\(\int \frac {100 e^{\frac {3 (8+2 x)}{x^2}} x^2+e^{\frac {2 (8+2 x)}{x^2}} (400+50 x+25 x^2)}{-8 x^5+e^{\frac {3 (8+2 x)}{x^2}} (8 e^3 x^2-96 e^2 x^3+384 e x^4-512 x^5)+e^{\frac {2 (8+2 x)}{x^2}} (-24 e^2 x^3+192 e x^4-384 x^5)+e^{\frac {8+2 x}{x^2}} (24 e x^4-96 x^5)} \, dx\) [6208]
Optimal result
Integrand size = 148, antiderivative size = 30 \[
\int \frac {100 e^{\frac {3 (8+2 x)}{x^2}} x^2+e^{\frac {2 (8+2 x)}{x^2}} \left (400+50 x+25 x^2\right )}{-8 x^5+e^{\frac {3 (8+2 x)}{x^2}} \left (8 e^3 x^2-96 e^2 x^3+384 e x^4-512 x^5\right )+e^{\frac {2 (8+2 x)}{x^2}} \left (-24 e^2 x^3+192 e x^4-384 x^5\right )+e^{\frac {8+2 x}{x^2}} \left (24 e x^4-96 x^5\right )} \, dx=\frac {1}{16 \left (-x+\frac {1}{5} \left (e+x-e^{-\frac {2 (4+x)}{x^2}} x\right )\right )^2}
\]
[Out]
1/4/(1/5*exp(1)-4/5*x-1/5*x/exp(2*(4+x)/x^2))/(4/5*exp(1)-16/5*x-4/5*x/exp(2*(4+x)/x^2))
Rubi [F]
\[
\int \frac {100 e^{\frac {3 (8+2 x)}{x^2}} x^2+e^{\frac {2 (8+2 x)}{x^2}} \left (400+50 x+25 x^2\right )}{-8 x^5+e^{\frac {3 (8+2 x)}{x^2}} \left (8 e^3 x^2-96 e^2 x^3+384 e x^4-512 x^5\right )+e^{\frac {2 (8+2 x)}{x^2}} \left (-24 e^2 x^3+192 e x^4-384 x^5\right )+e^{\frac {8+2 x}{x^2}} \left (24 e x^4-96 x^5\right )} \, dx=\int \frac {100 e^{\frac {3 (8+2 x)}{x^2}} x^2+e^{\frac {2 (8+2 x)}{x^2}} \left (400+50 x+25 x^2\right )}{-8 x^5+e^{\frac {3 (8+2 x)}{x^2}} \left (8 e^3 x^2-96 e^2 x^3+384 e x^4-512 x^5\right )+e^{\frac {2 (8+2 x)}{x^2}} \left (-24 e^2 x^3+192 e x^4-384 x^5\right )+e^{\frac {8+2 x}{x^2}} \left (24 e x^4-96 x^5\right )} \, dx
\]
[In]
Int[(100*E^((3*(8 + 2*x))/x^2)*x^2 + E^((2*(8 + 2*x))/x^2)*(400 + 50*x + 25*x^2))/(-8*x^5 + E^((3*(8 + 2*x))/x
^2)*(8*E^3*x^2 - 96*E^2*x^3 + 384*E*x^4 - 512*x^5) + E^((2*(8 + 2*x))/x^2)*(-24*E^2*x^3 + 192*E*x^4 - 384*x^5)
+ E^((8 + 2*x)/x^2)*(24*E*x^4 - 96*x^5)),x]
[Out]
(25*Defer[Int][E^(1 + (4*(4 + x))/x^2)/((E - 4*x)*(E^(1 + 8/x^2 + 2/x) - x - 4*E^(8/x^2 + 2/x)*x)^3), x])/8 +
(25*Defer[Int][E^((4*(4 + x))/x^2)/((E - 4*x)*(E^(1 + 8/x^2 + 2/x) - x - 4*E^(8/x^2 + 2/x)*x)^2), x])/2 - 50*D
efer[Int][E^((4*(4 + x))/x^2)/(x^2*(-E^(1 + 8/x^2 + 2/x) + x + 4*E^(8/x^2 + 2/x)*x)^3), x] - (25*Defer[Int][E^
((4*(4 + x))/x^2)/(x*(-E^(1 + 8/x^2 + 2/x) + x + 4*E^(8/x^2 + 2/x)*x)^3), x])/4
Rubi steps \begin{align*}
