Integrand size = 178, antiderivative size = 28 \[ \int \frac {e^{\frac {x^2}{e^{\frac {2}{3} \left (648+e^2 (8-3 x)-243 x\right )}+2 e^{\frac {1}{3} \left (648+e^2 (8-3 x)-243 x\right )} \log (x)+\log ^2(x)}} \left (-2 x+e^{\frac {1}{3} \left (648+e^2 (8-3 x)-243 x\right )} \left (2 x+162 x^2+2 e^2 x^2\right )+2 x \log (x)\right )}{e^{648+e^2 (8-3 x)-243 x}+3 e^{\frac {2}{3} \left (648+e^2 (8-3 x)-243 x\right )} \log (x)+3 e^{\frac {1}{3} \left (648+e^2 (8-3 x)-243 x\right )} \log ^2(x)+\log ^3(x)} \, dx=1+e^{\frac {x^2}{\left (e^{\left (81+e^2\right ) \left (\frac {8}{3}-x\right )}+\log (x)\right )^2}} \]
Time = 0.46 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.39 \[ \int \frac {e^{\frac {x^2}{e^{\frac {2}{3} \left (648+e^2 (8-3 x)-243 x\right )}+2 e^{\frac {1}{3} \left (648+e^2 (8-3 x)-243 x\right )} \log (x)+\log ^2(x)}} \left (-2 x+e^{\frac {1}{3} \left (648+e^2 (8-3 x)-243 x\right )} \left (2 x+162 x^2+2 e^2 x^2\right )+2 x \log (x)\right )}{e^{648+e^2 (8-3 x)-243 x}+3 e^{\frac {2}{3} \left (648+e^2 (8-3 x)-243 x\right )} \log (x)+3 e^{\frac {1}{3} \left (648+e^2 (8-3 x)-243 x\right )} \log ^2(x)+\log ^3(x)} \, dx=e^{\frac {e^{162 x} x^2}{\left (e^{216+\frac {8 e^2}{3}-e^2 x}+e^{81 x} \log (x)\right )^2}} \]
Integrate[(E^(x^2/(E^((2*(648 + E^2*(8 - 3*x) - 243*x))/3) + 2*E^((648 + E ^2*(8 - 3*x) - 243*x)/3)*Log[x] + Log[x]^2))*(-2*x + E^((648 + E^2*(8 - 3* x) - 243*x)/3)*(2*x + 162*x^2 + 2*E^2*x^2) + 2*x*Log[x]))/(E^(648 + E^2*(8 - 3*x) - 243*x) + 3*E^((2*(648 + E^2*(8 - 3*x) - 243*x))/3)*Log[x] + 3*E^ ((648 + E^2*(8 - 3*x) - 243*x)/3)*Log[x]^2 + Log[x]^3),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.
| \(\displaystyle \int \frac {\left (e^{\frac {1}{3} \left (e^2 (8-3 x)-243 x+648\right )} \left (2 e^2 x^2+162 x^2+2 x\right )-2 x+2 x \log (x)\right ) \exp \left (\frac {x^2}{e^{\frac {2}{3} \left (e^2 (8-3 x)-243 x+648\right )}+\log ^2(x)+2 e^{\frac {1}{3} \left (e^2 (8-3 x)-243 x+648\right )} \log (x)}\right )}{e^{e^2 (8-3 x)-243 x+648}+\log ^3(x)+3 e^{\frac {1}{3} \left (e^2 (8-3 x)-243 x+648\right )} \log ^2(x)+3 e^{\frac {2}{3} \left (e^2 (8-3 x)-243 x+648\right )} \log (x)} \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {\left (e^{\frac {1}{3} \left (e^2 (8-3 x)-243 x+648\right )} \left (2 e^2 x^2+162 x^2+2 x\right )-2 x+2 x \log (x)\right ) \exp \left (\frac {e^{162 x} x^2}{\left (e^{e^2 \left (\frac {8}{3}-x\right )+216}+e^{81 x} \log (x)\right )^2}+243 x\right )}{\left (e^{e^2 \left (\frac {8}{3}-x\right )+216}+e^{81 x} \log (x)\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (2 x \left (\left (81+e^2\right ) x+1\right ) \exp \left (\frac {e^{162 x} x^2}{\left (e^{e^2 \left (\frac {8}{3}-x\right )+216}+e^{81 x} \log (x)\right )^2}-\left (81-2 e^2\right ) x+243 x-\frac {16}{3} \left (81+e^2\right )\right )+\frac {2 x \left (-81 \left (1+\frac {e^2}{81}\right ) x \log (x)-1\right ) \exp \left (\frac {e^{162 x} x^2}{\left (e^{e^2 \left (\frac {8}{3}-x\right )+216}+e^{81 x} \log (x)\right )^2}+243 x\right )}{\left (e^{e^2 \left (\frac {8}{3}-x\right )+216}+e^{81 x} \log (x)\right )^3}+\frac {2 x \left (-\left (\left (81+e^2\right ) x\right )-1\right ) \log (x) \exp \left (\frac {e^{162 x} x^2}{\left (e^{e^2 \left (\frac {8}{3}-x\right )+216}+e^{81 x} \log (x)\right )^2}+243 x\right )}{e^{e^2 (8-3 x)+648}+e^{\frac {2}{3} e^2 (8-3 x)+81 x+432} \log (x)}+\frac {2 x \left (-\left (\left (81+e^2\right ) x\right )-1\right ) \log (x) \exp \left (\frac {e^{162 x} x^2}{\left (e^{e^2 \left (\frac {8}{3}-x\right )+216}+e^{81 x} \log (x)\right )^2}+3 e^2 x+243 x-8 \left (27+e^2\right )\right )}{\left (e^{81 x+\frac {1}{3} e^2 (3 x-8)} \log (x)+e^{216}\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 x \left (e^{e^2 \left (\frac {8}{3}-x\right )+218} x-e^{81 x}+e^{e^2 \left (\frac {8}{3}-x\right )+216} (81 x+1)+e^{81 x} \log (x)\right ) \exp \left (\frac {e^{162 x} x^2}{\left (e^{e^2 \left (\frac {8}{3}-x\right )+216}+e^{81 x} \log (x)\right )^2}+162 x\right )}{\left (e^{e^2 \left (\frac {8}{3}-x\right )+216}+e^{81 x} \log (x)\right )^3}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 2 \int -\frac {\exp \left (\frac {e^{162 x} x^2}{\left (e^{81 x} \log (x)+e^{\frac {1}{3} e^2 (8-3 x)+216}\right )^2}+162 x\right ) x \left (-e^{\frac {1}{3} e^2 (8-3 x)+218} x+e^{81 x}-e^{\frac {1}{3} e^2 (8-3 x)+216} (81 x+1)-e^{81 x} \log (x)\right )}{\left (e^{81 x} \log (x)+e^{\frac {1}{3} e^2 (8-3 x)+216}\right )^3}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -2 \int \frac {\exp \left (\frac {e^{162 x} x^2}{\left (e^{81 x} \log (x)+e^{\frac {1}{3} e^2 (8-3 x)+216}\right )^2}+162 x\right ) x \left (-e^{\frac {1}{3} e^2 (8-3 x)+218} x+e^{81 x}-e^{\frac {1}{3} e^2 (8-3 x)+216} (81 x+1)-e^{81 x} \log (x)\right )}{\left (e^{81 x} \log (x)+e^{\frac {1}{3} e^2 (8-3 x)+216}\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {\exp \left (\frac {e^{162 x} x^2}{\left (e^{81 x} \log (x)+e^{\frac {1}{3} e^2 (8-3 x)+216}\right )^2}+162 x\right ) (x-x \log (x))}{\log (x) \left (e^{81 x} \log (x)+e^{e^2 \left (\frac {8}{3}-x\right )+216}\right )^2}+\frac {\exp \left (\frac {e^{162 x} x^2}{\left (e^{81 x} \log (x)+e^{\frac {1}{3} e^2 (8-3 x)+216}\right )^2}-e^2 x+162 x+\frac {8}{3} \left (81+e^2\right )\right ) x \left (-81 \left (1+\frac {e^2}{81}\right ) x \log (x)-1\right )}{\log (x) \left (e^{81 x} \log (x)+e^{e^2 \left (\frac {8}{3}-x\right )+216}\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle -2 \int \left (\frac {\exp \left (\frac {e^{162 x} x^2}{\left (e^{81 x} \log (x)+e^{\frac {1}{3} e^2 (8-3 x)+216}\right )^2}+162 x\right ) (x-x \log (x))}{\log (x) \left (e^{81 x} \log (x)+e^{e^2 \left (\frac {8}{3}-x\right )+216}\right )^2}+\frac {\exp \left (\frac {e^{162 x} x^2}{\left (e^{81 x} \log (x)+e^{\frac {1}{3} e^2 (8-3 x)+216}\right )^2}+162 \left (1-\frac {e^2}{162}\right ) x+\frac {8}{3} \left (81+e^2\right )\right ) x \left (-81 \left (1+\frac {e^2}{81}\right ) x \log (x)-1\right )}{\log (x) \left (e^{81 x} \log (x)+e^{e^2 \left (\frac {8}{3}-x\right )+216}\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {\exp \left (\frac {e^{162 x} x^2}{\left (e^{81 x} \log (x)+e^{e^2 \left (\frac {8}{3}-x\right )+216}\right )^2}+162 x\right ) x (1-\log (x))}{\log (x) \left (e^{81 x} \log (x)+e^{e^2 \left (\frac {8}{3}-x\right )+216}\right )^2}+\frac {\exp \left (\frac {e^{162 x} x^2}{\left (e^{81 x} \log (x)+e^{e^2 \left (\frac {8}{3}-x\right )+216}\right )^2}+162 x+e^2 \left (\frac {8}{3}-x\right )+216\right ) x \left (-81 \left (1+\frac {e^2}{81}\right ) x \log (x)-1\right )}{\log (x) \left (e^{81 x} \log (x)+e^{e^2 \left (\frac {8}{3}-x\right )+216}\right )^3}\right )dx\) |
| \(\Big \downarrow \) 7299 |
| \(\displaystyle -2 \int \left (\frac {\exp \left (\frac {e^{162 x} x^2}{\left (e^{81 x} \log (x)+e^{e^2 \left (\frac {8}{3}-x\right )+216}\right )^2}+162 x\right ) x (1-\log (x))}{\log (x) \left (e^{81 x} \log (x)+e^{e^2 \left (\frac {8}{3}-x\right )+216}\right )^2}+\frac {\exp \left (\frac {e^{162 x} x^2}{\left (e^{81 x} \log (x)+e^{e^2 \left (\frac {8}{3}-x\right )+216}\right )^2}+162 x+e^2 \left (\frac {8}{3}-x\right )+216\right ) x \left (-81 \left (1+\frac {e^2}{81}\right ) x \log (x)-1\right )}{\log (x) \left (e^{81 x} \log (x)+e^{e^2 \left (\frac {8}{3}-x\right )+216}\right )^3}\right )dx\) |
Int[(E^(x^2/(E^((2*(648 + E^2*(8 - 3*x) - 243*x))/3) + 2*E^((648 + E^2*(8 - 3*x) - 243*x)/3)*Log[x] + Log[x]^2))*(-2*x + E^((648 + E^2*(8 - 3*x) - 2 43*x)/3)*(2*x + 162*x^2 + 2*E^2*x^2) + 2*x*Log[x]))/(E^(648 + E^2*(8 - 3*x ) - 243*x) + 3*E^((2*(648 + E^2*(8 - 3*x) - 243*x))/3)*Log[x] + 3*E^((648 + E^2*(8 - 3*x) - 243*x)/3)*Log[x]^2 + Log[x]^3),x]
