\(\int \frac {-16-32 x-16 x^2+e^{2 x+e^{2 x} (3 e^{\frac {2 x}{2+2 x}} x+6 e^{\frac {x}{2+2 x}} x^2+3 x^3)} (-108 x^2-288 x^3-252 x^4-72 x^5+e^{\frac {2 x}{2+2 x}} (-36-180 x-180 x^2-72 x^3)+e^{\frac {x}{2+2 x}} (-144 x-468 x^2-432 x^3-144 x^4))}{16 x^2+32 x^3+16 x^4+e^{2 e^{2 x} (3 e^{\frac {2 x}{2+2 x}} x+6 e^{\frac {x}{2+2 x}} x^2+3 x^3)} (9+18 x+9 x^2)+e^{e^{2 x} (3 e^{\frac {2 x}{2+2 x}} x+6 e^{\frac {x}{2+2 x}} x^2+3 x^3)} (24 x+48 x^2+24 x^3)} \, dx\) [1702]
Optimal result
Integrand size = 276, antiderivative size = 35 \[
\int \frac {-16-32 x-16 x^2+e^{2 x+e^{2 x} \left (3 e^{\frac {2 x}{2+2 x}} x+6 e^{\frac {x}{2+2 x}} x^2+3 x^3\right )} \left (-108 x^2-288 x^3-252 x^4-72 x^5+e^{\frac {2 x}{2+2 x}} \left (-36-180 x-180 x^2-72 x^3\right )+e^{\frac {x}{2+2 x}} \left (-144 x-468 x^2-432 x^3-144 x^4\right )\right )}{16 x^2+32 x^3+16 x^4+e^{2 e^{2 x} \left (3 e^{\frac {2 x}{2+2 x}} x+6 e^{\frac {x}{2+2 x}} x^2+3 x^3\right )} \left (9+18 x+9 x^2\right )+e^{e^{2 x} \left (3 e^{\frac {2 x}{2+2 x}} x+6 e^{\frac {x}{2+2 x}} x^2+3 x^3\right )} \left (24 x+48 x^2+24 x^3\right )} \, dx=\frac {4}{x+3 \left (e^{3 e^{2 x} x \left (e^{\frac {x}{2+2 x}}+x\right )^2}+x\right )}
\]
[Out]
4/(4*x+3*exp(3*exp(x)^2*(x+exp(x/(2+2*x)))^2*x))
Rubi [F(-1)]
Timed out. \[
\int \frac {-16-32 x-16 x^2+e^{2 x+e^{2 x} \left (3 e^{\frac {2 x}{2+2 x}} x+6 e^{\frac {x}{2+2 x}} x^2+3 x^3\right )} \left (-108 x^2-288 x^3-252 x^4-72 x^5+e^{\frac {2 x}{2+2 x}} \left (-36-180 x-180 x^2-72 x^3\right )+e^{\frac {x}{2+2 x}} \left (-144 x-468 x^2-432 x^3-144 x^4\right )\right )}{16 x^2+32 x^3+16 x^4+e^{2 e^{2 x} \left (3 e^{\frac {2 x}{2+2 x}} x+6 e^{\frac {x}{2+2 x}} x^2+3 x^3\right )} \left (9+18 x+9 x^2\right )+e^{e^{2 x} \left (3 e^{\frac {2 x}{2+2 x}} x+6 e^{\frac {x}{2+2 x}} x^2+3 x^3\right )} \left (24 x+48 x^2+24 x^3\right )} \, dx=\text {\$Aborted}
\]
[In]
Int[(-16 - 32*x - 16*x^2 + E^(2*x + E^(2*x)*(3*E^((2*x)/(2 + 2*x))*x + 6*E^(x/(2 + 2*x))*x^2 + 3*x^3))*(-108*x
^2 - 288*x^3 - 252*x^4 - 72*x^5 + E^((2*x)/(2 + 2*x))*(-36 - 180*x - 180*x^2 - 72*x^3) + E^(x/(2 + 2*x))*(-144
*x - 468*x^2 - 432*x^3 - 144*x^4)))/(16*x^2 + 32*x^3 + 16*x^4 + E^(2*E^(2*x)*(3*E^((2*x)/(2 + 2*x))*x + 6*E^(x
/(2 + 2*x))*x^2 + 3*x^3))*(9 + 18*x + 9*x^2) + E^(E^(2*x)*(3*E^((2*x)/(2 + 2*x))*x + 6*E^(x/(2 + 2*x))*x^2 + 3
*x^3))*(24*x + 48*x^2 + 24*x^3)),x]
[Out]
$Aborted
Rubi steps Aborted
Mathematica [A] (verified)
Time = 0.76 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.00
\[
\int \frac {-16-32 x-16 x^2+e^{2 x+e^{2 x} \left (3 e^{\frac {2 x}{2+2 x}} x+6 e^{\frac {x}{2+2 x}} x^2+3 x^3\right )} \left (-108 x^2-288 x^3-252 x^4-72 x^5+e^{\frac {2 x}{2+2 x}} \left (-36-180 x-180 x^2-72 x^3\right )+e^{\frac {x}{2+2 x}} \left (-144 x-468 x^2-432 x^3-144 x^4\right )\right )}{16 x^2+32 x^3+16 x^4+e^{2 e^{2 x} \left (3 e^{\frac {2 x}{2+2 x}} x+6 e^{\frac {x}{2+2 x}} x^2+3 x^3\right )} \left (9+18 x+9 x^2\right )+e^{e^{2 x} \left (3 e^{\frac {2 x}{2+2 x}} x+6 e^{\frac {x}{2+2 x}} x^2+3 x^3\right )} \left (24 x+48 x^2+24 x^3\right )} \, dx=\frac {4}{3 e^{3 e^{2 x} x \left (e^{\frac {x}{2+2 x}}+x\right )^2}+4 x}
\]
[In]
Integrate[(-16 - 32*x - 16*x^2 + E^(2*x + E^(2*x)*(3*E^((2*x)/(2 + 2*x))*x + 6*E^(x/(2 + 2*x))*x^2 + 3*x^3))*(
-108*x^2 - 288*x^3 - 252*x^4 - 72*x^5 + E^((2*x)/(2 + 2*x))*(-36 - 180*x - 180*x^2 - 72*x^3) + E^(x/(2 + 2*x))
*(-144*x - 468*x^2 - 432*x^3 - 144*x^4)))/(16*x^2 + 32*x^3 + 16*x^4 + E^(2*E^(2*x)*(3*E^((2*x)/(2 + 2*x))*x +
6*E^(x/(2 + 2*x))*x^2 + 3*x^3))*(9 + 18*x + 9*x^2) + E^(E^(2*x)*(3*E^((2*x)/(2 + 2*x))*x + 6*E^(x/(2 + 2*x))*x
^2 + 3*x^3))*(24*x + 48*x^2 + 24*x^3)),x]
[Out]
4/(3*E^(3*E^(2*x)*x*(E^(x/(2 + 2*x)) + x)^2) + 4*x)
Maple [A] (verified)
Time = 21.91 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.23
| | |
| method | result | size |
| | |
| risch |
\(\frac {4}{4 x +3 \,{\mathrm e}^{3 x \left (2 x \,{\mathrm e}^{\frac {x}{2+2 x}}+x^{2}+{\mathrm e}^{\frac {x}{1+x}}\right ) {\mathrm e}^{2 x}}}\) |
\(43\) |
| parallelrisch |
\(\frac {4}{4 x +3 \,{\mathrm e}^{\left (3 x \,{\mathrm e}^{\frac {x}{1+x}}+6 x^{2} {\mathrm e}^{\frac {x}{2+2 x}}+3 x^{3}\right ) {\mathrm e}^{2 x}}}\) |
\(51\) |
| | |
|
|
|
|
[In]
int((((-72*x^3-180*x^2-180*x-36)*exp(x/(2+2*x))^2+(-144*x^4-432*x^3-468*x^2-144*x)*exp(x/(2+2*x))-72*x^5-252*x
^4-288*x^3-108*x^2)*exp(x)^2*exp((3*x*exp(x/(2+2*x))^2+6*x^2*exp(x/(2+2*x))+3*x^3)*exp(x)^2)-16*x^2-32*x-16)/(
(9*x^2+18*x+9)*exp((3*x*exp(x/(2+2*x))^2+6*x^2*exp(x/(2+2*x))+3*x^3)*exp(x)^2)^2+(24*x^3+48*x^2+24*x)*exp((3*x
*exp(x/(2+2*x))^2+6*x^2*exp(x/(2+2*x))+3*x^3)*exp(x)^2)+16*x^4+32*x^3+16*x^2),x,method=_RETURNVERBOSE)
[Out]
4/(4*x+3*exp(3*x*(2*exp(1/2*x/(1+x))*x+x^2+exp(x/(1+x)))*exp(2*x)))
Fricas [A] (verification not implemented)
none
Time = 0.26 (sec) , antiderivative size = 57, normalized size of antiderivative = 1.63
\[
\int \frac {-16-32 x-16 x^2+e^{2 x+e^{2 x} \left (3 e^{\frac {2 x}{2+2 x}} x+6 e^{\frac {x}{2+2 x}} x^2+3 x^3\right )} \left (-108 x^2-288 x^3-252 x^4-72 x^5+e^{\frac {2 x}{2+2 x}} \left (-36-180 x-180 x^2-72 x^3\right )+e^{\frac {x}{2+2 x}} \left (-144 x-468 x^2-432 x^3-144 x^4\right )\right )}{16 x^2+32 x^3+16 x^4+e^{2 e^{2 x} \left (3 e^{\frac {2 x}{2+2 x}} x+6 e^{\frac {x}{2+2 x}} x^2+3 x^3\right )} \left (9+18 x+9 x^2\right )+e^{e^{2 x} \left (3 e^{\frac {2 x}{2+2 x}} x+6 e^{\frac {x}{2+2 x}} x^2+3 x^3\right )} \left (24 x+48 x^2+24 x^3\right )} \, dx=\frac {4 \, e^{\left (2 \, x\right )}}{4 \, x e^{\left (2 \, x\right )} + 3 \, e^{\left (3 \, {\left (x^{3} + 2 \, x^{2} e^{\left (\frac {x}{2 \, {\left (x + 1\right )}}\right )} + x e^{\left (\frac {x}{x + 1}\right )}\right )} e^{\left (2 \, x\right )} + 2 \, x\right )}}
\]
[In]
integrate((((-72*x^3-180*x^2-180*x-36)*exp(x/(2+2*x))^2+(-144*x^4-432*x^3-468*x^2-144*x)*exp(x/(2+2*x))-72*x^5
-252*x^4-288*x^3-108*x^2)*exp(x)^2*exp((3*x*exp(x/(2+2*x))^2+6*x^2*exp(x/(2+2*x))+3*x^3)*exp(x)^2)-16*x^2-32*x
-16)/((9*x^2+18*x+9)*exp((3*x*exp(x/(2+2*x))^2+6*x^2*exp(x/(2+2*x))+3*x^3)*exp(x)^2)^2+(24*x^3+48*x^2+24*x)*ex
p((3*x*exp(x/(2+2*x))^2+6*x^2*exp(x/(2+2*x))+3*x^3)*exp(x)^2)+16*x^4+32*x^3+16*x^2),x, algorithm="fricas")
[Out]
4*e^(2*x)/(4*x*e^(2*x) + 3*e^(3*(x^3 + 2*x^2*e^(1/2*x/(x + 1)) + x*e^(x/(x + 1)))*e^(2*x) + 2*x))
Sympy [A] (verification not implemented)
Time = 0.57 (sec) , antiderivative size = 44, normalized size of antiderivative = 1.26
\[
\int \frac {-16-32 x-16 x^2+e^{2 x+e^{2 x} \left (3 e^{\frac {2 x}{2+2 x}} x+6 e^{\frac {x}{2+2 x}} x^2+3 x^3\right )} \left (-108 x^2-288 x^3-252 x^4-72 x^5+e^{\frac {2 x}{2+2 x}} \left (-36-180 x-180 x^2-72 x^3\right )+e^{\frac {x}{2+2 x}} \left (-144 x-468 x^2-432 x^3-144 x^4\right )\right )}{16 x^2+32 x^3+16 x^4+e^{2 e^{2 x} \left (3 e^{\frac {2 x}{2+2 x}} x+6 e^{\frac {x}{2+2 x}} x^2+3 x^3\right )} \left (9+18 x+9 x^2\right )+e^{e^{2 x} \left (3 e^{\frac {2 x}{2+2 x}} x+6 e^{\frac {x}{2+2 x}} x^2+3 x^3\right )} \left (24 x+48 x^2+24 x^3\right )} \, dx=\frac {4}{4 x + 3 e^{\left (3 x^{3} + 6 x^{2} e^{\frac {x}{2 x + 2}} + 3 x e^{\frac {2 x}{2 x + 2}}\right ) e^{2 x}}}
\]
[In]