\text {integral}& = \int \frac {25 e^{\frac {4 (4+x)}{x^2}} \left (16+2 x+\left (1+4 e^{\frac {2 (4+x)}{x^2}}\right ) x^2\right )}{8 x^2 \left (e^{\frac {8+2 x+x^2}{x^2}}-x-4 e^{\frac {2 (4+x)}{x^2}} x\right )^3} \, dx \\ & = \frac {25}{8} \int \frac {e^{\frac {4 (4+x)}{x^2}} \left (16+2 x+\left (1+4 e^{\frac {2 (4+x)}{x^2}}\right ) x^2\right )}{x^2 \left (e^{\frac {8+2 x+x^2}{x^2}}-x-4 e^{\frac {2 (4+x)}{x^2}} x\right )^3} \, dx \\ & = \frac {25}{8} \int \left (\frac {4 e^{\frac {4 (4+x)}{x^2}}}{(e-4 x) \left (e^{1+\frac {8}{x^2}+\frac {2}{x}}-x-4 e^{\frac {8}{x^2}+\frac {2}{x}} x\right )^2}+\frac {e^{\frac {4 (4+x)}{x^2}} \left (16 e-2 (32-e) x-(8-e) x^2\right )}{(e-4 x) x^2 \left (e^{1+\frac {8}{x^2}+\frac {2}{x}}-x-4 e^{\frac {8}{x^2}+\frac {2}{x}} x\right )^3}\right ) \, dx \\ & = \frac {25}{8} \int \frac {e^{\frac {4 (4+x)}{x^2}} \left (16 e-2 (32-e) x-(8-e) x^2\right )}{(e-4 x) x^2 \left (e^{1+\frac {8}{x^2}+\frac {2}{x}}-x-4 e^{\frac {8}{x^2}+\frac {2}{x}} x\right )^3} \, dx+\frac {25}{2} \int \frac {e^{\frac {4 (4+x)}{x^2}}}{(e-4 x) \left (e^{1+\frac {8}{x^2}+\frac {2}{x}}-x-4 e^{\frac {8}{x^2}+\frac {2}{x}} x\right )^2} \, dx \\ & = \frac {25}{8} \int \left (\frac {e^{1+\frac {4 (4+x)}{x^2}}}{(e-4 x) \left (e^{1+\frac {8}{x^2}+\frac {2}{x}}-x-4 e^{\frac {8}{x^2}+\frac {2}{x}} x\right )^3}-\frac {16 e^{\frac {4 (4+x)}{x^2}}}{x^2 \left (-e^{1+\frac {8}{x^2}+\frac {2}{x}}+x+4 e^{\frac {8}{x^2}+\frac {2}{x}} x\right )^3}-\frac {2 e^{\frac {4 (4+x)}{x^2}}}{x \left (-e^{1+\frac {8}{x^2}+\frac {2}{x}}+x+4 e^{\frac {8}{x^2}+\frac {2}{x}} x\right )^3}\right ) \, dx+\frac {25}{2} \int \frac {e^{\frac {4 (4+x)}{x^2}}}{(e-4 x) \left (e^{1+\frac {8}{x^2}+\frac {2}{x}}-x-4 e^{\frac {8}{x^2}+\frac {2}{x}} x\right )^2} \, dx \\ & = \frac {25}{8} \int \frac {e^{1+\frac {4 (4+x)}{x^2}}}{(e-4 x) \left (e^{1+\frac {8}{x^2}+\frac {2}{x}}-x-4 e^{\frac {8}{x^2}+\frac {2}{x}} x\right )^3} \, dx-\frac {25}{4} \int \frac {e^{\frac {4 (4+x)}{x^2}}}{x \left (-e^{1+\frac {8}{x^2}+\frac {2}{x}}+x+4 e^{\frac {8}{x^2}+\frac {2}{x}} x\right )^3} \, dx+\frac {25}{2} \int \frac {e^{\frac {4 (4+x)}{x^2}}}{(e-4 x) \left (e^{1+\frac {8}{x^2}+\frac {2}{x}}-x-4 e^{\frac {8}{x^2}+\frac {2}{x}} x\right )^2} \, dx-50 \int \frac {e^{\frac {4 (4+x)}{x^2}}}{x^2 \left (-e^{1+\frac {8}{x^2}+\frac {2}{x}}+x+4 e^{\frac {8}{x^2}+\frac {2}{x}} x\right )^3} \, dx \\
\end{align*}
Mathematica [A] (verified)
Time = 1.63 (sec) , antiderivative size = 47, normalized size of antiderivative = 1.57
\[
