\(\int \frac {e^{\frac {144 x^2-e^{4 x^2} x^2-288 x^3-2 e^{2 x^2} x^3+143 x^4+(288 x-288 x^2) \log (x)+144 \log ^2(x)}{9 e^{4 x^2}+18 e^{2 x^2} x+9 x^2}} (288 x^2-2 e^{6 x^2} x^2-288 x^3-6 e^{4 x^2} x^3-288 x^4+286 x^5+e^{2 x^2} (288 x-864 x^3-582 x^4+2304 x^5-1152 x^6)+(288 x-288 x^2+e^{2 x^2} (288+288 x-576 x^2-2304 x^3+2304 x^4)) \log (x)+(-288 x-1152 e^{2 x^2} x^2) \log ^2(x))}{9 e^{6 x^2} x+27 e^{4 x^2} x^2+27 e^{2 x^2} x^3+9 x^4} \, dx\) [5070]

Optimal result

Integrand size = 269, antiderivative size = 36 \[ \int \frac {e^{\frac {144 x^2-e^{4 x^2} x^2-288 x^3-2 e^{2 x^2} x^3+143 x^4+\left (288 x-288 x^2\right ) \log (x)+144 \log ^2(x)}{9 e^{4 x^2}+18 e^{2 x^2} x+9 x^2}} \left (288 x^2-2 e^{6 x^2} x^2-288 x^3-6 e^{4 x^2} x^3-288 x^4+286 x^5+e^{2 x^2} \left (288 x-864 x^3-582 x^4+2304 x^5-1152 x^6\right )+\left (288 x-288 x^2+e^{2 x^2} \left (288+288 x-576 x^2-2304 x^3+2304 x^4\right )\right ) \log (x)+\left (-288 x-1152 e^{2 x^2} x^2\right ) \log ^2(x)\right )}{9 e^{6 x^2} x+27 e^{4 x^2} x^2+27 e^{2 x^2} x^3+9 x^4} \, dx=e^{-\frac {x^2}{9}+\frac {16 \left (-x+x^2-\log (x)\right )^2}{\left (e^{2 x^2}+x\right )^2}} \]

[Out]

exp(16/(exp(x^2)^2+x)^2*(x^2-x-ln(x))^2-1/9*x^2)

Rubi [F(-1)]

Timed out. \[ \int \frac {e^{\frac {144 x^2-e^{4 x^2} x^2-288 x^3-2 e^{2 x^2} x^3+143 x^4+\left (288 x-288 x^2\right ) \log (x)+144 \log ^2(x)}{9 e^{4 x^2}+18 e^{2 x^2} x+9 x^2}} \left (288 x^2-2 e^{6 x^2} x^2-288 x^3-6 e^{4 x^2} x^3-288 x^4+286 x^5+e^{2 x^2} \left (288 x-864 x^3-582 x^4+2304 x^5-1152 x^6\right )+\left (288 x-288 x^2+e^{2 x^2} \left (288+288 x-576 x^2-2304 x^3+2304 x^4\right )\right ) \log (x)+\left (-288 x-1152 e^{2 x^2} x^2\right ) \log ^2(x)\right )}{9 e^{6 x^2} x+27 e^{4 x^2} x^2+27 e^{2 x^2} x^3+9 x^4} \, dx=\text {\$Aborted} \]

[In]

Int[(E^((144*x^2 - E^(4*x^2)*x^2 - 288*x^3 - 2*E^(2*x^2)*x^3 + 143*x^4 + (288*x - 288*x^2)*Log[x] + 144*Log[x]
^2)/(9*E^(4*x^2) + 18*E^(2*x^2)*x + 9*x^2))*(288*x^2 - 2*E^(6*x^2)*x^2 - 288*x^3 - 6*E^(4*x^2)*x^3 - 288*x^4 +
286*x^5 + E^(2*x^2)*(288*x - 864*x^3 - 582*x^4 + 2304*x^5 - 1152*x^6) + (288*x - 288*x^2 + E^(2*x^2)*(288 + 2
88*x - 576*x^2 - 2304*x^3 + 2304*x^4))*Log[x] + (-288*x - 1152*E^(2*x^2)*x^2)*Log[x]^2))/(9*E^(6*x^2)*x + 27*E
^(4*x^2)*x^2 + 27*E^(2*x^2)*x^3 + 9*x^4),x]

[Out]

$Aborted

Rubi steps Aborted

Mathematica [B] (verified)

Leaf count is larger than twice the leaf count of optimal. \(77\) vs. \(2(36)=72\).