integrate((((-72*x**3-180*x**2-180*x-36)*exp(x/(2+2*x))**2+(-144*x**4-432*x**3-468*x**2-144*x)*exp(x/(2+2*x))-
72*x**5-252*x**4-288*x**3-108*x**2)*exp(x)**2*exp((3*x*exp(x/(2+2*x))**2+6*x**2*exp(x/(2+2*x))+3*x**3)*exp(x)*
*2)-16*x**2-32*x-16)/((9*x**2+18*x+9)*exp((3*x*exp(x/(2+2*x))**2+6*x**2*exp(x/(2+2*x))+3*x**3)*exp(x)**2)**2+(
24*x**3+48*x**2+24*x)*exp((3*x*exp(x/(2+2*x))**2+6*x**2*exp(x/(2+2*x))+3*x**3)*exp(x)**2)+16*x**4+32*x**3+16*x
**2),x)
[Out]
4/(4*x + 3*exp((3*x**3 + 6*x**2*exp(x/(2*x + 2)) + 3*x*exp(2*x/(2*x + 2)))*exp(2*x)))
Maxima [F]
\[
\int \frac {-16-32 x-16 x^2+e^{2 x+e^{2 x} \left (3 e^{\frac {2 x}{2+2 x}} x+6 e^{\frac {x}{2+2 x}} x^2+3 x^3\right )} \left (-108 x^2-288 x^3-252 x^4-72 x^5+e^{\frac {2 x}{2+2 x}} \left (-36-180 x-180 x^2-72 x^3\right )+e^{\frac {x}{2+2 x}} \left (-144 x-468 x^2-432 x^3-144 x^4\right )\right )}{16 x^2+32 x^3+16 x^4+e^{2 e^{2 x} \left (3 e^{\frac {2 x}{2+2 x}} x+6 e^{\frac {x}{2+2 x}} x^2+3 x^3\right )} \left (9+18 x+9 x^2\right )+e^{e^{2 x} \left (3 e^{\frac {2 x}{2+2 x}} x+6 e^{\frac {x}{2+2 x}} x^2+3 x^3\right )} \left (24 x+48 x^2+24 x^3\right )} \, dx=\int { -\frac {4 \, {\left (4 \, x^{2} + 9 \, {\left (2 \, x^{5} + 7 \, x^{4} + 8 \, x^{3} + 3 \, x^{2} + {\left (2 \, x^{3} + 5 \, x^{2} + 5 \, x + 1\right )} e^{\left (\frac {x}{x + 1}\right )} + {\left (4 \, x^{4} + 12 \, x^{3} + 13 \, x^{2} + 4 \, x\right )} e^{\left (\frac {x}{2 \, {\left (x + 1\right )}}\right )}\right )} e^{\left (3 \, {\left (x^{3} + 2 \, x^{2} e^{\left (\frac {x}{2 \, {\left (x + 1\right )}}\right )} + x e^{\left (\frac {x}{x + 1}\right )}\right )} e^{\left (2 \, x\right )} + 2 \, x\right )} + 8 \, x + 4\right )}}{16 \, x^{4} + 32 \, x^{3} + 16 \, x^{2} + 9 \, {\left (x^{2} + 2 \, x + 1\right )} e^{\left (6 \, {\left (x^{3} + 2 \, x^{2} e^{\left (\frac {x}{2 \, {\left (x + 1\right )}}\right )} + x e^{\left (\frac {x}{x + 1}\right )}\right )} e^{\left (2 \, x\right )}\right )} + 24 \, {\left (x^{3} + 2 \, x^{2} + x\right )} e^{\left (3 \, {\left (x^{3} + 2 \, x^{2} e^{\left (\frac {x}{2 \, {\left (x + 1\right )}}\right )} + x e^{\left (\frac {x}{x + 1}\right )}\right )} e^{\left (2 \, x\right )}\right )}} \,d x }
\]
[In]
integrate((((-72*x^3-180*x^2-180*x-36)*exp(x/(2+2*x))^2+(-144*x^4-432*x^3-468*x^2-144*x)*exp(x/(2+2*x))-72*x^5
-252*x^4-288*x^3-108*x^2)*exp(x)^2*exp((3*x*exp(x/(2+2*x))^2+6*x^2*exp(x/(2+2*x))+3*x^3)*exp(x)^2)-16*x^2-32*x
-16)/((9*x^2+18*x+9)*exp((3*x*exp(x/(2+2*x))^2+6*x^2*exp(x/(2+2*x))+3*x^3)*exp(x)^2)^2+(24*x^3+48*x^2+24*x)*ex
p((3*x*exp(x/(2+2*x))^2+6*x^2*exp(x/(2+2*x))+3*x^3)*exp(x)^2)+16*x^4+32*x^3+16*x^2),x, algorithm="maxima")
[Out]
4*(3*(4*x^5*e^(1/2) + 12*x^4*e^(1/2) + 13*x^3*e^(1/2) + 4*x^2*e^(1/2))*e^(2*x + 3/2/(x + 1)) + 3*(2*x^4*e + 5*
x^3*e + 5*x^2*e + x*e)*e^(2*x + 1/(x + 1)) - (x^2 - 3*(2*x^6 + 7*x^5 + 8*x^4 + 3*x^3)*e^(2*x) + 2*x + 1)*e^(2/
(x + 1)))/(3*(3*(4*x^5*e^(1/2) + 12*x^4*e^(1/2) + 13*x^3*e^(1/2) + 4*x^2*e^(1/2))*e^(2*x + 3/2/(x + 1)) + (3*(
2*x^4*e + 5*x^3*e + 5*x^2*e + x*e)*e^(2*x) - (x^2 - 3*(2*x^6 + 7*x^5 + 8*x^4 + 3*x^3)*e^(2*x) + 2*x + 1)*e^(1/
(x + 1)))*e^(1/(x + 1)))*e^(3*x^3*e^(2*x) + 6*x^2*e^(2*x - 1/2/(x + 1) + 1/2) + 3*x*e^(2*x - 1/(x + 1) + 1)) +
12*(4*x^6*e^(1/2) + 12*x^5*e^(1/2) + 13*x^4*e^(1/2) + 4*x^3*e^(1/2))*e^(2*x + 3/2/(x + 1)) + 4*(3*(2*x^5*e +
5*x^4*e + 5*x^3*e + x^2*e)*e^(2*x) - (x^3 + 2*x^2 - 3*(2*x^7 + 7*x^6 + 8*x^5 + 3*x^4)*e^(2*x) + x)*e^(1/(x + 1
)))*e^(1/(x + 1))) - 4*integrate(3*((3*(4*x^9*e^2 + 28*x^8*e^2 + 89*x^7*e^2 + 164*x^6*e^2 + 188*x^5*e^2 + 134*
x^4*e^2 + 56*x^3*e^2 + 12*x^2*e^2 + x*e^2)*e^(4*x) + (3*(12*x^11*e + 88*x^10*e + 295*x^9*e + 581*x^8*e + 722*x
^7*e + 572*x^6*e + 280*x^5*e + 77*x^4*e + 9*x^3*e)*e^(4*x) + (4*x^8*e + 28*x^7*e + 88*x^6*e + 156*x^5*e + 167*
x^4*e + 108*x^3*e + 39*x^2*e + 6*x*e)*e^(2*x))*e^(1/(x + 1)))*e^(3/2/(x + 1)) - (3*(4*x^9*e^2 + 28*x^8*e^2 + 8
9*x^7*e^2 + 164*x^6*e^2 + 188*x^5*e^2 + 134*x^4*e^2 + 56*x^3*e^2 + 12*x^2*e^2 + x*e^2)*e^(4*x + 1/(x + 1)) + (
3*(12*x^11*e + 88*x^10*e + 295*x^9*e + 581*x^8*e + 722*x^7*e + 572*x^6*e + 280*x^5*e + 77*x^4*e + 9*x^3*e)*e^(
4*x) + (4*x^8*e + 28*x^7*e + 88*x^6*e + 156*x^5*e + 167*x^4*e + 108*x^3*e + 39*x^2*e + 6*x*e)*e^(2*x))*e^(2/(x
+ 1)))*e^(1/2/(x + 1)))/(3*(9*(16*x^12*e + 128*x^11*e + 456*x^10*e + 936*x^9*e + 1201*x^8*e + 978*x^7*e + 489
*x^6*e + 136*x^5*e + 16*x^4*e)*e^(4*x + 5/2/(x + 1)) + (9*(4*x^10*e^2 + 28*x^9*e^2 + 89*x^8*e^2 + 164*x^7*e^2
+ 188*x^6*e^2 + 134*x^5*e^2 + 56*x^4*e^2 + 12*x^3*e^2 + x^2*e^2)*e^(4*x) + (x^6 + 6*x^5 + 15*x^4 + 20*x^3 + 15
*x^2 + 9*(4*x^14 + 36*x^13 + 141*x^12 + 314*x^11 + 435*x^10 + 384*x^9 + 211*x^8 + 66*x^7 + 9*x^6)*e^(4*x) - 6*
(2*x^10 + 15*x^9 + 48*x^8 + 85*x^7 + 90*x^6 + 57*x^5 + 20*x^4 + 3*x^3)*e^(2*x) + 6*x + 1)*e^(2/(x + 1)) + 6*(3
*(4*x^12*e + 32*x^11*e + 113*x^10*e + 229*x^9*e + 289*x^8*e + 230*x^7*e + 111*x^6*e + 29*x^5*e + 3*x^4*e)*e^(4
*x) - (2*x^8*e + 13*x^7*e + 37*x^6*e + 59*x^5*e + 56*x^4*e + 31*x^3*e + 9*x^2*e + x*e)*e^(2*x))*e^(1/(x + 1)))
*e^(3/2/(x + 1)) + 6*(3*(8*x^11*e^(3/2) + 60*x^10*e^(3/2) + 202*x^9*e^(3/2) + 393*x^8*e^(3/2) + 477*x^7*e^(3/2
) + 364*x^6*e^(3/2) + 167*x^5*e^(3/2) + 41*x^4*e^(3/2) + 4*x^3*e^(3/2))*e^(4*x + 1/(x + 1)) + (3*(8*x^13*e^(1/
2) + 68*x^12*e^(1/2) + 254*x^11*e^(1/2) + 543*x^10*e^(1/2) + 724*x^9*e^(1/2) + 614*x^8*e^(1/2) + 322*x^7*e^(1/
2) + 95*x^6*e^(1/2) + 12*x^5*e^(1/2))*e^(4*x) - (4*x^9*e^(1/2) + 28*x^8*e^(1/2) + 85*x^7*e^(1/2) + 144*x^6*e^(
1/2) + 146*x^5*e^(1/2) + 88*x^4*e^(1/2) + 29*x^3*e^(1/2) + 4*x^2*e^(1/2))*e^(2*x))*e^(2/(x + 1)))*e^(1/(x + 1)
))*e^(3*x^3*e^(2*x) + 6*x^2*e^(2*x - 1/2/(x + 1) + 1/2) + 3*x*e^(2*x - 1/(x + 1) + 1)) + 36*(16*x^13*e + 128*x
^12*e + 456*x^11*e + 936*x^10*e + 1201*x^9*e + 978*x^8*e + 489*x^7*e + 136*x^6*e + 16*x^5*e)*e^(4*x + 5/2/(x +
1)) + 4*(9*(4*x^11*e^2 + 28*x^10*e^2 + 89*x^9*e^2 + 164*x^8*e^2 + 188*x^7*e^2 + 134*x^6*e^2 + 56*x^5*e^2 + 12
*x^4*e^2 + x^3*e^2)*e^(4*x) + (x^7 + 6*x^6 + 15*x^5 + 20*x^4 + 15*x^3 + 6*x^2 + 9*(4*x^15 + 36*x^14 + 141*x^13
+ 314*x^12 + 435*x^11 + 384*x^10 + 211*x^9 + 66*x^8 + 9*x^7)*e^(4*x) - 6*(2*x^11 + 15*x^10 + 48*x^9 + 85*x^8
+ 90*x^7 + 57*x^6 + 20*x^5 + 3*x^4)*e^(2*x) + x)*e^(2/(x + 1)) + 6*(3*(4*x^13*e + 32*x^12*e + 113*x^11*e + 229
*x^10*e + 289*x^9*e + 230*x^8*e + 111*x^7*e + 29*x^6*e + 3*x^5*e)*e^(4*x) - (2*x^9*e + 13*x^8*e + 37*x^7*e + 5
9*x^6*e + 56*x^5*e + 31*x^4*e + 9*x^3*e + x^2*e)*e^(2*x))*e^(1/(x + 1)))*e^(3/2/(x + 1)) + 24*(3*(8*x^12*e^(3/
2) + 60*x^11*e^(3/2) + 202*x^10*e^(3/2) + 393*x^9*e^(3/2) + 477*x^8*e^(3/2) + 364*x^7*e^(3/2) + 167*x^6*e^(3/2
) + 41*x^5*e^(3/2) + 4*x^4*e^(3/2))*e^(4*x + 1/(x + 1)) + (3*(8*x^14*e^(1/2) + 68*x^13*e^(1/2) + 254*x^12*e^(1
/2) + 543*x^11*e^(1/2) + 724*x^10*e^(1/2) + 614*x^9*e^(1/2) + 322*x^8*e^(1/2) + 95*x^7*e^(1/2) + 12*x^6*e^(1/2
))*e^(4*x) - (4*x^10*e^(1/2) + 28*x^9*e^(1/2) + 85*x^8*e^(1/2) + 144*x^7*e^(1/2) + 146*x^6*e^(1/2) + 88*x^5*e^
(1/2) + 29*x^4*e^(1/2) + 4*x^3*e^(1/2))*e^(2*x))*e^(2/(x + 1)))*e^(1/(x + 1))), x)
Giac [B] (verification not implemented)
Leaf count of result is larger than twice the leaf count of optimal. 27917 vs. \(2 (31) = 62\).