\int \frac {100 e^{\frac {3 (8+2 x)}{x^2}} x^2+e^{\frac {2 (8+2 x)}{x^2}} \left (400+50 x+25 x^2\right )}{-8 x^5+e^{\frac {3 (8+2 x)}{x^2}} \left (8 e^3 x^2-96 e^2 x^3+384 e x^4-512 x^5\right )+e^{\frac {2 (8+2 x)}{x^2}} \left (-24 e^2 x^3+192 e x^4-384 x^5\right )+e^{\frac {8+2 x}{x^2}} \left (24 e x^4-96 x^5\right )} \, dx=\frac {25 e^{\frac {4 (4+x)}{x^2}}}{16 \left (-e^{\frac {8+2 x+x^2}{x^2}}+x+4 e^{\frac {2 (4+x)}{x^2}} x\right )^2}
\]
[In]
Integrate[(100*E^((3*(8 + 2*x))/x^2)*x^2 + E^((2*(8 + 2*x))/x^2)*(400 + 50*x + 25*x^2))/(-8*x^5 + E^((3*(8 + 2
*x))/x^2)*(8*E^3*x^2 - 96*E^2*x^3 + 384*E*x^4 - 512*x^5) + E^((2*(8 + 2*x))/x^2)*(-24*E^2*x^3 + 192*E*x^4 - 38
4*x^5) + E^((8 + 2*x)/x^2)*(24*E*x^4 - 96*x^5)),x]
[Out]
(25*E^((4*(4 + x))/x^2))/(16*(-E^((8 + 2*x + x^2)/x^2) + x + 4*E^((2*(4 + x))/x^2)*x)^2)
Maple [A] (verified)
Time = 1.02 (sec) , antiderivative size = 47, normalized size of antiderivative = 1.57
| | |
method | result | size |
| | |
norman |
\(\frac {25 \,{\mathrm e}^{\frac {4 x +16}{x^{2}}}}{16 \left ({\mathrm e} \,{\mathrm e}^{\frac {2 x +8}{x^{2}}}-4 x \,{\mathrm e}^{\frac {2 x +8}{x^{2}}}-x \right )^{2}}\) |
\(47\) |
risch |
\(\frac {25 \,{\mathrm e}^{\frac {4 x +16}{x^{2}}} x^{2}-\frac {25 x \,{\mathrm e}^{\frac {x^{2}+4 x +16}{x^{2}}}}{2}+\frac {25 \,{\mathrm e}^{\frac {2 x^{2}+4 x +16}{x^{2}}}}{16}}{\left ({\mathrm e}^{2}-8 x \,{\mathrm e}+16 x^{2}\right ) \left (4 x \,{\mathrm e}^{\frac {2 x +8}{x^{2}}}-{\mathrm e}^{\frac {x^{2}+2 x +8}{x^{2}}}+x \right )^{2}}\) |
\(94\) |
parallelrisch |
\(\frac {25 \,{\mathrm e}^{\frac {4 x +16}{x^{2}}}}{16 \left ({\mathrm e}^{\frac {4 x +16}{x^{2}}} {\mathrm e}^{2}-8 \,{\mathrm e} \,{\mathrm e}^{\frac {4 x +16}{x^{2}}} x +16 \,{\mathrm e}^{\frac {4 x +16}{x^{2}}} x^{2}-2 \,{\mathrm e} \,{\mathrm e}^{\frac {2 x +8}{x^{2}}} x +8 x^{2} {\mathrm e}^{\frac {2 x +8}{x^{2}}}+x^{2}\right )}\) |
\(96\) |
| | |
|
|
|
[In]
int((100*x^2*exp((2*x+8)/x^2)^3+(25*x^2+50*x+400)*exp((2*x+8)/x^2)^2)/((8*x^2*exp(1)^3-96*x^3*exp(1)^2+384*x^4
*exp(1)-512*x^5)*exp((2*x+8)/x^2)^3+(-24*x^3*exp(1)^2+192*x^4*exp(1)-384*x^5)*exp((2*x+8)/x^2)^2+(24*x^4*exp(1
)-96*x^5)*exp((2*x+8)/x^2)-8*x^5),x,method=_RETURNVERBOSE)
[Out]
25/16*exp((2*x+8)/x^2)^2/(exp(1)*exp((2*x+8)/x^2)-4*x*exp((2*x+8)/x^2)-x)^2
Fricas [B] (verification not implemented)
Leaf count of result is larger than twice the leaf count of optimal. 62 vs. \(2 (23) = 46\).