Time = 0.68 (sec) , antiderivative size = 77, normalized size of antiderivative = 2.14 \[ \int \frac {e^{\frac {144 x^2-e^{4 x^2} x^2-288 x^3-2 e^{2 x^2} x^3+143 x^4+\left (288 x-288 x^2\right ) \log (x)+144 \log ^2(x)}{9 e^{4 x^2}+18 e^{2 x^2} x+9 x^2}} \left (288 x^2-2 e^{6 x^2} x^2-288 x^3-6 e^{4 x^2} x^3-288 x^4+286 x^5+e^{2 x^2} \left (288 x-864 x^3-582 x^4+2304 x^5-1152 x^6\right )+\left (288 x-288 x^2+e^{2 x^2} \left (288+288 x-576 x^2-2304 x^3+2304 x^4\right )\right ) \log (x)+\left (-288 x-1152 e^{2 x^2} x^2\right ) \log ^2(x)\right )}{9 e^{6 x^2} x+27 e^{4 x^2} x^2+27 e^{2 x^2} x^3+9 x^4} \, dx=e^{\frac {x^2 \left (144-e^{4 x^2}-288 x-2 e^{2 x^2} x+143 x^2\right )+144 \log ^2(x)}{9 \left (e^{2 x^2}+x\right )^2}} x^{-\frac {32 (-1+x) x}{\left (e^{2 x^2}+x\right )^2}} \]

[In]

Integrate[(E^((144*x^2 - E^(4*x^2)*x^2 - 288*x^3 - 2*E^(2*x^2)*x^3 + 143*x^4 + (288*x - 288*x^2)*Log[x] + 144*
Log[x]^2)/(9*E^(4*x^2) + 18*E^(2*x^2)*x + 9*x^2))*(288*x^2 - 2*E^(6*x^2)*x^2 - 288*x^3 - 6*E^(4*x^2)*x^3 - 288
*x^4 + 286*x^5 + E^(2*x^2)*(288*x - 864*x^3 - 582*x^4 + 2304*x^5 - 1152*x^6) + (288*x - 288*x^2 + E^(2*x^2)*(2
88 + 288*x - 576*x^2 - 2304*x^3 + 2304*x^4))*Log[x] + (-288*x - 1152*E^(2*x^2)*x^2)*Log[x]^2))/(9*E^(6*x^2)*x
+ 27*E^(4*x^2)*x^2 + 27*E^(2*x^2)*x^3 + 9*x^4),x]

[Out]

E^((x^2*(144 - E^(4*x^2) - 288*x - 2*E^(2*x^2)*x + 143*x^2) + 144*Log[x]^2)/(9*(E^(2*x^2) + x)^2))/x^((32*(-1
+ x)*x)/(E^(2*x^2) + x)^2)

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(80\) vs. \(2(32)=64\).

Time = 0.07 (sec) , antiderivative size = 81, normalized size of antiderivative = 2.25

\[{\mathrm e}^{\frac {-2 \,{\mathrm e}^{2 x^{2}} x^{3}+143 x^{4}-x^{2} {\mathrm e}^{4 x^{2}}-288 x^{2} \ln \left (x \right )-288 x^{3}+144 \ln \left (x \right )^{2}+288 x \ln \left (x \right )+144 x^{2}}{9 \,{\mathrm e}^{4 x^{2}}+18 x \,{\mathrm e}^{2 x^{2}}+9 x^{2}}}\]

[In]

int(((-1152*x^2*exp(x^2)^2-288*x)*ln(x)^2+((2304*x^4-2304*x^3-576*x^2+288*x+288)*exp(x^2)^2-288*x^2+288*x)*ln(
x)-2*x^2*exp(x^2)^6-6*x^3*exp(x^2)^4+(-1152*x^6+2304*x^5-582*x^4-864*x^3+288*x)*exp(x^2)^2+286*x^5-288*x^4-288
*x^3+288*x^2)*exp((144*ln(x)^2+(-288*x^2+288*x)*ln(x)-x^2*exp(x^2)^4-2*x^3*exp(x^2)^2+143*x^4-288*x^3+144*x^2)
/(9*exp(x^2)^4+18*x*exp(x^2)^2+9*x^2))/(9*x*exp(x^2)^6+27*x^2*exp(x^2)^4+27*x^3*exp(x^2)^2+9*x^4),x)

[Out]

exp(1/9*(-2*exp(2*x^2)*x^3+143*x^4-x^2*exp(4*x^2)-288*x^2*ln(x)-288*x^3+144*ln(x)^2+288*x*ln(x)+144*x^2)/(2*x*
exp(2*x^2)+x^2+exp(4*x^2)))

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 79 vs. \(2 (32) = 64\).