3.29.53.3.1 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 = 13.88 (sec) , antiderivative size = 41, normalized size of antiderivative = 1.46
| method | result | size |
| risch | \({\mathrm e}^{\frac {x^{2}}{\ln \left (x \right )^{2}+2 \,{\mathrm e}^{-\frac {\left (3 x -8\right ) \left (81+{\mathrm e}^{2}\right )}{3}} \ln \left (x \right )+{\mathrm e}^{-\frac {2 \left (3 x -8\right ) \left (81+{\mathrm e}^{2}\right )}{3}}}}\) | \(41\) |
| parallelrisch | \({\mathrm e}^{\frac {x^{2}}{\ln \left (x \right )^{2}+2 \,{\mathrm e}^{\frac {\left (-3 x +8\right ) {\mathrm e}^{2}}{3}-81 x +216} \ln \left (x \right )+{\mathrm e}^{\frac {2 \left (-3 x +8\right ) {\mathrm e}^{2}}{3}-162 x +432}}}\) | \(49\) |
int((2*x*ln(x)+(2*x^2*exp(2)+162*x^2+2*x)*exp(1/3*(-3*x+8)*exp(2)-81*x+216 )-2*x)*exp(x^2/(ln(x)^2+2*exp(1/3*(-3*x+8)*exp(2)-81*x+216)*ln(x)+exp(1/3* (-3*x+8)*exp(2)-81*x+216)^2))/(ln(x)^3+3*exp(1/3*(-3*x+8)*exp(2)-81*x+216) *ln(x)^2+3*exp(1/3*(-3*x+8)*exp(2)-81*x+216)^2*ln(x)+exp(1/3*(-3*x+8)*exp( 2)-81*x+216)^3),x,method=_RETURNVERBOSE)
Time = 0.26 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.64 \[ \int \frac {e^{\frac {x^2}{e^{\frac {2}{3} \left (648+e^2 (8-3 x)-243 x\right )}+2 e^{\frac {1}{3} \left (648+e^2 (8-3 x)-243 x\right )} \log (x)+\log ^2(x)}} \left (-2 x+e^{\frac {1}{3} \left (648+e^2 (8-3 x)-243 x\right )} \left (2 x+162 x^2+2 e^2 x^2\right )+2 x \log (x)\right )}{e^{648+e^2 (8-3 x)-243 x}+3 e^{\frac {2}{3} \left (648+e^2 (8-3 x)-243 x\right )} \log (x)+3 e^{\frac {1}{3} \left (648+e^2 (8-3 x)-243 x\right )} \log ^2(x)+\log ^3(x)} \, dx=e^{\left (\frac {x^{2}}{2 \, e^{\left (-\frac {1}{3} \, {\left (3 \, x - 8\right )} e^{2} - 81 \, x + 216\right )} \log \left (x\right ) + \log \left (x\right )^{2} + e^{\left (-\frac {2}{3} \, {\left (3 \, x - 8\right )} e^{2} - 162 \, x + 432\right )}}\right )} \]
integrate((2*x*log(x)+(2*x^2*exp(2)+162*x^2+2*x)*exp(1/3*(-3*x+8)*exp(2)-8 1*x+216)-2*x)*exp(x^2/(log(x)^2+2*exp(1/3*(-3*x+8)*exp(2)-81*x+216)*log(x) +exp(1/3*(-3*x+8)*exp(2)-81*x+216)^2))/(log(x)^3+3*exp(1/3*(-3*x+8)*exp(2) -81*x+216)*log(x)^2+3*exp(1/3*(-3*x+8)*exp(2)-81*x+216)^2*log(x)+exp(1/3*( -3*x+8)*exp(2)-81*x+216)^3),x, algorithm=\
e^(x^2/(2*e^(-1/3*(3*x - 8)*e^2 - 81*x + 216)*log(x) + log(x)^2 + e^(-2/3* (3*x - 8)*e^2 - 162*x + 432)))
Leaf count of result is larger than twice the leaf count of optimal. 46 vs. \(2 (22) = 44\).