Time = 0.28 (sec) , antiderivative size = 62, normalized size of antiderivative = 2.07
\[
\int \frac {100 e^{\frac {3 (8+2 x)}{x^2}} x^2+e^{\frac {2 (8+2 x)}{x^2}} \left (400+50 x+25 x^2\right )}{-8 x^5+e^{\frac {3 (8+2 x)}{x^2}} \left (8 e^3 x^2-96 e^2 x^3+384 e x^4-512 x^5\right )+e^{\frac {2 (8+2 x)}{x^2}} \left (-24 e^2 x^3+192 e x^4-384 x^5\right )+e^{\frac {8+2 x}{x^2}} \left (24 e x^4-96 x^5\right )} \, dx=\frac {25 \, e^{\left (\frac {4 \, {\left (x + 4\right )}}{x^{2}}\right )}}{16 \, {\left (x^{2} + {\left (16 \, x^{2} - 8 \, x e + e^{2}\right )} e^{\left (\frac {4 \, {\left (x + 4\right )}}{x^{2}}\right )} + 2 \, {\left (4 \, x^{2} - x e\right )} e^{\left (\frac {2 \, {\left (x + 4\right )}}{x^{2}}\right )}\right )}}
\]
[In]
integrate((100*x^2*exp((2*x+8)/x^2)^3+(25*x^2+50*x+400)*exp((2*x+8)/x^2)^2)/((8*x^2*exp(1)^3-96*x^3*exp(1)^2+3
84*x^4*exp(1)-512*x^5)*exp((2*x+8)/x^2)^3+(-24*x^3*exp(1)^2+192*x^4*exp(1)-384*x^5)*exp((2*x+8)/x^2)^2+(24*x^4
*exp(1)-96*x^5)*exp((2*x+8)/x^2)-8*x^5),x, algorithm="fricas")
[Out]
25/16*e^(4*(x + 4)/x^2)/(x^2 + (16*x^2 - 8*x*e + e^2)*e^(4*(x + 4)/x^2) + 2*(4*x^2 - x*e)*e^(2*(x + 4)/x^2))
Sympy [B] (verification not implemented)
Leaf count of result is larger than twice the leaf count of optimal. 150 vs. \(2 (53) = 106\).