Time = 0.27 (sec) , antiderivative size = 79, normalized size of antiderivative = 2.19 \[ \int \frac {e^{\frac {144 x^2-e^{4 x^2} x^2-288 x^3-2 e^{2 x^2} x^3+143 x^4+\left (288 x-288 x^2\right ) \log (x)+144 \log ^2(x)}{9 e^{4 x^2}+18 e^{2 x^2} x+9 x^2}} \left (288 x^2-2 e^{6 x^2} x^2-288 x^3-6 e^{4 x^2} x^3-288 x^4+286 x^5+e^{2 x^2} \left (288 x-864 x^3-582 x^4+2304 x^5-1152 x^6\right )+\left (288 x-288 x^2+e^{2 x^2} \left (288+288 x-576 x^2-2304 x^3+2304 x^4\right )\right ) \log (x)+\left (-288 x-1152 e^{2 x^2} x^2\right ) \log ^2(x)\right )}{9 e^{6 x^2} x+27 e^{4 x^2} x^2+27 e^{2 x^2} x^3+9 x^4} \, dx=e^{\left (\frac {143 \, x^{4} - 2 \, x^{3} e^{\left (2 \, x^{2}\right )} - 288 \, x^{3} - x^{2} e^{\left (4 \, x^{2}\right )} + 144 \, x^{2} - 288 \, {\left (x^{2} - x\right )} \log \left (x\right ) + 144 \, \log \left (x\right )^{2}}{9 \, {\left (x^{2} + 2 \, x e^{\left (2 \, x^{2}\right )} + e^{\left (4 \, x^{2}\right )}\right )}}\right )} \]

[In]

integrate(((-1152*x^2*exp(x^2)^2-288*x)*log(x)^2+((2304*x^4-2304*x^3-576*x^2+288*x+288)*exp(x^2)^2-288*x^2+288
*x)*log(x)-2*x^2*exp(x^2)^6-6*x^3*exp(x^2)^4+(-1152*x^6+2304*x^5-582*x^4-864*x^3+288*x)*exp(x^2)^2+286*x^5-288
*x^4-288*x^3+288*x^2)*exp((144*log(x)^2+(-288*x^2+288*x)*log(x)-x^2*exp(x^2)^4-2*x^3*exp(x^2)^2+143*x^4-288*x^
3+144*x^2)/(9*exp(x^2)^4+18*x*exp(x^2)^2+9*x^2))/(9*x*exp(x^2)^6+27*x^2*exp(x^2)^4+27*x^3*exp(x^2)^2+9*x^4),x,
algorithm="fricas")

[Out]

e^(1/9*(143*x^4 - 2*x^3*e^(2*x^2) - 288*x^3 - x^2*e^(4*x^2) + 144*x^2 - 288*(x^2 - x)*log(x) + 144*log(x)^2)/(
x^2 + 2*x*e^(2*x^2) + e^(4*x^2)))

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 80 vs. \(2 (27) = 54\).

Time = 1.19 (sec) , antiderivative size = 80, normalized size of antiderivative = 2.22 \[ \int \frac {e^{\frac {144 x^2-e^{4 x^2} x^2-288 x^3-2 e^{2 x^2} x^3+143 x^4+\left (288 x-288 x^2\right ) \log (x)+144 \log ^2(x)}{9 e^{4 x^2}+18 e^{2 x^2} x+9 x^2}} \left (288 x^2-2 e^{6 x^2} x^2-288 x^3-6 e^{4 x^2} x^3-288 x^4+286 x^5+e^{2 x^2} \left (288 x-864 x^3-582 x^4+2304 x^5-1152 x^6\right )+\left (288 x-288 x^2+e^{2 x^2} \left (288+288 x-576 x^2-2304 x^3+2304 x^4\right )\right ) \log (x)+\left (-288 x-1152 e^{2 x^2} x^2\right ) \log ^2(x)\right )}{9 e^{6 x^2} x+27 e^{4 x^2} x^2+27 e^{2 x^2} x^3+9 x^4} \, dx=e^{\frac {143 x^{4} - 2 x^{3} e^{2 x^{2}} - 288 x^{3} - x^{2} e^{4 x^{2}} + 144 x^{2} + \left (- 288 x^{2} + 288 x\right ) \log {\left (x \right )} + 144 \log {\left (x \right )}^{2}}{9 x^{2} + 18 x e^{2 x^{2}} + 9 e^{4 x^{2}}}} \]