Time = 1.46 (sec) , antiderivative size = 27917, normalized size of antiderivative = 797.63
\[
\int \frac {-16-32 x-16 x^2+e^{2 x+e^{2 x} \left (3 e^{\frac {2 x}{2+2 x}} x+6 e^{\frac {x}{2+2 x}} x^2+3 x^3\right )} \left (-108 x^2-288 x^3-252 x^4-72 x^5+e^{\frac {2 x}{2+2 x}} \left (-36-180 x-180 x^2-72 x^3\right )+e^{\frac {x}{2+2 x}} \left (-144 x-468 x^2-432 x^3-144 x^4\right )\right )}{16 x^2+32 x^3+16 x^4+e^{2 e^{2 x} \left (3 e^{\frac {2 x}{2+2 x}} x+6 e^{\frac {x}{2+2 x}} x^2+3 x^3\right )} \left (9+18 x+9 x^2\right )+e^{e^{2 x} \left (3 e^{\frac {2 x}{2+2 x}} x+6 e^{\frac {x}{2+2 x}} x^2+3 x^3\right )} \left (24 x+48 x^2+24 x^3\right )} \, dx=\text {Too large to display}
\]
[In]
integrate((((-72*x^3-180*x^2-180*x-36)*exp(x/(2+2*x))^2+(-144*x^4-432*x^3-468*x^2-144*x)*exp(x/(2+2*x))-72*x^5
-252*x^4-288*x^3-108*x^2)*exp(x)^2*exp((3*x*exp(x/(2+2*x))^2+6*x^2*exp(x/(2+2*x))+3*x^3)*exp(x)^2)-16*x^2-32*x
-16)/((9*x^2+18*x+9)*exp((3*x*exp(x/(2+2*x))^2+6*x^2*exp(x/(2+2*x))+3*x^3)*exp(x)^2)^2+(24*x^3+48*x^2+24*x)*ex
p((3*x*exp(x/(2+2*x))^2+6*x^2*exp(x/(2+2*x))+3*x^3)*exp(x)^2)+16*x^4+32*x^3+16*x^2),x, algorithm="giac")
[Out]
4*(96*x^8*e^(3*x + 3/2*(2*x^2 + 3*x)/(x + 1)) + 72*x^7*e^(3*x + (3*x^4*e^(2*x) + 3*x^3*e^(2*x) + 6*x^3*e^(x +
1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 2*x^2
+ 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 3*x)/(x + 1) + 1/2*(2*x^2 + 3*x)/(x + 1)) + 336*x^7*e^(3*x + 3/2*(2*x^2 + 3
*x)/(x + 1)) + 72*x^7*e^(2*x + 1/2*(6*x^4*e^(2*x) + 6*x^3*e^(2*x) + 12*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) +
12*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 4*x^2 + 6*x*e^((2*x^2 + 3*x)/(x
+ 1)) + 5*x)/(x + 1) + (2*x^2 + 3*x)/(x + 1)) + 192*x^7*e^(2*x + 2*(2*x^2 + 3*x)/(x + 1)) + 144*x^6*e^(3*x^3*e
^(2*x) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 2*x + 2*(2*x^2 + 3*x)/(x +
1)) + 252*x^6*e^(3*x + (3*x^4*e^(2*x) + 3*x^3*e^(2*x) + 6*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^(x +
1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 2*x^2 + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 3*x)/(
x + 1) + 1/2*(2*x^2 + 3*x)/(x + 1)) + 384*x^6*e^(3*x + 3/2*(2*x^2 + 3*x)/(x + 1)) + 54*x^6*e^(2*x + 1/2*(6*x^4
*e^(2*x) + 6*x^3*e^(2*x) + 12*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 12*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1))
+ 6*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 4*x^2 + 6*x*e^((2*x^2 + 3*x)/(x + 1)) + 5*x)/(x + 1) + (3*x^4*e^(2*x) + 3
*x^3*e^(2*x) + 6*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x^2*e^((2
*x^2 + 3*x)/(x + 1)) + 2*x^2 + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 3*x)/(x + 1)) + 252*x^6*e^(2*x + 1/2*(6*x^4*e^(
2*x) + 6*x^3*e^(2*x) + 12*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 12*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6
*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 4*x^2 + 6*x*e^((2*x^2 + 3*x)/(x + 1)) + 5*x)/(x + 1) + (2*x^2 + 3*x)/(x + 1))
+ 144*x^6*e^(2*x + (3*x^4*e^(2*x) + 3*x^3*e^(2*x) + 6*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^(x + 1/
2*(2*x^2 + 3*x)/(x + 1)) + 3*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 2*x^2 + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 3*x)/(x +
1) + (2*x^2 + 3*x)/(x + 1)) + 576*x^6*e^(2*x + 2*(2*x^2 + 3*x)/(x + 1)) + 96*x^6*e^(x + 5/2*(2*x^2 + 3*x)/(x
+ 1)) + 108*x^5*e^(3*x^3*e^(2*x) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 2
*x + (3*x^4*e^(2*x) + 3*x^3*e^(2*x) + 6*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)
/(x + 1)) + 3*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 2*x^2 + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 3*x)/(x + 1) + (2*x^2 +
3*x)/(x + 1)) + 432*x^5*e^(3*x^3*e^(2*x) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x*e^((2*x^2 + 3*x)/(x +
1)) + 2*x + 2*(2*x^2 + 3*x)/(x + 1)) + 72*x^5*e^(3*x^3*e^(2*x) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*
x*e^((2*x^2 + 3*x)/(x + 1)) + x + 5/2*(2*x^2 + 3*x)/(x + 1)) + 288*x^5*e^(3*x + (3*x^4*e^(2*x) + 3*x^3*e^(2*x)
+ 6*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x^2*e^((2*x^2 + 3*x)/
(x + 1)) + 2*x^2 + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 3*x)/(x + 1) + 1/2*(2*x^2 + 3*x)/(x + 1)) + 144*x^5*e^(3*x
+ 3/2*(2*x^2 + 3*x)/(x + 1)) + 189*x^5*e^(2*x + 1/2*(6*x^4*e^(2*x) + 6*x^3*e^(2*x) + 12*x^3*e^(x + 1/2*(2*x^2
+ 3*x)/(x + 1)) + 12*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 4*x^2 + 6*x*e^(
(2*x^2 + 3*x)/(x + 1)) + 5*x)/(x + 1) + (3*x^4*e^(2*x) + 3*x^3*e^(2*x) + 6*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1
)) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 2*x^2 + 3*x*e^((2*x^2 + 3*x)/
(x + 1)) + 3*x)/(x + 1)) + 288*x^5*e^(2*x + 1/2*(6*x^4*e^(2*x) + 6*x^3*e^(2*x) + 12*x^3*e^(x + 1/2*(2*x^2 + 3*
x)/(x + 1)) + 12*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 4*x^2 + 6*x*e^((2*x
^2 + 3*x)/(x + 1)) + 5*x)/(x + 1) + (2*x^2 + 3*x)/(x + 1)) + 432*x^5*e^(2*x + (3*x^4*e^(2*x) + 3*x^3*e^(2*x) +
6*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x^2*e^((2*x^2 + 3*x)/(x
+ 1)) + 2*x^2 + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 3*x)/(x + 1) + (2*x^2 + 3*x)/(x + 1)) + 624*x^5*e^(2*x + 2*(2
*x^2 + 3*x)/(x + 1)) + 240*x^5*e^(x + 5/2*(2*x^2 + 3*x)/(x + 1)) + 72*x^5*e^(1/2*(6*x^4*e^(2*x) + 6*x^3*e^(2*x
) + 12*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 12*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^((2*x^2 + 3*
x)/(x + 1)) + 4*x^2 + 6*x*e^((2*x^2 + 3*x)/(x + 1)) + 5*x)/(x + 1) + 2*(2*x^2 + 3*x)/(x + 1)) + 324*x^4*e^(3*x
^3*e^(2*x) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 2*x + (3*x^4*e^(2*x) +
3*x^3*e^(2*x) + 6*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x^2*e^((
2*x^2 + 3*x)/(x + 1)) + 2*x^2 + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 3*x)/(x + 1) + (2*x^2 + 3*x)/(x + 1)) + 468*x^
4*e^(3*x^3*e^(2*x) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 2*x + 2*(2*x^2
+ 3*x)/(x + 1)) + 180*x^4*e^(3*x^3*e^(2*x) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x*e^((2*x^2 + 3*x)/(x
+ 1)) + x + 5/2*(2*x^2 + 3*x)/(x + 1)) + 54*x^4*e^(3*x^3*e^(2*x) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) +
3*x*e^((2*x^2 + 3*x)/(x + 1)) + 1/2*(6*x^4*e^(2*x) + 6*x^3*e^(2*x) + 12*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1))
+ 12*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 4*x^2 + 6*x*e^((2*x^2 + 3*x)/(x
+ 1)) + 5*x)/(x + 1) + 2*(2*x^2 + 3*x)/(x + 1)) + 108*x^4*e^(3*x + (3*x^4*e^(2*x) + 3*x^3*e^(2*x) + 6*x^3*e^(
x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 2
*x^2 + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 3*x)/(x + 1) + 1/2*(2*x^2 + 3*x)/(x + 1)) + 216*x^4*e^(2*x + 1/2*(6*x^4
*e^(2*x) + 6*x^3*e^(2*x) + 12*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 12*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1))
+ 6*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 4*x^2 + 6*x*e^((2*x^2 + 3*x)/(x + 1)) + 5*x)/(x + 1) + (3*x^4*e^(2*x) + 3
*x^3*e^(2*x) + 6*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x^2*e^((2
*x^2 + 3*x)/(x + 1)) + 2*x^2 + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 3*x)/(x + 1)) + 108*x^4*e^(2*x + 1/2*(6*x^4*e^(
2*x) + 6*x^3*e^(2*x) + 12*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 12*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6
*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 4*x^2 + 6*x*e^((2*x^2 + 3*x)/(x + 1)) + 5*x)/(x + 1) + (2*x^2 + 3*x)/(x + 1))
+ 468*x^4*e^(2*x + (3*x^4*e^(2*x) + 3*x^3*e^(2*x) + 6*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^(x + 1/
2*(2*x^2 + 3*x)/(x + 1)) + 3*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 2*x^2 + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 3*x)/(x +
1) + (2*x^2 + 3*x)/(x + 1)) + 192*x^4*e^(2*x + 2*(2*x^2 + 3*x)/(x + 1)) + 240*x^4*e^(x + 5/2*(2*x^2 + 3*x)/(x
+ 1)) - 16*x^4*e^(x + 3/2*(2*x^2 + 3*x)/(x + 1)) + 180*x^4*e^(1/2*(6*x^4*e^(2*x) + 6*x^3*e^(2*x) + 12*x^3*e^(
x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 12*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^((2*x^2 + 3*x)/(x + 1)) +
4*x^2 + 6*x*e^((2*x^2 + 3*x)/(x + 1)) + 5*x)/(x + 1) + 2*(2*x^2 + 3*x)/(x + 1)) + 351*x^3*e^(3*x^3*e^(2*x) + 6
*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 2*x + (3*x^4*e^(2*x) + 3*x^3*e^(2*x)
+ 6*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x^2*e^((2*x^2 + 3*x)/(
x + 1)) + 2*x^2 + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 3*x)/(x + 1) + (2*x^2 + 3*x)/(x + 1)) + 144*x^3*e^(3*x^3*e^(
2*x) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 2*x + 2*(2*x^2 + 3*x)/(x + 1)
) + 180*x^3*e^(3*x^3*e^(2*x) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + x + 5
/2*(2*x^2 + 3*x)/(x + 1)) + 135*x^3*e^(3*x^3*e^(2*x) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x*e^((2*x^2