Time = 0.38 (sec) , antiderivative size = 150, normalized size of antiderivative = 5.00
\[
\int \frac {100 e^{\frac {3 (8+2 x)}{x^2}} x^2+e^{\frac {2 (8+2 x)}{x^2}} \left (400+50 x+25 x^2\right )}{-8 x^5+e^{\frac {3 (8+2 x)}{x^2}} \left (8 e^3 x^2-96 e^2 x^3+384 e x^4-512 x^5\right )+e^{\frac {2 (8+2 x)}{x^2}} \left (-24 e^2 x^3+192 e x^4-384 x^5\right )+e^{\frac {8+2 x}{x^2}} \left (24 e x^4-96 x^5\right )} \, dx=\frac {- 25 x^{2} + \left (- 200 x^{2} + 50 e x\right ) e^{\frac {2 x + 8}{x^{2}}}}{256 x^{4} - 128 e x^{3} + 16 x^{2} e^{2} + \left (2048 x^{4} - 1536 e x^{3} + 384 x^{2} e^{2} - 32 x e^{3}\right ) e^{\frac {2 x + 8}{x^{2}}} + \left (4096 x^{4} - 4096 e x^{3} + 1536 x^{2} e^{2} - 256 x e^{3} + 16 e^{4}\right ) e^{\frac {2 \cdot \left (2 x + 8\right )}{x^{2}}}} + \frac {25}{256 x^{2} - 128 e x + 16 e^{2}}
\]
[In]
integrate((100*x**2*exp((2*x+8)/x**2)**3+(25*x**2+50*x+400)*exp((2*x+8)/x**2)**2)/((8*x**2*exp(1)**3-96*x**3*e
xp(1)**2+384*x**4*exp(1)-512*x**5)*exp((2*x+8)/x**2)**3+(-24*x**3*exp(1)**2+192*x**4*exp(1)-384*x**5)*exp((2*x
+8)/x**2)**2+(24*x**4*exp(1)-96*x**5)*exp((2*x+8)/x**2)-8*x**5),x)
[Out]
(-25*x**2 + (-200*x**2 + 50*E*x)*exp((2*x + 8)/x**2))/(256*x**4 - 128*E*x**3 + 16*x**2*exp(2) + (2048*x**4 - 1
536*E*x**3 + 384*x**2*exp(2) - 32*x*exp(3))*exp((2*x + 8)/x**2) + (4096*x**4 - 4096*E*x**3 + 1536*x**2*exp(2)
- 256*x*exp(3) + 16*exp(4))*exp(2*(2*x + 8)/x**2)) + 25/(256*x**2 - 128*E*x + 16*exp(2))
Maxima [B] (verification not implemented)
Leaf count of result is larger than twice the leaf count of optimal. 71 vs. \(2 (23) = 46\).
Time = 0.29 (sec) , antiderivative size = 71, normalized size of antiderivative = 2.37
\[
\int \frac {100 e^{\frac {3 (8+2 x)}{x^2}} x^2+e^{\frac {2 (8+2 x)}{x^2}} \left (400+50 x+25 x^2\right )}{-8 x^5+e^{\frac {3 (8+2 x)}{x^2}} \left (8 e^3 x^2-96 e^2 x^3+384 e x^4-512 x^5\right )+e^{\frac {2 (8+2 x)}{x^2}} \left (-24 e^2 x^3+192 e x^4-384 x^5\right )+e^{\frac {8+2 x}{x^2}} \left (24 e x^4-96 x^5\right )} \, dx=\frac {25 \, e^{\left (\frac {4}{x} + \frac {16}{x^{2}}\right )}}{16 \, {\left (x^{2} + {\left (16 \, x^{2} - 8 \, x e + e^{2}\right )} e^{\left (\frac {4}{x} + \frac {16}{x^{2}}\right )} + 2 \, {\left (4 \, x^{2} - x e\right )} e^{\left (\frac {2}{x} + \frac {8}{x^{2}}\right )}\right )}}
\]
[In]
integrate((100*x^2*exp((2*x+8)/x^2)^3+(25*x^2+50*x+400)*exp((2*x+8)/x^2)^2)/((8*x^2*exp(1)^3-96*x^3*exp(1)^2+3
84*x^4*exp(1)-512*x^5)*exp((2*x+8)/x^2)^3+(-24*x^3*exp(1)^2+192*x^4*exp(1)-384*x^5)*exp((2*x+8)/x^2)^2+(24*x^4
*exp(1)-96*x^5)*exp((2*x+8)/x^2)-8*x^5),x, algorithm="maxima")
[Out]
25/16*e^(4/x + 16/x^2)/(x^2 + (16*x^2 - 8*x*e + e^2)*e^(4/x + 16/x^2) + 2*(4*x^2 - x*e)*e^(2/x + 8/x^2))
Giac [B] (verification not implemented)
Leaf count of result is larger than twice the leaf count of optimal. 28878 vs. \(2 (23) = 46\).