[In]

integrate(((-1152*x**2*exp(x**2)**2-288*x)*ln(x)**2+((2304*x**4-2304*x**3-576*x**2+288*x+288)*exp(x**2)**2-288
*x**2+288*x)*ln(x)-2*x**2*exp(x**2)**6-6*x**3*exp(x**2)**4+(-1152*x**6+2304*x**5-582*x**4-864*x**3+288*x)*exp(
x**2)**2+286*x**5-288*x**4-288*x**3+288*x**2)*exp((144*ln(x)**2+(-288*x**2+288*x)*ln(x)-x**2*exp(x**2)**4-2*x*
*3*exp(x**2)**2+143*x**4-288*x**3+144*x**2)/(9*exp(x**2)**4+18*x*exp(x**2)**2+9*x**2))/(9*x*exp(x**2)**6+27*x*
*2*exp(x**2)**4+27*x**3*exp(x**2)**2+9*x**4),x)

[Out]

exp((143*x**4 - 2*x**3*exp(2*x**2) - 288*x**3 - x**2*exp(4*x**2) + 144*x**2 + (-288*x**2 + 288*x)*log(x) + 144
*log(x)**2)/(9*x**2 + 18*x*exp(2*x**2) + 9*exp(4*x**2)))

Maxima [F]

\[ \int \frac {e^{\frac {144 x^2-e^{4 x^2} x^2-288 x^3-2 e^{2 x^2} x^3+143 x^4+\left (288 x-288 x^2\right ) \log (x)+144 \log ^2(x)}{9 e^{4 x^2}+18 e^{2 x^2} x+9 x^2}} \left (288 x^2-2 e^{6 x^2} x^2-288 x^3-6 e^{4 x^2} x^3-288 x^4+286 x^5+e^{2 x^2} \left (288 x-864 x^3-582 x^4+2304 x^5-1152 x^6\right )+\left (288 x-288 x^2+e^{2 x^2} \left (288+288 x-576 x^2-2304 x^3+2304 x^4\right )\right ) \log (x)+\left (-288 x-1152 e^{2 x^2} x^2\right ) \log ^2(x)\right )}{9 e^{6 x^2} x+27 e^{4 x^2} x^2+27 e^{2 x^2} x^3+9 x^4} \, dx=\int { \frac {2 \, {\left (143 \, x^{5} - 144 \, x^{4} - 3 \, x^{3} e^{\left (4 \, x^{2}\right )} - 144 \, x^{3} - x^{2} e^{\left (6 \, x^{2}\right )} - 144 \, {\left (4 \, x^{2} e^{\left (2 \, x^{2}\right )} + x\right )} \log \left (x\right )^{2} + 144 \, x^{2} - 3 \, {\left (192 \, x^{6} - 384 \, x^{5} + 97 \, x^{4} + 144 \, x^{3} - 48 \, x\right )} e^{\left (2 \, x^{2}\right )} - 144 \, {\left (x^{2} - {\left (8 \, x^{4} - 8 \, x^{3} - 2 \, x^{2} + x + 1\right )} e^{\left (2 \, x^{2}\right )} - x\right )} \log \left (x\right )\right )} e^{\left (\frac {143 \, x^{4} - 2 \, x^{3} e^{\left (2 \, x^{2}\right )} - 288 \, x^{3} - x^{2} e^{\left (4 \, x^{2}\right )} + 144 \, x^{2} - 288 \, {\left (x^{2} - x\right )} \log \left (x\right ) + 144 \, \log \left (x\right )^{2}}{9 \, {\left (x^{2} + 2 \, x e^{\left (2 \, x^{2}\right )} + e^{\left (4 \, x^{2}\right )}\right )}}\right )}}{9 \, {\left (x^{4} + 3 \, x^{3} e^{\left (2 \, x^{2}\right )} + 3 \, x^{2} e^{\left (4 \, x^{2}\right )} + x e^{\left (6 \, x^{2}\right )}\right )}} \,d x } \]