+ 3*x)/(x + 1)) + 1/2*(6*x^4*e^(2*x) + 6*x^3*e^(2*x) + 12*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 12*x^2*e^(x
+ 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 4*x^2 + 6*x*e^((2*x^2 + 3*x)/(x + 1)) + 5*x)
/(x + 1) + 2*(2*x^2 + 3*x)/(x + 1)) + 81*x^3*e^(2*x + 1/2*(6*x^4*e^(2*x) + 6*x^3*e^(2*x) + 12*x^3*e^(x + 1/2*(
2*x^2 + 3*x)/(x + 1)) + 12*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 4*x^2 + 6
*x*e^((2*x^2 + 3*x)/(x + 1)) + 5*x)/(x + 1) + (3*x^4*e^(2*x) + 3*x^3*e^(2*x) + 6*x^3*e^(x + 1/2*(2*x^2 + 3*x)/
(x + 1)) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 2*x^2 + 3*x*e^((2*x^2 +
3*x)/(x + 1)) + 3*x)/(x + 1)) + 144*x^3*e^(2*x + (3*x^4*e^(2*x) + 3*x^3*e^(2*x) + 6*x^3*e^(x + 1/2*(2*x^2 + 3
*x)/(x + 1)) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 2*x^2 + 3*x*e^((2*x
^2 + 3*x)/(x + 1)) + 3*x)/(x + 1) + (2*x^2 + 3*x)/(x + 1)) - 12*x^3*e^(x + (3*x^4*e^(2*x) + 3*x^3*e^(2*x) + 6*
x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x^2*e^((2*x^2 + 3*x)/(x +
1)) + 2*x^2 + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 3*x)/(x + 1) + 1/2*(2*x^2 + 3*x)/(x + 1)) + 48*x^3*e^(x + 5/2*(2
*x^2 + 3*x)/(x + 1)) - 32*x^3*e^(x + 3/2*(2*x^2 + 3*x)/(x + 1)) + 180*x^3*e^(1/2*(6*x^4*e^(2*x) + 6*x^3*e^(2*x
) + 12*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 12*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^((2*x^2 + 3*
x)/(x + 1)) + 4*x^2 + 6*x*e^((2*x^2 + 3*x)/(x + 1)) + 5*x)/(x + 1) + 2*(2*x^2 + 3*x)/(x + 1)) - 12*x^3*e^(1/2*
(6*x^4*e^(2*x) + 6*x^3*e^(2*x) + 12*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 12*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x
+ 1)) + 6*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 4*x^2 + 6*x*e^((2*x^2 + 3*x)/(x + 1)) + 5*x)/(x + 1) + (2*x^2 + 3*x
)/(x + 1)) + 108*x^2*e^(3*x^3*e^(2*x) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x*e^((2*x^2 + 3*x)/(x + 1)
) + 2*x + (3*x^4*e^(2*x) + 3*x^3*e^(2*x) + 6*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^(x + 1/2*(2*x^2 +
3*x)/(x + 1)) + 3*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 2*x^2 + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 3*x)/(x + 1) + (2*x
^2 + 3*x)/(x + 1)) + 36*x^2*e^(3*x^3*e^(2*x) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x*e^((2*x^2 + 3*x)/
(x + 1)) + x + 5/2*(2*x^2 + 3*x)/(x + 1)) + 135*x^2*e^(3*x^3*e^(2*x) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1))
+ 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 1/2*(6*x^4*e^(2*x) + 6*x^3*e^(2*x) + 12*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1
)) + 12*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 4*x^2 + 6*x*e^((2*x^2 + 3*x)
/(x + 1)) + 5*x)/(x + 1) + 2*(2*x^2 + 3*x)/(x + 1)) - 24*x^2*e^(x + (3*x^4*e^(2*x) + 3*x^3*e^(2*x) + 6*x^3*e^(
x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 2
*x^2 + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 3*x)/(x + 1) + 1/2*(2*x^2 + 3*x)/(x + 1)) - 16*x^2*e^(x + 3/2*(2*x^2 +
3*x)/(x + 1)) - 9*x^2*e^(1/2*(6*x^4*e^(2*x) + 6*x^3*e^(2*x) + 12*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 12*x^
2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 4*x^2 + 6*x*e^((2*x^2 + 3*x)/(x + 1))
+ 5*x)/(x + 1) + (3*x^4*e^(2*x) + 3*x^3*e^(2*x) + 6*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^(x + 1/2*(
2*x^2 + 3*x)/(x + 1)) + 3*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 2*x^2 + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 3*x)/(x + 1)
) + 36*x^2*e^(1/2*(6*x^4*e^(2*x) + 6*x^3*e^(2*x) + 12*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 12*x^2*e^(x + 1/
2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 4*x^2 + 6*x*e^((2*x^2 + 3*x)/(x + 1)) + 5*x)/(x +
1) + 2*(2*x^2 + 3*x)/(x + 1)) - 24*x^2*e^(1/2*(6*x^4*e^(2*x) + 6*x^3*e^(2*x) + 12*x^3*e^(x + 1/2*(2*x^2 + 3*x
)/(x + 1)) + 12*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 4*x^2 + 6*x*e^((2*x^
2 + 3*x)/(x + 1)) + 5*x)/(x + 1) + (2*x^2 + 3*x)/(x + 1)) + 27*x*e^(3*x^3*e^(2*x) + 6*x^2*e^(x + 1/2*(2*x^2 +
3*x)/(x + 1)) + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 1/2*(6*x^4*e^(2*x) + 6*x^3*e^(2*x) + 12*x^3*e^(x + 1/2*(2*x^2
+ 3*x)/(x + 1)) + 12*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 4*x^2 + 6*x*e^(
(2*x^2 + 3*x)/(x + 1)) + 5*x)/(x + 1) + 2*(2*x^2 + 3*x)/(x + 1)) - 12*x*e^(x + (3*x^4*e^(2*x) + 3*x^3*e^(2*x)
+ 6*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x^2*e^((2*x^2 + 3*x)/(
x + 1)) + 2*x^2 + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 3*x)/(x + 1) + 1/2*(2*x^2 + 3*x)/(x + 1)) - 18*x*e^(1/2*(6*x
^4*e^(2*x) + 6*x^3*e^(2*x) + 12*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 12*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1
)) + 6*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 4*x^2 + 6*x*e^((2*x^2 + 3*x)/(x + 1)) + 5*x)/(x + 1) + (3*x^4*e^(2*x) +
3*x^3*e^(2*x) + 6*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x^2*e^(
(2*x^2 + 3*x)/(x + 1)) + 2*x^2 + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 3*x)/(x + 1)) - 12*x*e^(1/2*(6*x^4*e^(2*x) +
6*x^3*e^(2*x) + 12*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 12*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^
((2*x^2 + 3*x)/(x + 1)) + 4*x^2 + 6*x*e^((2*x^2 + 3*x)/(x + 1)) + 5*x)/(x + 1) + (2*x^2 + 3*x)/(x + 1)) - 9*e^
(1/2*(6*x^4*e^(2*x) + 6*x^3*e^(2*x) + 12*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 12*x^2*e^(x + 1/2*(2*x^2 + 3*
x)/(x + 1)) + 6*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 4*x^2 + 6*x*e^((2*x^2 + 3*x)/(x + 1)) + 5*x)/(x + 1) + (3*x^4*
e^(2*x) + 3*x^3*e^(2*x) + 6*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) +
3*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 2*x^2 + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 3*x)/(x + 1)))/(384*x^9*e^(3*x + 3/2
*(2*x^2 + 3*x)/(x + 1)) + 288*x^8*e^(3*x^3*e^(2*x) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x*e^((2*x^2 +
3*x)/(x + 1)) + 3*x + 3/2*(2*x^2 + 3*x)/(x + 1)) + 288*x^8*e^(3*x + (3*x^4*e^(2*x) + 3*x^3*e^(2*x) + 6*x^3*e^
(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x^2*e^((2*x^2 + 3*x)/(x + 1)) +
2*x^2 + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 3*x)/(x + 1) + 1/2*(2*x^2 + 3*x)/(x + 1)) + 1344*x^8*e^(3*x + 3/2*(2*x
^2 + 3*x)/(x + 1)) + 288*x^8*e^(2*x + 1/2*(6*x^4*e^(2*x) + 6*x^3*e^(2*x) + 12*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x
+ 1)) + 12*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 4*x^2 + 6*x*e^((2*x^2 + 3
*x)/(x + 1)) + 5*x)/(x + 1) + (2*x^2 + 3*x)/(x + 1)) + 768*x^8*e^(2*x + 2*(2*x^2 + 3*x)/(x + 1)) + 216*x^7*e^(
3*x^3*e^(2*x) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 3*x + (3*x^4*e^(2*x)
+ 3*x^3*e^(2*x) + 6*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x^2*e
^((2*x^2 + 3*x)/(x + 1)) + 2*x^2 + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 3*x)/(x + 1) + 1/2*(2*x^2 + 3*x)/(x + 1)) +
1008*x^7*e^(3*x^3*e^(2*x) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 3*x + 3
/2*(2*x^2 + 3*x)/(x + 1)) + 216*x^7*e^(3*x^3*e^(2*x) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x*e^((2*x^2
+ 3*x)/(x + 1)) + 2*x + 1/2*(6*x^4*e^(2*x) + 6*x^3*e^(2*x) + 12*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 12*x^
2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 4*x^2 + 6*x*e^((2*x^2 + 3*x)/(x + 1))
+ 5*x)/(x + 1) + (2*x^2 + 3*x)/(x + 1)) + 576*x^7*e^(3*x^3*e^(2*x) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) +
3*x*e^((2*x^2 + 3*x)/(x + 1)) + 2*x + 2*(2*x^2 + 3*x)/(x + 1)) + 1008*x^7*e^(3*x + (3*x^4*e^(2*x) + 3*x^3*e^(
2*x) + 6*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x^2*e^((2*x^2 + 3
*x)/(x + 1)) + 2*x^2 + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 3*x)/(x + 1) + 1/2*(2*x^2 + 3*x)/(x + 1)) + 1536*x^7*e^
(3*x + 3/2*(2*x^2 + 3*x)/(x + 1)) + 216*x^7*e^(2*x + 1/2*(6*x^4*e^(2*x) + 6*x^3*e^(2*x) + 12*x^3*e^(x + 1/2*(2
*x^2 + 3*x)/(x + 1)) + 12*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 4*x^2 + 6*
x*e^((2*x^2 + 3*x)/(x + 1)) + 5*x)/(x + 1) + (3*x^4*e^(2*x) + 3*x^3*e^(2*x) + 6*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(
x + 1)) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 2*x^2 + 3*x*e^((2*x^2 +
3*x)/(x + 1)) + 3*x)/(x + 1)) + 1008*x^7*e^(2*x + 1/2*(6*x^4*e^(2*x) + 6*x^3*e^(2*x) + 12*x^3*e^(x + 1/2*(2*x^
2 + 3*x)/(x + 1)) + 12*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 4*x^2 + 6*x*e
^((2*x^2 + 3*x)/(x + 1)) + 5*x)/(x + 1) + (2*x^2 + 3*x)/(x + 1)) + 576*x^7*e^(2*x + (3*x^4*e^(2*x) + 3*x^3*e^(
2*x) + 6*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x^2*e^((2*x^2 + 3
*x)/(x + 1)) + 2*x^2 + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 3*x)/(x + 1) + (2*x^2 + 3*x)/(x + 1)) + 2304*x^7*e^(2*x