Time = 0.72 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.64 \[ \int \frac {e^{\frac {x^2}{e^{\frac {2}{3} \left (648+e^2 (8-3 x)-243 x\right )}+2 e^{\frac {1}{3} \left (648+e^2 (8-3 x)-243 x\right )} \log (x)+\log ^2(x)}} \left (-2 x+e^{\frac {1}{3} \left (648+e^2 (8-3 x)-243 x\right )} \left (2 x+162 x^2+2 e^2 x^2\right )+2 x \log (x)\right )}{e^{648+e^2 (8-3 x)-243 x}+3 e^{\frac {2}{3} \left (648+e^2 (8-3 x)-243 x\right )} \log (x)+3 e^{\frac {1}{3} \left (648+e^2 (8-3 x)-243 x\right )} \log ^2(x)+\log ^3(x)} \, dx=e^{\frac {x^{2}}{e^{- 162 x + 2 \cdot \left (\frac {8}{3} - x\right ) e^{2} + 432} + 2 e^{- 81 x + \left (\frac {8}{3} - x\right ) e^{2} + 216} \log {\left (x \right )} + \log {\left (x \right )}^{2}}} \]
integrate((2*x*ln(x)+(2*x**2*exp(2)+162*x**2+2*x)*exp(1/3*(-3*x+8)*exp(2)- 81*x+216)-2*x)*exp(x**2/(ln(x)**2+2*exp(1/3*(-3*x+8)*exp(2)-81*x+216)*ln(x )+exp(1/3*(-3*x+8)*exp(2)-81*x+216)**2))/(ln(x)**3+3*exp(1/3*(-3*x+8)*exp( 2)-81*x+216)*ln(x)**2+3*exp(1/3*(-3*x+8)*exp(2)-81*x+216)**2*ln(x)+exp(1/3 *(-3*x+8)*exp(2)-81*x+216)**3),x)
exp(x**2/(exp(-162*x + 2*(8/3 - x)*exp(2) + 432) + 2*exp(-81*x + (8/3 - x) *exp(2) + 216)*log(x) + log(x)**2))
Timed out. \[ \int \frac {e^{\frac {x^2}{e^{\frac {2}{3} \left (648+e^2 (8-3 x)-243 x\right )}+2 e^{\frac {1}{3} \left (648+e^2 (8-3 x)-243 x\right )} \log (x)+\log ^2(x)}} \left (-2 x+e^{\frac {1}{3} \left (648+e^2 (8-3 x)-243 x\right )} \left (2 x+162 x^2+2 e^2 x^2\right )+2 x \log (x)\right )}{e^{648+e^2 (8-3 x)-243 x}+3 e^{\frac {2}{3} \left (648+e^2 (8-3 x)-243 x\right )} \log (x)+3 e^{\frac {1}{3} \left (648+e^2 (8-3 x)-243 x\right )} \log ^2(x)+\log ^3(x)} \, dx=\text {Timed out} \]
integrate((2*x*log(x)+(2*x^2*exp(2)+162*x^2+2*x)*exp(1/3*(-3*x+8)*exp(2)-8 1*x+216)-2*x)*exp(x^2/(log(x)^2+2*exp(1/3*(-3*x+8)*exp(2)-81*x+216)*log(x) +exp(1/3*(-3*x+8)*exp(2)-81*x+216)^2))/(log(x)^3+3*exp(1/3*(-3*x+8)*exp(2) -81*x+216)*log(x)^2+3*exp(1/3*(-3*x+8)*exp(2)-81*x+216)^2*log(x)+exp(1/3*( -3*x+8)*exp(2)-81*x+216)^3),x, algorithm=\
\[ \int \frac {e^{\frac {x^2}{e^{\frac {2}{3} \left (648+e^2 (8-3 x)-243 x\right )}+2 e^{\frac {1}{3} \left (648+e^2 (8-3 x)-243 x\right )} \log (x)+\log ^2(x)}} \left (-2 x+e^{\frac {1}{3} \left (648+e^2 (8-3 x)-243 x\right )} \left (2 x+162 x^2+2 e^2 x^2\right )+2 x \log (x)\right )}{e^{648+e^2 (8-3 x)-243 x}+3 e^{\frac {2}{3} \left (648+e^2 (8-3 x)-243 x\right )} \log (x)+3 e^{\frac {1}{3} \left (648+e^2 (8-3 x)-243 x\right )} \log ^2(x)+\log ^3(x)} \, dx=\int { \frac {2 \, {\left ({\left (x^{2} e^{2} + 81 \, x^{2} + x\right )} e^{\left (-\frac {1}{3} \, {\left (3 \, x - 8\right )} e^{2} - 