[In]

integrate(((-1152*x^2*exp(x^2)^2-288*x)*log(x)^2+((2304*x^4-2304*x^3-576*x^2+288*x+288)*exp(x^2)^2-288*x^2+288
*x)*log(x)-2*x^2*exp(x^2)^6-6*x^3*exp(x^2)^4+(-1152*x^6+2304*x^5-582*x^4-864*x^3+288*x)*exp(x^2)^2+286*x^5-288
*x^4-288*x^3+288*x^2)*exp((144*log(x)^2+(-288*x^2+288*x)*log(x)-x^2*exp(x^2)^4-2*x^3*exp(x^2)^2+143*x^4-288*x^
3+144*x^2)/(9*exp(x^2)^4+18*x*exp(x^2)^2+9*x^2))/(9*x*exp(x^2)^6+27*x^2*exp(x^2)^4+27*x^3*exp(x^2)^2+9*x^4),x,
algorithm="maxima")

[Out]

2/9*integrate((143*x^5 - 144*x^4 - 3*x^3*e^(4*x^2) - 144*x^3 - x^2*e^(6*x^2) - 144*(4*x^2*e^(2*x^2) + x)*log(x
)^2 + 144*x^2 - 3*(192*x^6 - 384*x^5 + 97*x^4 + 144*x^3 - 48*x)*e^(2*x^2) - 144*(x^2 - (8*x^4 - 8*x^3 - 2*x^2
+ x + 1)*e^(2*x^2) - x)*log(x))*e^(1/9*(143*x^4 - 2*x^3*e^(2*x^2) - 288*x^3 - x^2*e^(4*x^2) + 144*x^2 - 288*(x
^2 - x)*log(x) + 144*log(x)^2)/(x^2 + 2*x*e^(2*x^2) + e^(4*x^2)))/(x^4 + 3*x^3*e^(2*x^2) + 3*x^2*e^(4*x^2) + x
*e^(6*x^2)), x)

Giac [F(-2)]

Exception generated. \[ \int \frac {e^{\frac {144 x^2-e^{4 x^2} x^2-288 x^3-2 e^{2 x^2} x^3+143 x^4+\left (288 x-288 x^2\right ) \log (x)+144 \log ^2(x)}{9 e^{4 x^2}+18 e^{2 x^2} x+9 x^2}} \left (288 x^2-2 e^{6 x^2} x^2-288 x^3-6 e^{4 x^2} x^3-288 x^4+286 x^5+e^{2 x^2} \left (288 x-864 x^3-582 x^4+2304 x^5-1152 x^6\right )+\left (288 x-288 x^2+e^{2 x^2} \left (288+288 x-576 x^2-2304 x^3+2304 x^4\right )\right ) \log (x)+\left (-288 x-1152 e^{2 x^2} x^2\right ) \log ^2(x)\right )}{9 e^{6 x^2} x+27 e^{4 x^2} x^2+27 e^{2 x^2} x^3+9 x^4} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate(((-1152*x^2*exp(x^2)^2-288*x)*log(x)^2+((2304*x^4-2304*x^3-576*x^2+288*x+288)*exp(x^2)^2-288*x^2+288
*x)*log(x)-2*x^2*exp(x^2)^6-6*x^3*exp(x^2)^4+(-1152*x^6+2304*x^5-582*x^4-864*x^3+288*x)*exp(x^2)^2+286*x^5-288
*x^4-288*x^3+288*x^2)*exp((144*log(x)^2+(-288*x^2+288*x)*log(x)-x^2*exp(x^2)^4-2*x^3*exp(x^2)^2+143*x^4-288*x^
3+144*x^2)/(9*exp(x^2)^4+18*x*exp(x^2)^2+9*x^2))/(9*x*exp(x^2)^6+27*x^2*exp(x^2)^4+27*x^3*exp(x^2)^2+9*x^4),x,
algorithm="giac")

[Out]

Exception raised: TypeError >> an error occurred running a Giac command:INPUT:sage2:=int(sage0,sageVARx):;OUTP
UT:Unable to divide, perhaps due to rounding error%%%{-339738624,[2,9,18]%%%}+%%%{339738624,[2,9,16]%%%}+%%%{-
127401984,[

Mupad [B] (verification not implemented)