+ 2*(2*x^2 + 3*x)/(x + 1)) + 576*x^7*e^(x + 1/2*(6*x^4*e^(2*x) + 6*x^3*e^(2*x) + 12*x^3*e^(x + 1/2*(2*x^2 + 3
*x)/(x + 1)) + 12*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 4*x^2 + 6*x*e^((2*
x^2 + 3*x)/(x + 1)) + 5*x)/(x + 1) + 3/2*(2*x^2 + 3*x)/(x + 1)) + 384*x^7*e^(x + 5/2*(2*x^2 + 3*x)/(x + 1)) +
756*x^6*e^(3*x^3*e^(2*x) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 3*x + (3*
x^4*e^(2*x) + 3*x^3*e^(2*x) + 6*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)
) + 3*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 2*x^2 + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 3*x)/(x + 1) + 1/2*(2*x^2 + 3*x)
/(x + 1)) + 1152*x^6*e^(3*x^3*e^(2*x) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x*e^((2*x^2 + 3*x)/(x + 1)
) + 3*x + 3/2*(2*x^2 + 3*x)/(x + 1)) + 162*x^6*e^(3*x^3*e^(2*x) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*
x*e^((2*x^2 + 3*x)/(x + 1)) + 2*x + 1/2*(6*x^4*e^(2*x) + 6*x^3*e^(2*x) + 12*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x +
1)) + 12*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 4*x^2 + 6*x*e^((2*x^2 + 3*x
)/(x + 1)) + 5*x)/(x + 1) + (3*x^4*e^(2*x) + 3*x^3*e^(2*x) + 6*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e
^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 2*x^2 + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 3
*x)/(x + 1)) + 756*x^6*e^(3*x^3*e^(2*x) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x*e^((2*x^2 + 3*x)/(x +
1)) + 2*x + 1/2*(6*x^4*e^(2*x) + 6*x^3*e^(2*x) + 12*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 12*x^2*e^(x + 1/2*
(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 4*x^2 + 6*x*e^((2*x^2 + 3*x)/(x + 1)) + 5*x)/(x + 1
) + (2*x^2 + 3*x)/(x + 1)) + 432*x^6*e^(3*x^3*e^(2*x) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x*e^((2*x^
2 + 3*x)/(x + 1)) + 2*x + (3*x^4*e^(2*x) + 3*x^3*e^(2*x) + 6*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^(
x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 2*x^2 + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 3*x
)/(x + 1) + (2*x^2 + 3*x)/(x + 1)) + 1728*x^6*e^(3*x^3*e^(2*x) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x
*e^((2*x^2 + 3*x)/(x + 1)) + 2*x + 2*(2*x^2 + 3*x)/(x + 1)) + 432*x^6*e^(3*x^3*e^(2*x) + 6*x^2*e^(x + 1/2*(2*x
^2 + 3*x)/(x + 1)) + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + x + 1/2*(6*x^4*e^(2*x) + 6*x^3*e^(2*x) + 12*x^3*e^(x + 1/
2*(2*x^2 + 3*x)/(x + 1)) + 12*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 4*x^2
+ 6*x*e^((2*x^2 + 3*x)/(x + 1)) + 5*x)/(x + 1) + 3/2*(2*x^2 + 3*x)/(x + 1)) + 288*x^6*e^(3*x^3*e^(2*x) + 6*x^2
*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + x + 5/2*(2*x^2 + 3*x)/(x + 1)) + 1152*x^6
*e^(3*x + (3*x^4*e^(2*x) + 3*x^3*e^(2*x) + 6*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^(x + 1/2*(2*x^2 +
3*x)/(x + 1)) + 3*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 2*x^2 + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 3*x)/(x + 1) + 1/2*
(2*x^2 + 3*x)/(x + 1)) + 576*x^6*e^(3*x + 3/2*(2*x^2 + 3*x)/(x + 1)) + 756*x^6*e^(2*x + 1/2*(6*x^4*e^(2*x) + 6
*x^3*e^(2*x) + 12*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 12*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^(
(2*x^2 + 3*x)/(x + 1)) + 4*x^2 + 6*x*e^((2*x^2 + 3*x)/(x + 1)) + 5*x)/(x + 1) + (3*x^4*e^(2*x) + 3*x^3*e^(2*x)
+ 6*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x^2*e^((2*x^2 + 3*x)/
(x + 1)) + 2*x^2 + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 3*x)/(x + 1)) + 1152*x^6*e^(2*x + 1/2*(6*x^4*e^(2*x) + 6*x^
3*e^(2*x) + 12*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 12*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^((2*
x^2 + 3*x)/(x + 1)) + 4*x^2 + 6*x*e^((2*x^2 + 3*x)/(x + 1)) + 5*x)/(x + 1) + (2*x^2 + 3*x)/(x + 1)) + 1728*x^6
*e^(2*x + (3*x^4*e^(2*x) + 3*x^3*e^(2*x) + 6*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^(x + 1/2*(2*x^2 +
3*x)/(x + 1)) + 3*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 2*x^2 + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 3*x)/(x + 1) + (2*x
^2 + 3*x)/(x + 1)) + 2496*x^6*e^(2*x + 2*(2*x^2 + 3*x)/(x + 1)) + 432*x^6*e^(x + 1/2*(6*x^4*e^(2*x) + 6*x^3*e^
(2*x) + 12*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 12*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^((2*x^2
+ 3*x)/(x + 1)) + 4*x^2 + 6*x*e^((2*x^2 + 3*x)/(x + 1)) + 5*x)/(x + 1) + (3*x^4*e^(2*x) + 3*x^3*e^(2*x) + 6*x^
3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x^2*e^((2*x^2 + 3*x)/(x + 1)
) + 2*x^2 + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 3*x)/(x + 1) + 1/2*(2*x^2 + 3*x)/(x + 1)) + 1728*x^6*e^(x + 1/2*(6
*x^4*e^(2*x) + 6*x^3*e^(2*x) + 12*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 12*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x +
1)) + 6*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 4*x^2 + 6*x*e^((2*x^2 + 3*x)/(x + 1)) + 5*x)/(x + 1) + 3/2*(2*x^2 + 3
*x)/(x + 1)) + 288*x^6*e^(x + (3*x^4*e^(2*x) + 3*x^3*e^(2*x) + 6*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2
*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 2*x^2 + 3*x*e^((2*x^2 + 3*x)/(x + 1)) +
3*x)/(x + 1) + 3/2*(2*x^2 + 3*x)/(x + 1)) + 960*x^6*e^(x + 5/2*(2*x^2 + 3*x)/(x + 1)) + 288*x^6*e^(1/2*(6*x^4
*e^(2*x) + 6*x^3*e^(2*x) + 12*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 12*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1))
+ 6*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 4*x^2 + 6*x*e^((2*x^2 + 3*x)/(x + 1)) + 5*x)/(x + 1) + 2*(2*x^2 + 3*x)/(x
+ 1)) + 864*x^5*e^(3*x^3*e^(2*x) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x*e^((2*x^2 + 3*x)/(x + 1)) +
3*x + (3*x^4*e^(2*x) + 3*x^3*e^(2*x) + 6*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x
)/(x + 1)) + 3*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 2*x^2 + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 3*x)/(x + 1) + 1/2*(2*x
^2 + 3*x)/(x + 1)) + 432*x^5*e^(3*x^3*e^(2*x) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x*e^((2*x^2 + 3*x)
/(x + 1)) + 3*x + 3/2*(2*x^2 + 3*x)/(x + 1)) + 567*x^5*e^(3*x^3*e^(2*x) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x +
1)) + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 2*x + 1/2*(6*x^4*e^(2*x) + 6*x^3*e^(2*x) + 12*x^3*e^(x + 1/2*(2*x^2 + 3*
x)/(x + 1)) + 12*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 4*x^2 + 6*x*e^((2*x
^2 + 3*x)/(x + 1)) + 5*x)/(x + 1) + (3*x^4*e^(2*x) + 3*x^3*e^(2*x) + 6*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) +
6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 2*x^2 + 3*x*e^((2*x^2 + 3*x)/(x +
1)) + 3*x)/(x + 1)) + 864*x^5*e^(3*x^3*e^(2*x) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x*e^((2*x^2 + 3*
x)/(x + 1)) + 2*x + 1/2*(6*x^4*e^(2*x) + 6*x^3*e^(2*x) + 12*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 12*x^2*e^(
x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 4*x^2 + 6*x*e^((2*x^2 + 3*x)/(x + 1)) + 5*x
)/(x + 1) + (2*x^2 + 3*x)/(x + 1)) + 1296*x^5*e^(3*x^3*e^(2*x) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x
*e^((2*x^2 + 3*x)/(x + 1)) + 2*x + (3*x^4*e^(2*x) + 3*x^3*e^(2*x) + 6*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) +
6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 2*x^2 + 3*x*e^((2*x^2 + 3*x)/(x +
1)) + 3*x)/(x + 1) + (2*x^2 + 3*x)/(x + 1)) + 1872*x^5*e^(3*x^3*e^(2*x) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x +
1)) + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 2*x + 2*(2*x^2 + 3*x)/(x + 1)) + 324*x^5*e^(3*x^3*e^(2*x) + 6*x^2*e^(x +
1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + x + 1/2*(6*x^4*e^(2*x) + 6*x^3*e^(2*x) + 12*x^3*
e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 12*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^((2*x^2 + 3*x)/(x + 1))
+ 4*x^2 + 6*x*e^((2*x^2 + 3*x)/(x + 1)) + 5*x)/(x + 1) + (3*x^4*e^(2*x) + 3*x^3*e^(2*x) + 6*x^3*e^(x + 1/2*(2
*x^2 + 3*x)/(x + 1)) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 2*x^2 + 3*x
*e^((2*x^2 + 3*x)/(x + 1)) + 3*x)/(x + 1) + 1/2*(2*x^2 + 3*x)/(x + 1)) + 1296*x^5*e^(3*x^3*e^(2*x) + 6*x^2*e^(
x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + x + 1/2*(6*x^4*e^(2*x) + 6*x^3*e^(2*x) + 12*x
^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 12*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^((2*x^2 + 3*x)/(x +
1)) + 4*x^2 + 6*x*e^((2*x^2 + 3*x)/(x + 1)) + 5*x)/(x + 1) + 3/2*(2*x^2 + 3*x)/(x + 1)) + 216*x^5*e^(3*x^3*e^(
2*x) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + x + (3*x^4*e^(2*x) + 3*x^3*e^
(2*x) + 6*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x^2*e^((2*x^2 +
3*x)/(x + 1)) + 2*x^2 + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 3*x)/(x + 1) + 3/2*(2*x^2 + 3*x)/(x + 1)) + 720*x^5*e^
(3*x^3*e^(2*x) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + x + 5/2*(2*x^2 + 3*