Time = 0.63 (sec) , antiderivative size = 28878, normalized size of antiderivative = 962.60
\[
\int \frac {100 e^{\frac {3 (8+2 x)}{x^2}} x^2+e^{\frac {2 (8+2 x)}{x^2}} \left (400+50 x+25 x^2\right )}{-8 x^5+e^{\frac {3 (8+2 x)}{x^2}} \left (8 e^3 x^2-96 e^2 x^3+384 e x^4-512 x^5\right )+e^{\frac {2 (8+2 x)}{x^2}} \left (-24 e^2 x^3+192 e x^4-384 x^5\right )+e^{\frac {8+2 x}{x^2}} \left (24 e x^4-96 x^5\right )} \, dx=\text {Too large to display}
\]
[In]
integrate((100*x^2*exp((2*x+8)/x^2)^3+(25*x^2+50*x+400)*exp((2*x+8)/x^2)^2)/((8*x^2*exp(1)^3-96*x^3*exp(1)^2+3
84*x^4*exp(1)-512*x^5)*exp((2*x+8)/x^2)^3+(-24*x^3*exp(1)^2+192*x^4*exp(1)-384*x^5)*exp((2*x+8)/x^2)^2+(24*x^4
*exp(1)-96*x^5)*exp((2*x+8)/x^2)-8*x^5),x, algorithm="giac")
[Out]
25/16*(65536*x^14*e^(22*(x + 4)/x^2) + 131072*x^14*e^(20*(x + 4)/x^2) + 114688*x^14*e^(18*(x + 4)/x^2) + 57344
*x^14*e^(16*(x + 4)/x^2) + 17920*x^14*e^(14*(x + 4)/x^2) + 3584*x^14*e^(12*(x + 4)/x^2) + 448*x^14*e^(10*(x +
4)/x^2) + 32*x^14*e^(8*(x + 4)/x^2) + x^14*e^(6*(x + 4)/x^2) - 8192*x^13*e^((x^2 + 3*x + 12)/x^2 + 17*(x + 4)/
x^2) - 12288*x^13*e^((x^2 + 3*x + 12)/x^2 + 15*(x + 4)/x^2) - 7680*x^13*e^((x^2 + 3*x + 12)/x^2 + 13*(x + 4)/x
^2) - 2560*x^13*e^((x^2 + 3*x + 12)/x^2 + 11*(x + 4)/x^2) - 480*x^13*e^((x^2 + 3*x + 12)/x^2 + 9*(x + 4)/x^2)
- 48*x^13*e^((x^2 + 3*x + 12)/x^2 + 7*(x + 4)/x^2) - 2*x^13*e^((x^2 + 3*x + 12)/x^2 + 5*(x + 4)/x^2) - 32768*x
^13*e^((x^2 + 2*x + 8)/x^2 + 20*(x + 4)/x^2) - 49152*x^13*e^((x^2 + 2*x + 8)/x^2 + 18*(x + 4)/x^2) - 30720*x^1
3*e^((x^2 + 2*x + 8)/x^2 + 16*(x + 4)/x^2) - 10240*x^13*e^((x^2 + 2*x + 8)/x^2 + 14*(x + 4)/x^2) - 1920*x^13*e
^((x^2 + 2*x + 8)/x^2 + 12*(x + 4)/x^2) - 192*x^13*e^((x^2 + 2*x + 8)/x^2 + 10*(x + 4)/x^2) - 8*x^13*e^((x^2 +
2*x + 8)/x^2 + 8*(x + 4)/x^2) + 196608*x^13*e^(20*(x + 4)/x^2) + 344064*x^13*e^(18*(x + 4)/x^2) + 258048*x^13
*e^(16*(x + 4)/x^2) + 107520*x^13*e^(14*(x + 4)/x^2) + 26880*x^13*e^(12*(x + 4)/x^2) + 4032*x^13*e^(10*(x + 4)