81 \, x + 216\right )} + x \log \left (x\right ) - x\right )} e^{\left (\frac {x^{2}}{2 \, e^{\left (-\frac {1}{3} \, {\left (3 \, x - 8\right )} e^{2} - 81 \, x + 216\right )} \log \left (x\right ) + \log \left (x\right )^{2} + e^{\left (-\frac {2}{3} \, {\left (3 \, x - 8\right )} e^{2} - 162 \, x + 432\right )}}\right )}}{3 \, e^{\left (-\frac {1}{3} \, {\left (3 \, x - 8\right )} e^{2} - 81 \, x + 216\right )} \log \left (x\right )^{2} + \log \left (x\right )^{3} + 3 \, e^{\left (-\frac {2}{3} \, {\left (3 \, x - 8\right )} e^{2} - 162 \, x + 432\right )} \log \left (x\right ) + e^{\left (-{\left (3 \, x - 8\right )} e^{2} - 243 \, x + 648\right )}} \,d x } \]
integrate((2*x*log(x)+(2*x^2*exp(2)+162*x^2+2*x)*exp(1/3*(-3*x+8)*exp(2)-8 1*x+216)-2*x)*exp(x^2/(log(x)^2+2*exp(1/3*(-3*x+8)*exp(2)-81*x+216)*log(x) +exp(1/3*(-3*x+8)*exp(2)-81*x+216)^2))/(log(x)^3+3*exp(1/3*(-3*x+8)*exp(2) -81*x+216)*log(x)^2+3*exp(1/3*(-3*x+8)*exp(2)-81*x+216)^2*log(x)+exp(1/3*( -3*x+8)*exp(2)-81*x+216)^3),x, algorithm=\
integrate(2*((x^2*e^2 + 81*x^2 + x)*e^(-1/3*(3*x - 8)*e^2 - 81*x + 216) + x*log(x) - x)*e^(x^2/(2*e^(-1/3*(3*x - 8)*e^2 - 81*x + 216)*log(x) + log(x )^2 + e^(-2/3*(3*x - 8)*e^2 - 162*x + 432)))/(3*e^(-1/3*(3*x - 8)*e^2 - 81 *x + 216)*log(x)^2 + log(x)^3 + 3*e^(-2/3*(3*x - 8)*e^2 - 162*x + 432)*log (x) + e^(-(3*x - 8)*e^2 - 243*x + 648)), x)
Time = 9.36 (sec) , antiderivative size = 51, normalized size of antiderivative = 1.82 \[ \int \frac {e^{\frac {x^2}{e^{\frac {2}{3} \left (648+e^2 (8-3 x)-243 x\right )}+2 e^{\frac {1}{3} \left (648+e^2 (8-3 x)-243 x\right )} \log (x)+\log ^2(x)}} \left (-2 x+e^{\frac {1}{3} \left (648+e^2 (8-3 x)-243 x\right )} \left (2 x+162 x^2+2 e^2 x^2\right )+2 x \log (x)\right )}{e^{648+e^2 (8-3 x)-243 x}+3 e^{\frac {2}{3} \left (648+e^2 (8-3 x)-243 x\right )} \log (x)+3 e^{\frac {1}{3} \left (648+e^2 (8-3 x)-243 x\right )} \log ^2(x)+\log ^3(x)} \, dx={\mathrm {e}}^{\frac {x^2}{{\ln \left (x\right )}^2+2\,{\mathrm {e}}^{\frac {8\,{\mathrm {e}}^2}{3}}\,{\mathrm {e}}^{-81\,x}\,{\mathrm {e}}^{216}\,{\mathrm {e}}^{-x\,{\mathrm {e}}^2}\,\ln \left (x\right )+{\mathrm {e}}^{\frac {16\,{\mathrm {e}}^2}{3}}\,{\mathrm {e}}^{-162\,x}\,{\mathrm {e}}^{432}\,{\mathrm {e}}^{-2\,x\,{\mathrm {e}}^2}}} \]
int((exp(x^2/(exp(432 - (2*exp(2)*(3*x - 8))/3 - 162*x) + log(x)^2 + 2*exp (216 - (exp(2)*(3*x - 8))/3 - 81*x)*log(x)))*(exp(216 - (exp(2)*(3*x - 8)) /3 - 81*x)*(2*x + 2*x^2*exp(2) + 162*x^2) - 2*x + 2*x*log(x)))/(exp(648 - exp(2)*(3*x - 8) - 243*x) + 3*exp(216 - (exp(2)*(3*x - 8))/3 - 81*x)*log(x )^2 + log(x)^3 + 3*exp(432 - (2*exp(2)*(3*x - 8))/3 - 162*x)*log(x)),x)