x)/(x + 1)) + 216*x^5*e^(3*x^3*e^(2*x) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x*e^((2*x^2 + 3*x)/(x + 1
)) + 1/2*(6*x^4*e^(2*x) + 6*x^3*e^(2*x) + 12*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 12*x^2*e^(x + 1/2*(2*x^2
+ 3*x)/(x + 1)) + 6*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 4*x^2 + 6*x*e^((2*x^2 + 3*x)/(x + 1)) + 5*x)/(x + 1) + 2*(
2*x^2 + 3*x)/(x + 1)) + 432*x^5*e^(3*x + (3*x^4*e^(2*x) + 3*x^3*e^(2*x) + 6*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x +
1)) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 2*x^2 + 3*x*e^((2*x^2 + 3*x)
/(x + 1)) + 3*x)/(x + 1) + 1/2*(2*x^2 + 3*x)/(x + 1)) + 864*x^5*e^(2*x + 1/2*(6*x^4*e^(2*x) + 6*x^3*e^(2*x) +
12*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 12*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^((2*x^2 + 3*x)/(
x + 1)) + 4*x^2 + 6*x*e^((2*x^2 + 3*x)/(x + 1)) + 5*x)/(x + 1) + (3*x^4*e^(2*x) + 3*x^3*e^(2*x) + 6*x^3*e^(x +
1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 2*x^
2 + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 3*x)/(x + 1)) + 432*x^5*e^(2*x + 1/2*(6*x^4*e^(2*x) + 6*x^3*e^(2*x) + 12*x
^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 12*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^((2*x^2 + 3*x)/(x +
1)) + 4*x^2 + 6*x*e^((2*x^2 + 3*x)/(x + 1)) + 5*x)/(x + 1) + (2*x^2 + 3*x)/(x + 1)) + 1872*x^5*e^(2*x + (3*x^4
*e^(2*x) + 3*x^3*e^(2*x) + 6*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) +
3*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 2*x^2 + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 3*x)/(x + 1) + (2*x^2 + 3*x)/(x + 1
)) + 768*x^5*e^(2*x + 2*(2*x^2 + 3*x)/(x + 1)) + 1296*x^5*e^(x + 1/2*(6*x^4*e^(2*x) + 6*x^3*e^(2*x) + 12*x^3*e
^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 12*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^((2*x^2 + 3*x)/(x + 1))
+ 4*x^2 + 6*x*e^((2*x^2 + 3*x)/(x + 1)) + 5*x)/(x + 1) + (3*x^4*e^(2*x) + 3*x^3*e^(2*x) + 6*x^3*e^(x + 1/2*(2*
x^2 + 3*x)/(x + 1)) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 2*x^2 + 3*x*
e^((2*x^2 + 3*x)/(x + 1)) + 3*x)/(x + 1) + 1/2*(2*x^2 + 3*x)/(x + 1)) + 1872*x^5*e^(x + 1/2*(6*x^4*e^(2*x) + 6
*x^3*e^(2*x) + 12*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 12*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^(
(2*x^2 + 3*x)/(x + 1)) + 4*x^2 + 6*x*e^((2*x^2 + 3*x)/(x + 1)) + 5*x)/(x + 1) + 3/2*(2*x^2 + 3*x)/(x + 1)) + 7
20*x^5*e^(x + (3*x^4*e^(2*x) + 3*x^3*e^(2*x) + 6*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^(x + 1/2*(2*x
^2 + 3*x)/(x + 1)) + 3*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 2*x^2 + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 3*x)/(x + 1) +
3/2*(2*x^2 + 3*x)/(x + 1)) + 960*x^5*e^(x + 5/2*(2*x^2 + 3*x)/(x + 1)) - 64*x^5*e^(x + 3/2*(2*x^2 + 3*x)/(x +
1)) + 216*x^5*e^(1/2*(6*x^4*e^(2*x) + 6*x^3*e^(2*x) + 12*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 12*x^2*e^(x +
1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 4*x^2 + 6*x*e^((2*x^2 + 3*x)/(x + 1)) + 5*x)/(
x + 1) + (3*x^4*e^(2*x) + 3*x^3*e^(2*x) + 6*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^(x + 1/2*(2*x^2 +
3*x)/(x + 1)) + 3*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 2*x^2 + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 3*x)/(x + 1) + (2*x^
2 + 3*x)/(x + 1)) + 720*x^5*e^(1/2*(6*x^4*e^(2*x) + 6*x^3*e^(2*x) + 12*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) +
12*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 4*x^2 + 6*x*e^((2*x^2 + 3*x)/(x
+ 1)) + 5*x)/(x + 1) + 2*(2*x^2 + 3*x)/(x + 1)) + 324*x^4*e^(3*x^3*e^(2*x) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x
+ 1)) + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 3*x + (3*x^4*e^(2*x) + 3*x^3*e^(2*x) + 6*x^3*e^(x + 1/2*(2*x^2 + 3*x)
/(x + 1)) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 2*x^2 + 3*x*e^((2*x^2
+ 3*x)/(x + 1)) + 3*x)/(x + 1) + 1/2*(2*x^2 + 3*x)/(x + 1)) + 648*x^4*e^(3*x^3*e^(2*x) + 6*x^2*e^(x + 1/2*(2*x
^2 + 3*x)/(x + 1)) + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 2*x + 1/2*(6*x^4*e^(2*x) + 6*x^3*e^(2*x) + 12*x^3*e^(x +
1/2*(2*x^2 + 3*x)/(x + 1)) + 12*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 4*x^
2 + 6*x*e^((2*x^2 + 3*x)/(x + 1)) + 5*x)/(x + 1) + (3*x^4*e^(2*x) + 3*x^3*e^(2*x) + 6*x^3*e^(x + 1/2*(2*x^2 +
3*x)/(x + 1)) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 2*x^2 + 3*x*e^((2*
x^2 + 3*x)/(x + 1)) + 3*x)/(x + 1)) + 324*x^4*e^(3*x^3*e^(2*x) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x
*e^((2*x^2 + 3*x)/(x + 1)) + 2*x + 1/2*(6*x^4*e^(2*x) + 6*x^3*e^(2*x) + 12*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1
)) + 12*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 4*x^2 + 6*x*e^((2*x^2 + 3*x)
/(x + 1)) + 5*x)/(x + 1) + (2*x^2 + 3*x)/(x + 1)) + 1404*x^4*e^(3*x^3*e^(2*x) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)
/(x + 1)) + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 2*x + (3*x^4*e^(2*x) + 3*x^3*e^(2*x) + 6*x^3*e^(x + 1/2*(2*x^2 + 3
*x)/(x + 1)) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 2*x^2 + 3*x*e^((2*x
^2 + 3*x)/(x + 1)) + 3*x)/(x + 1) + (2*x^2 + 3*x)/(x + 1)) + 576*x^4*e^(3*x^3*e^(2*x) + 6*x^2*e^(x + 1/2*(2*x^
2 + 3*x)/(x + 1)) + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 2*x + 2*(2*x^2 + 3*x)/(x + 1)) + 972*x^4*e^(3*x^3*e^(2*x)
+ 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + x + 1/2*(6*x^4*e^(2*x) + 6*x^3*e^(
2*x) + 12*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 12*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^((2*x^2 +
3*x)/(x + 1)) + 4*x^2 + 6*x*e^((2*x^2 + 3*x)/(x + 1)) + 5*x)/(x + 1) + (3*x^4*e^(2*x) + 3*x^3*e^(2*x) + 6*x^3
*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x^2*e^((2*x^2 + 3*x)/(x + 1))
+ 2*x^2 + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 3*x)/(x + 1) + 1/2*(2*x^2 + 3*x)/(x + 1)) + 1404*x^4*e^(3*x^3*e^(2*
x) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + x + 1/2*(6*x^4*e^(2*x) + 6*x^3*
e^(2*x) + 12*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 12*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^((2*x^
2 + 3*x)/(x + 1)) + 4*x^2 + 6*x*e^((2*x^2 + 3*x)/(x + 1)) + 5*x)/(x + 1) + 3/2*(2*x^2 + 3*x)/(x + 1)) + 540*x^
4*e^(3*x^3*e^(2*x) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + x + (3*x^4*e^(2
*x) + 3*x^3*e^(2*x) + 6*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x^
2*e^((2*x^2 + 3*x)/(x + 1)) + 2*x^2 + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 3*x)/(x + 1) + 3/2*(2*x^2 + 3*x)/(x + 1)
) + 720*x^4*e^(3*x^3*e^(2*x) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + x + 5
/2*(2*x^2 + 3*x)/(x + 1)) - 48*x^4*e^(3*x^3*e^(2*x) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x*e^((2*x^2
+ 3*x)/(x + 1)) + x + 3/2*(2*x^2 + 3*x)/(x + 1)) + 162*x^4*e^(3*x^3*e^(2*x) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(
x + 1)) + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 1/2*(6*x^4*e^(2*x) + 6*x^3*e^(2*x) + 12*x^3*e^(x + 1/2*(2*x^2 + 3*x)
/(x + 1)) + 12*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 4*x^2 + 6*x*e^((2*x^2
+ 3*x)/(x + 1)) + 5*x)/(x + 1) + (3*x^4*e^(2*x) + 3*x^3*e^(2*x) + 6*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6
*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 2*x^2 + 3*x*e^((2*x^2 + 3*x)/(x + 1
)) + 3*x)/(x + 1) + (2*x^2 + 3*x)/(x + 1)) + 540*x^4*e^(3*x^3*e^(2*x) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)
) + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 1/2*(6*x^4*e^(2*x) + 6*x^3*e^(2*x) + 12*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x +
1)) + 12*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 4*x^2 + 6*x*e^((2*x^2 + 3*x
)/(x + 1)) + 5*x)/(x + 1) + 2*(2*x^2 + 3*x)/(x + 1)) + 324*x^4*e^(2*x + 1/2*(6*x^4*e^(2*x) + 6*x^3*e^(2*x) + 1
2*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 12*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^((2*x^2 + 3*x)/(x
+ 1)) + 4*x^2 + 6*x*e^((2*x^2 + 3*x)/(x + 1)) + 5*x)/(x + 1) + (3*x^4*e^(2*x) + 3*x^3*e^(2*x) + 6*x^3*e^(x +
1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 2*x^2
+ 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 3*x)/(x + 1)) + 576*x^4*e^(2*x + (3*x^4*e^(2*x) + 3*x^3*e^(2*x) + 6*x^3*e^(
x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 2
*x^2 + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 3*x)/(x + 1) + (2*x^2 + 3*x)/(x + 1)) + 1404*x^4*e^(x + 1/2*(6*x^4*e^(2
*x) + 6*x^3*e^(2*x) + 12*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 12*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*
x^2*e^((2*x^2 + 3*x)/(x + 1)) + 4*x^2 + 6*x*e^((2*x^2 + 3*x)/(x + 1)) + 5*x)/(x + 1) + (3*x^4*e^(2*x) + 3*x^3*
e^(2*x) + 6*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x^2*e^((2*x^2