/x^2) + 336*x^13*e^(8*(x + 4)/x^2) + 12*x^13*e^(6*(x + 4)/x^2) + 1024*x^12*e^(2*(x^2 + 3*x + 12)/x^2 + 14*(x +
4)/x^2) + 1280*x^12*e^(2*(x^2 + 3*x + 12)/x^2 + 12*(x + 4)/x^2) + 640*x^12*e^(2*(x^2 + 3*x + 12)/x^2 + 10*(x
+ 4)/x^2) + 160*x^12*e^(2*(x^2 + 3*x + 12)/x^2 + 8*(x + 4)/x^2) + 20*x^12*e^(2*(x^2 + 3*x + 12)/x^2 + 6*(x + 4
)/x^2) + x^12*e^(2*(x^2 + 3*x + 12)/x^2 + 4*(x + 4)/x^2) - 16384*x^12*e^((x^2 + 3*x + 12)/x^2 + 17*(x + 4)/x^2
) - 45056*x^12*e^((x^2 + 3*x + 12)/x^2 + 15*(x + 4)/x^2) - 40960*x^12*e^((x^2 + 3*x + 12)/x^2 + 13*(x + 4)/x^2
) - 17920*x^12*e^((x^2 + 3*x + 12)/x^2 + 11*(x + 4)/x^2) - 4160*x^12*e^((x^2 + 3*x + 12)/x^2 + 9*(x + 4)/x^2)
- 496*x^12*e^((x^2 + 3*x + 12)/x^2 + 7*(x + 4)/x^2) - 24*x^12*e^((x^2 + 3*x + 12)/x^2 + 5*(x + 4)/x^2) + 4096*
x^12*e^(2*(x^2 + 2*x + 8)/x^2 + 18*(x + 4)/x^2) + 5120*x^12*e^(2*(x^2 + 2*x + 8)/x^2 + 16*(x + 4)/x^2) + 2560*
x^12*e^(2*(x^2 + 2*x + 8)/x^2 + 14*(x + 4)/x^2) + 640*x^12*e^(2*(x^2 + 2*x + 8)/x^2 + 12*(x + 4)/x^2) + 80*x^1
2*e^(2*(x^2 + 2*x + 8)/x^2 + 10*(x + 4)/x^2) + 4*x^12*e^(2*(x^2 + 2*x + 8)/x^2 + 8*(x + 4)/x^2) - 81920*x^12*e
^((x^2 + 2*x + 8)/x^2 + 18*(x + 4)/x^2) - 102400*x^12*e^((x^2 + 2*x + 8)/x^2 + 16*(x + 4)/x^2) - 51200*x^12*e^
((x^2 + 2*x + 8)/x^2 + 14*(x + 4)/x^2) - 12800*x^12*e^((x^2 + 2*x + 8)/x^2 + 12*(x + 4)/x^2) - 1600*x^12*e^((x
^2 + 2*x + 8)/x^2 + 10*(x + 4)/x^2) - 80*x^12*e^((x^2 + 2*x + 8)/x^2 + 8*(x + 4)/x^2) + 1572864*x^12*e^(20*(x
+ 4)/x^2) + 2998272*x^12*e^(18*(x + 4)/x^2) + 2433024*x^12*e^(16*(x + 4)/x^2) + 1090560*x^12*e^(14*(x + 4)/x^2
) + 291840*x^12*e^(12*(x + 4)/x^2) + 46656*x^12*e^(10*(x + 4)/x^2) + 4128*x^12*e^(8*(x + 4)/x^2) + 156*x^12*e^
(6*(x + 4)/x^2) + 2048*x^11*e^(2*(x^2 + 3*x + 12)/x^2 + 14*(x + 4)/x^2) + 5120*x^11*e^(2*(x^2 + 3*x + 12)/x^2
+ 12*(x + 4)/x^2) + 3840*x^11*e^(2*(x^2 + 3*x + 12)/x^2 + 10*(x + 4)/x^2) + 1280*x^11*e^(2*(x^2 + 3*x + 12)/x^
