162) ) + 18*x*log(x/(2*log(x)))^2*log(x))/(81*x^7*log(x) + log(x/(2*log(x)))^2* (54*x^5*log(x) + 18*x^3*exp(exp(x)/x)*log(x)) - log(x/(2*log(x)))*(108*x^6 *log(x) + 108*x^4*exp(exp(x)/x)*log(x)) + x^3*log(x/(2*log(x)))^4*log(x) - 12*x^4*log(x/(2*log(x)))^3*log(x) + 81*x^3*exp((2*exp(x))/x)*log(x) + 162 *x^5*exp(exp(x)/x)*log(x)), x)