+ 3*x)/(x + 1)) + 2*x^2 + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 3*x)/(x + 1) + 1/2*(2*x^2 + 3*x)/(x + 1)) + 576*x^4*
e^(x + 1/2*(6*x^4*e^(2*x) + 6*x^3*e^(2*x) + 12*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 12*x^2*e^(x + 1/2*(2*x^
2 + 3*x)/(x + 1)) + 6*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 4*x^2 + 6*x*e^((2*x^2 + 3*x)/(x + 1)) + 5*x)/(x + 1) + 3
/2*(2*x^2 + 3*x)/(x + 1)) + 720*x^4*e^(x + (3*x^4*e^(2*x) + 3*x^3*e^(2*x) + 6*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x
+ 1)) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 2*x^2 + 3*x*e^((2*x^2 + 3*
x)/(x + 1)) + 3*x)/(x + 1) + 3/2*(2*x^2 + 3*x)/(x + 1)) - 48*x^4*e^(x + (3*x^4*e^(2*x) + 3*x^3*e^(2*x) + 6*x^3
*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x^2*e^((2*x^2 + 3*x)/(x + 1))
+ 2*x^2 + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 3*x)/(x + 1) + 1/2*(2*x^2 + 3*x)/(x + 1)) + 192*x^4*e^(x + 5/2*(2*x
^2 + 3*x)/(x + 1)) - 128*x^4*e^(x + 3/2*(2*x^2 + 3*x)/(x + 1)) + 540*x^4*e^(1/2*(6*x^4*e^(2*x) + 6*x^3*e^(2*x)
+ 12*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 12*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^((2*x^2 + 3*x
)/(x + 1)) + 4*x^2 + 6*x*e^((2*x^2 + 3*x)/(x + 1)) + 5*x)/(x + 1) + (3*x^4*e^(2*x) + 3*x^3*e^(2*x) + 6*x^3*e^(
x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 2
*x^2 + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 3*x)/(x + 1) + (2*x^2 + 3*x)/(x + 1)) + 720*x^4*e^(1/2*(6*x^4*e^(2*x) +
6*x^3*e^(2*x) + 12*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 12*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e
^((2*x^2 + 3*x)/(x + 1)) + 4*x^2 + 6*x*e^((2*x^2 + 3*x)/(x + 1)) + 5*x)/(x + 1) + 2*(2*x^2 + 3*x)/(x + 1)) - 4
8*x^4*e^(1/2*(6*x^4*e^(2*x) + 6*x^3*e^(2*x) + 12*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 12*x^2*e^(x + 1/2*(2*
x^2 + 3*x)/(x + 1)) + 6*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 4*x^2 + 6*x*e^((2*x^2 + 3*x)/(x + 1)) + 5*x)/(x + 1) +
(2*x^2 + 3*x)/(x + 1)) + 243*x^3*e^(3*x^3*e^(2*x) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x*e^((2*x^2 +
3*x)/(x + 1)) + 2*x + 1/2*(6*x^4*e^(2*x) + 6*x^3*e^(2*x) + 12*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 12*x^2*
e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 4*x^2 + 6*x*e^((2*x^2 + 3*x)/(x + 1)) +
5*x)/(x + 1) + (3*x^4*e^(2*x) + 3*x^3*e^(2*x) + 6*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^(x + 1/2*(2*
x^2 + 3*x)/(x + 1)) + 3*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 2*x^2 + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 3*x)/(x + 1))
+ 432*x^3*e^(3*x^3*e^(2*x) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 2*x + (
3*x^4*e^(2*x) + 3*x^3*e^(2*x) + 6*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x +
1)) + 3*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 2*x^2 + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 3*x)/(x + 1) + (2*x^2 + 3*x)/(
x + 1)) + 1053*x^3*e^(3*x^3*e^(2*x) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x*e^((2*x^2 + 3*x)/(x + 1))
+ x + 1/2*(6*x^4*e^(2*x) + 6*x^3*e^(2*x) + 12*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 12*x^2*e^(x + 1/2*(2*x^2
+ 3*x)/(x + 1)) + 6*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 4*x^2 + 6*x*e^((2*x^2 + 3*x)/(x + 1)) + 5*x)/(x + 1) + (3
*x^4*e^(2*x) + 3*x^3*e^(2*x) + 6*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1
)) + 3*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 2*x^2 + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 3*x)/(x + 1) + 1/2*(2*x^2 + 3*x
)/(x + 1)) + 432*x^3*e^(3*x^3*e^(2*x) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x*e^((2*x^2 + 3*x)/(x + 1)
) + x + 1/2*(6*x^4*e^(2*x) + 6*x^3*e^(2*x) + 12*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 12*x^2*e^(x + 1/2*(2*x
^2 + 3*x)/(x + 1)) + 6*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 4*x^2 + 6*x*e^((2*x^2 + 3*x)/(x + 1)) + 5*x)/(x + 1) +
3/2*(2*x^2 + 3*x)/(x + 1)) + 540*x^3*e^(3*x^3*e^(2*x) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x*e^((2*x^
2 + 3*x)/(x + 1)) + x + (3*x^4*e^(2*x) + 3*x^3*e^(2*x) + 6*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^(x
+ 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 2*x^2 + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 3*x)/
(x + 1) + 3/2*(2*x^2 + 3*x)/(x + 1)) - 36*x^3*e^(3*x^3*e^(2*x) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x
*e^((2*x^2 + 3*x)/(x + 1)) + x + (3*x^4*e^(2*x) + 3*x^3*e^(2*x) + 6*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*
x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 2*x^2 + 3*x*e^((2*x^2 + 3*x)/(x + 1)
) + 3*x)/(x + 1) + 1/2*(2*x^2 + 3*x)/(x + 1)) + 144*x^3*e^(3*x^3*e^(2*x) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x +
1)) + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + x + 5/2*(2*x^2 + 3*x)/(x + 1)) - 96*x^3*e^(3*x^3*e^(2*x) + 6*x^2*e^(x +
1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + x + 3/2*(2*x^2 + 3*x)/(x + 1)) + 405*x^3*e^(3*x^
3*e^(2*x) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 1/2*(6*x^4*e^(2*x) + 6*x
^3*e^(2*x) + 12*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 12*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^((2
*x^2 + 3*x)/(x + 1)) + 4*x^2 + 6*x*e^((2*x^2 + 3*x)/(x + 1)) + 5*x)/(x + 1) + (3*x^4*e^(2*x) + 3*x^3*e^(2*x) +
6*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x^2*e^((2*x^2 + 3*x)/(x
+ 1)) + 2*x^2 + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 3*x)/(x + 1) + (2*x^2 + 3*x)/(x + 1)) + 540*x^3*e^(3*x^3*e^(2
*x) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 1/2*(6*x^4*e^(2*x) + 6*x^3*e^(
2*x) + 12*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 12*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^((2*x^2 +
3*x)/(x + 1)) + 4*x^2 + 6*x*e^((2*x^2 + 3*x)/(x + 1)) + 5*x)/(x + 1) + 2*(2*x^2 + 3*x)/(x + 1)) - 36*x^3*e^(3
*x^3*e^(2*x) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 1/2*(6*x^4*e^(2*x) +
6*x^3*e^(2*x) + 12*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 12*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^
((2*x^2 + 3*x)/(x + 1)) + 4*x^2 + 6*x*e^((2*x^2 + 3*x)/(x + 1)) + 5*x)/(x + 1) + (2*x^2 + 3*x)/(x + 1)) + 432*
x^3*e^(x + 1/2*(6*x^4*e^(2*x) + 6*x^3*e^(2*x) + 12*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 12*x^2*e^(x + 1/2*(
2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 4*x^2 + 6*x*e^((2*x^2 + 3*x)/(x + 1)) + 5*x)/(x + 1)
+ (3*x^4*e^(2*x) + 3*x^3*e^(2*x) + 6*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(
x + 1)) + 3*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 2*x^2 + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 3*x)/(x + 1) + 1/2*(2*x^2
+ 3*x)/(x + 1)) + 144*x^3*e^(x + (3*x^4*e^(2*x) + 3*x^3*e^(2*x) + 6*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*
x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 2*x^2 + 3*x*e^((2*x^2 + 3*x)/(x + 1)
) + 3*x)/(x + 1) + 3/2*(2*x^2 + 3*x)/(x + 1)) - 96*x^3*e^(x + (3*x^4*e^(2*x) + 3*x^3*e^(2*x) + 6*x^3*e^(x + 1/
2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 2*x^2 +
3*x*e^((2*x^2 + 3*x)/(x + 1)) + 3*x)/(x + 1) + 1/2*(2*x^2 + 3*x)/(x + 1)) - 64*x^3*e^(x + 3/2*(2*x^2 + 3*x)/(
x + 1)) + 540*x^3*e^(1/2*(6*x^4*e^(2*x) + 6*x^3*e^(2*x) + 12*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 12*x^2*e^
(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 4*x^2 + 6*x*e^((2*x^2 + 3*x)/(x + 1)) + 5*
x)/(x + 1) + (3*x^4*e^(2*x) + 3*x^3*e^(2*x) + 6*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^(x + 1/2*(2*x^
2 + 3*x)/(x + 1)) + 3*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 2*x^2 + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 3*x)/(x + 1) + (
2*x^2 + 3*x)/(x + 1)) - 36*x^3*e^(1/2*(6*x^4*e^(2*x) + 6*x^3*e^(2*x) + 12*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)
) + 12*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 4*x^2 + 6*x*e^((2*x^2 + 3*x)/
(x + 1)) + 5*x)/(x + 1) + (3*x^4*e^(2*x) + 3*x^3*e^(2*x) + 6*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^(
x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 2*x^2 + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 3*x
)/(x + 1)) + 144*x^3*e^(1/2*(6*x^4*e^(2*x) + 6*x^3*e^(2*x) + 12*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 12*x^2
*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 4*x^2 + 6*x*e^((2*x^2 + 3*x)/(x + 1)) +
5*x)/(x + 1) + 2*(2*x^2 + 3*x)/(x + 1)) - 96*x^3*e^(1/2*(6*x^4*e^(2*x) + 6*x^3*e^(2*x) + 12*x^3*e^(x + 1/2*(2
*x^2 + 3*x)/(x + 1)) + 12*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 4*x^2 + 6*
x*e^((2*x^2 + 3*x)/(x + 1)) + 5*x)/(x + 1) + (2*x^2 + 3*x)/(x + 1)) + 324*x^2*e^(3*x^3*e^(2*x) + 6*x^2*e^(x +
1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + x + 1/2*(6*x^4*e^(2*x) + 6*x^3*e^(2*x) + 12*x^3*e