Time = 12.19 (sec) , antiderivative size = 232, normalized size of antiderivative = 6.44 \[ \int \frac {e^{\frac {144 x^2-e^{4 x^2} x^2-288 x^3-2 e^{2 x^2} x^3+143 x^4+\left (288 x-288 x^2\right ) \log (x)+144 \log ^2(x)}{9 e^{4 x^2}+18 e^{2 x^2} x+9 x^2}} \left (288 x^2-2 e^{6 x^2} x^2-288 x^3-6 e^{4 x^2} x^3-288 x^4+286 x^5+e^{2 x^2} \left (288 x-864 x^3-582 x^4+2304 x^5-1152 x^6\right )+\left (288 x-288 x^2+e^{2 x^2} \left (288+288 x-576 x^2-2304 x^3+2304 x^4\right )\right ) \log (x)+\left (-288 x-1152 e^{2 x^2} x^2\right ) \log ^2(x)\right )}{9 e^{6 x^2} x+27 e^{4 x^2} x^2+27 e^{2 x^2} x^3+9 x^4} \, dx=x^{\frac {32\,\left (x-x^2\right )}{{\mathrm {e}}^{4\,x^2}+2\,x\,{\mathrm {e}}^{2\,x^2}+x^2}}\,{\mathrm {e}}^{\frac {144\,x^2}{9\,{\mathrm {e}}^{4\,x^2}+18\,x\,{\mathrm {e}}^{2\,x^2}+9\,x^2}}\,{\mathrm {e}}^{\frac {143\,x^4}{9\,{\mathrm {e}}^{4\,x^2}+18\,x\,{\mathrm {e}}^{2\,x^2}+9\,x^2}}\,{\mathrm {e}}^{-\frac {288\,x^3}{9\,{\mathrm {e}}^{4\,x^2}+18\,x\,{\mathrm {e}}^{2\,x^2}+9\,x^2}}\,{\mathrm {e}}^{\frac {144\,{\ln \left (x\right )}^2}{9\,{\mathrm {e}}^{4\,x^2}+18\,x\,{\mathrm {e}}^{2\,x^2}+9\,x^2}}\,{\mathrm {e}}^{-\frac {x^2\,{\mathrm {e}}^{4\,x^2}}{9\,{\mathrm {e}}^{4\,x^2}+18\,x\,{\mathrm {e}}^{2\,x^2}+9\,x^2}}\,{\mathrm {e}}^{-\frac {2\,x^3\,{\mathrm {e}}^{2\,x^2}}{9\,{\mathrm {e}}^{4\,x^2}+18\,x\,{\mathrm {e}}^{2\,x^2}+9\,x^2}} \]

[In]

int(-(exp((144*log(x)^2 + log(x)*(288*x - 288*x^2) - 2*x^3*exp(2*x^2) - x^2*exp(4*x^2) + 144*x^2 - 288*x^3 + 1
43*x^4)/(9*exp(4*x^2) + 18*x*exp(2*x^2) + 9*x^2))*(exp(2*x^2)*(864*x^3 - 288*x + 582*x^4 - 2304*x^5 + 1152*x^6
) - log(x)*(288*x + exp(2*x^2)*(288*x - 576*x^2 - 2304*x^3 + 2304*x^4 + 288) - 288*x^2) + log(x)^2*(288*x + 11
52*x^2*exp(2*x^2)) + 6*x^3*exp(4*x^2) + 2*x^2*exp(6*x^2) - 288*x^2 + 288*x^3 + 288*x^4 - 286*x^5))/(9*x*exp(6*
x^2) + 27*x^3*exp(2*x^2) + 27*x^2*exp(4*x^2) + 9*x^4),x)

[Out]

x^((32*(x - x^2))/(exp(4*x^2) + 2*x*exp(2*x^2) + x^2))*exp((144*x^2)/(9*exp(4*x^2) + 18*x*exp(2*x^2) + 9*x^2))
*exp((143*x^4)/(9*exp(4*x^2) + 18*x*exp(2*x^2) + 9*x^2))*exp(-(288*x^3)/(9*exp(4*x^2) + 18*x*exp(2*x^2) + 9*x^
2))*exp((144*log(x)^2)/(9*exp(4*x^2) + 18*x*exp(2*x^2) + 9*x^2))*exp(-(x^2*exp(4*x^2))/(9*exp(4*x^2) + 18*x*ex
p(2*x^2) + 9*x^2))*exp(-(2*x^3*exp(2*x^2))/(9*exp(4*x^2) + 18*x*exp(2*x^2) + 9*x^2))