^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 12*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^((2*x^2 + 3*x)/(x + 1))
+ 4*x^2 + 6*x*e^((2*x^2 + 3*x)/(x + 1)) + 5*x)/(x + 1) + (3*x^4*e^(2*x) + 3*x^3*e^(2*x) + 6*x^3*e^(x + 1/2*(2*
x^2 + 3*x)/(x + 1)) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 2*x^2 + 3*x*
e^((2*x^2 + 3*x)/(x + 1)) + 3*x)/(x + 1) + 1/2*(2*x^2 + 3*x)/(x + 1)) + 108*x^2*e^(3*x^3*e^(2*x) + 6*x^2*e^(x
+ 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + x + (3*x^4*e^(2*x) + 3*x^3*e^(2*x) + 6*x^3*e^(x
+ 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 2*
x^2 + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 3*x)/(x + 1) + 3/2*(2*x^2 + 3*x)/(x + 1)) - 72*x^2*e^(3*x^3*e^(2*x) + 6*
x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + x + (3*x^4*e^(2*x) + 3*x^3*e^(2*x) + 6
*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x^2*e^((2*x^2 + 3*x)/(x +
1)) + 2*x^2 + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 3*x)/(x + 1) + 1/2*(2*x^2 + 3*x)/(x + 1)) - 48*x^2*e^(3*x^3*e^(
2*x) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + x + 3/2*(2*x^2 + 3*x)/(x + 1)
) + 405*x^2*e^(3*x^3*e^(2*x) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 1/2*(
6*x^4*e^(2*x) + 6*x^3*e^(2*x) + 12*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 12*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x
+ 1)) + 6*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 4*x^2 + 6*x*e^((2*x^2 + 3*x)/(x + 1)) + 5*x)/(x + 1) + (3*x^4*e^(2*x
) + 3*x^3*e^(2*x) + 6*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x^2*
e^((2*x^2 + 3*x)/(x + 1)) + 2*x^2 + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 3*x)/(x + 1) + (2*x^2 + 3*x)/(x + 1)) - 27
*x^2*e^(3*x^3*e^(2*x) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 1/2*(6*x^4*e
^(2*x) + 6*x^3*e^(2*x) + 12*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 12*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) +
6*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 4*x^2 + 6*x*e^((2*x^2 + 3*x)/(x + 1)) + 5*x)/(x + 1) + (3*x^4*e^(2*x) + 3*x
^3*e^(2*x) + 6*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x^2*e^((2*x
^2 + 3*x)/(x + 1)) + 2*x^2 + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 3*x)/(x + 1)) + 108*x^2*e^(3*x^3*e^(2*x) + 6*x^2*
e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 1/2*(6*x^4*e^(2*x) + 6*x^3*e^(2*x) + 12*x^
3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 12*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^((2*x^2 + 3*x)/(x + 1
)) + 4*x^2 + 6*x*e^((2*x^2 + 3*x)/(x + 1)) + 5*x)/(x + 1) + 2*(2*x^2 + 3*x)/(x + 1)) - 72*x^2*e^(3*x^3*e^(2*x)
+ 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 1/2*(6*x^4*e^(2*x) + 6*x^3*e^(2*x
) + 12*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 12*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^((2*x^2 + 3*
x)/(x + 1)) + 4*x^2 + 6*x*e^((2*x^2 + 3*x)/(x + 1)) + 5*x)/(x + 1) + (2*x^2 + 3*x)/(x + 1)) - 48*x^2*e^(x + (3
*x^4*e^(2*x) + 3*x^3*e^(2*x) + 6*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1
)) + 3*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 2*x^2 + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 3*x)/(x + 1) + 1/2*(2*x^2 + 3*x
)/(x + 1)) + 108*x^2*e^(1/2*(6*x^4*e^(2*x) + 6*x^3*e^(2*x) + 12*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 12*x^2
*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 4*x^2 + 6*x*e^((2*x^2 + 3*x)/(x + 1)) +
5*x)/(x + 1) + (3*x^4*e^(2*x) + 3*x^3*e^(2*x) + 6*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^(x + 1/2*(2
*x^2 + 3*x)/(x + 1)) + 3*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 2*x^2 + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 3*x)/(x + 1)
+ (2*x^2 + 3*x)/(x + 1)) - 72*x^2*e^(1/2*(6*x^4*e^(2*x) + 6*x^3*e^(2*x) + 12*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x +
1)) + 12*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 4*x^2 + 6*x*e^((2*x^2 + 3*
x)/(x + 1)) + 5*x)/(x + 1) + (3*x^4*e^(2*x) + 3*x^3*e^(2*x) + 6*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*
e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 2*x^2 + 3*x*e^((2*x^2 + 3*x)/(x + 1)) +
3*x)/(x + 1)) - 48*x^2*e^(1/2*(6*x^4*e^(2*x) + 6*x^3*e^(2*x) + 12*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 12*x
^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 4*x^2 + 6*x*e^((2*x^2 + 3*x)/(x + 1))
+ 5*x)/(x + 1) + (2*x^2 + 3*x)/(x + 1)) - 36*x*e^(3*x^3*e^(2*x) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3
*x*e^((2*x^2 + 3*x)/(x + 1)) + x + (3*x^4*e^(2*x) + 3*x^3*e^(2*x) + 6*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) +
6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 2*x^2 + 3*x*e^((2*x^2 + 3*x)/(x +
1)) + 3*x)/(x + 1) + 1/2*(2*x^2 + 3*x)/(x + 1)) + 81*x*e^(3*x^3*e^(2*x) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x +
1)) + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 1/2*(6*x^4*e^(2*x) + 6*x^3*e^(2*x) + 12*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x
+ 1)) + 12*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 4*x^2 + 6*x*e^((2*x^2 + 3
*x)/(x + 1)) + 5*x)/(x + 1) + (3*x^4*e^(2*x) + 3*x^3*e^(2*x) + 6*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2
*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 2*x^2 + 3*x*e^((2*x^2 + 3*x)/(x + 1)) +
3*x)/(x + 1) + (2*x^2 + 3*x)/(x + 1)) - 54*x*e^(3*x^3*e^(2*x) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x
*e^((2*x^2 + 3*x)/(x + 1)) + 1/2*(6*x^4*e^(2*x) + 6*x^3*e^(2*x) + 12*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 1
2*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 4*x^2 + 6*x*e^((2*x^2 + 3*x)/(x +
1)) + 5*x)/(x + 1) + (3*x^4*e^(2*x) + 3*x^3*e^(2*x) + 6*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^(x + 1
/2*(2*x^2 + 3*x)/(x + 1)) + 3*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 2*x^2 + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 3*x)/(x
+ 1)) - 36*x*e^(3*x^3*e^(2*x) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 1/2*
(6*x^4*e^(2*x) + 6*x^3*e^(2*x) + 12*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 12*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x
+ 1)) + 6*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 4*x^2 + 6*x*e^((2*x^2 + 3*x)/(x + 1)) + 5*x)/(x + 1) + (2*x^2 + 3*x
)/(x + 1)) - 36*x*e^(1/2*(6*x^4*e^(2*x) + 6*x^3*e^(2*x) + 12*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 12*x^2*e^
(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 4*x^2 + 6*x*e^((2*x^2 + 3*x)/(x + 1)) + 5*
x)/(x + 1) + (3*x^4*e^(2*x) + 3*x^3*e^(2*x) + 6*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^(x + 1/2*(2*x^
2 + 3*x)/(x + 1)) + 3*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 2*x^2 + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 3*x)/(x + 1)) -
27*e^(3*x^3*e^(2*x) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 1/2*(6*x^4*e^(
2*x) + 6*x^3*e^(2*x) + 12*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 12*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6
*x^2*e^((2*x^2 + 3*x)/(x + 1)) + 4*x^2 + 6*x*e^((2*x^2 + 3*x)/(x + 1)) + 5*x)/(x + 1) + (3*x^4*e^(2*x) + 3*x^3
*e^(2*x) + 6*x^3*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 6*x^2*e^(x + 1/2*(2*x^2 + 3*x)/(x + 1)) + 3*x^2*e^((2*x^2
+ 3*x)/(x + 1)) + 2*x^2 + 3*x*e^((2*x^2 + 3*x)/(x + 1)) + 3*x)/(x + 1)))
Mupad [B] (verification not implemented)
Time = 12.20 (sec) , antiderivative size = 56, normalized size of antiderivative = 1.60
\[
\int \frac {-16-32 x-16 x^2+e^{2 x+e^{2 x} \left (3 e^{\frac {2 x}{2+2 x}} x+6 e^{\frac {x}{2+2 x}} x^2+3 x^3\right )} \left (-108 x^2-288 x^3-252 x^4-72 x^5+e^{\frac {2 x}{2+2 x}} \left (-36-180 x-180 x^2-72 x^3\right )+e^{\frac {x}{2+2 x}} \left (-144 x-468 x^2-432 x^3-144 x^4\right )\right )}{16 x^2+32 x^3+16 x^4+e^{2 e^{2 x} \left (3 e^{\frac {2 x}{2+2 x}} x+6 e^{\frac {x}{2+2 x}} x^2+3 x^3\right )} \left (9+18 x+9 x^2\right )+e^{e^{2 x} \left (3 e^{\frac {2 x}{2+2 x}} x+6 e^{\frac {x}{2+2 x}} x^2+3 x^3\right )} \left (24 x+48 x^2+24 x^3\right )} \, dx=\frac {4}{4\,x+3\,{\mathrm {e}}^{6\,x^2\,{\mathrm {e}}^{2\,x}\,{\mathrm {e}}^{\frac {x}{2\,x+2}}}\,{\mathrm {e}}^{3\,x^3\,{\mathrm {e}}^{2\,x}}\,{\mathrm {e}}^{3\,x\,{\mathrm {e}}^{2\,x}\,{\mathrm {e}}^{\frac {x}{x+1}}}}
\]
[In]
int(-(32*x + 16*x^2 + exp(2*x)*exp(exp(2*x)*(6*x^2*exp(x/(2*x + 2)) + 3*x*exp((2*x)/(2*x + 2)) + 3*x^3))*(exp(
x/(2*x + 2))*(144*x + 468*x^2 + 432*x^3 + 144*x^4) + exp((2*x)/(2*x + 2))*(180*x + 180*x^2 + 72*x^3 + 36) + 10
8*x^2 + 288*x^3 + 252*x^4 + 72*x^5) + 16)/(exp(2*exp(2*x)*(6*x^2*exp(x/(2*x + 2)) + 3*x*exp((2*x)/(2*x + 2)) +
3*x^3))*(18*x + 9*x^2 + 9) + exp(exp(2*x)*(6*x^2*exp(x/(2*x + 2)) + 3*x*exp((2*x)/(2*x + 2)) + 3*x^3))*(24*x
+ 48*x^2 + 24*x^3) + 16*x^2 + 32*x^3 + 16*x^4),x)
[Out]
4/(4*x + 3*exp(6*x^2*exp(2*x)*exp(x/(2*x + 2)))*exp(3*x^3*exp(2*x))*exp(3*x*exp(2*x)*exp(x/(x + 1))))