2 + 8*(x + 4)/x^2) + 200*x^11*e^(2*(x^2 + 3*x + 12)/x^2 + 6*(x + 4)/x^2) + 12*x^11*e^(2*(x^2 + 3*x + 12)/x^2 +
4*(x + 4)/x^2) - 81920*x^11*e^((x^2 + 3*x + 12)/x^2 + 17*(x + 4)/x^2) - 339968*x^11*e^((x^2 + 3*x + 12)/x^2 +
15*(x + 4)/x^2) - 368640*x^11*e^((x^2 + 3*x + 12)/x^2 + 13*(x + 4)/x^2) - 181760*x^11*e^((x^2 + 3*x + 12)/x^2
+ 11*(x + 4)/x^2) - 46400*x^11*e^((x^2 + 3*x + 12)/x^2 + 9*(x + 4)/x^2) - 6000*x^11*e^((x^2 + 3*x + 12)/x^2 +
7*(x + 4)/x^2) - 312*x^11*e^((x^2 + 3*x + 12)/x^2 + 5*(x + 4)/x^2) + 10240*x^11*e^(2*(x^2 + 2*x + 8)/x^2 + 16
*(x + 4)/x^2) + 10240*x^11*e^(2*(x^2 + 2*x + 8)/x^2 + 14*(x + 4)/x^2) + 3840*x^11*e^(2*(x^2 + 2*x + 8)/x^2 + 1
2*(x + 4)/x^2) + 640*x^11*e^(2*(x^2 + 2*x + 8)/x^2 + 10*(x + 4)/x^2) + 40*x^11*e^(2*(x^2 + 2*x + 8)/x^2 + 8*(x
+ 4)/x^2) - 704512*x^11*e^((x^2 + 2*x + 8)/x^2 + 18*(x + 4)/x^2) - 962560*x^11*e^((x^2 + 2*x + 8)/x^2 + 16*(x
+ 4)/x^2) - 522240*x^11*e^((x^2 + 2*x + 8)/x^2 + 14*(x + 4)/x^2) - 140800*x^11*e^((x^2 + 2*x + 8)/x^2 + 12*(x
+ 4)/x^2) - 18880*x^11*e^((x^2 + 2*x + 8)/x^2 + 10*(x + 4)/x^2) - 1008*x^11*e^((x^2 + 2*x + 8)/x^2 + 8*(x + 4
)/x^2) + 3932160*x^11*e^(18*(x + 4)/x^2) + 6062080*x^11*e^(16*(x + 4)/x^2) + 3891200*x^11*e^(14*(x + 4)/x^2) +
1331200*x^11*e^(12*(x + 4)/x^2) + 256000*x^11*e^(10*(x + 4)/x^2) + 26240*x^11*e^(8*(x + 4)/x^2) + 1120*x^11*e
^(6*(x + 4)/x^2) + 4096*x^10*e^(2*(x^2 + 3*x + 12)/x^2 + 14*(x + 4)/x^2) + 33792*x^10*e^(2*(x^2 + 3*x + 12)/x^
2 + 12*(x + 4)/x^2) + 33792*x^10*e^(2*(x^2 + 3*x + 12)/x^2 + 10*(x + 4)/x^2) + 13312*x^10*e^(2*(x^2 + 3*x + 12
)/x^2 + 8*(x + 4)/x^2) + 2352*x^10*e^(2*(x^2 + 3*x + 12)/x^2 + 6*(x + 4)/x^2) + 156*x^10*e^(2*(x^2 + 3*x + 12)
/x^2 + 4*(x + 4)/x^2) - 262144*x^10*e^((x^2 + 3*x + 12)/x^2 + 17*(x + 4)/x^2) - 909312*x^10*e^((x^2 + 3*x + 12
)/x^2 + 15*(x + 4)/x^2) - 1277952*x^10*e^((x^2 + 3*x + 12)/x^2 + 13*(x + 4)/x^2) - 801792*x^10*e^((x^2 + 3*x +
12)/x^2 + 11*(x + 4)/x^2) - 248832*x^10*e^((x^2 + 3*x + 12)/x^2 + 9*(x + 4)/x^2) - 37728*x^10*e^((x^2 + 3*x +
12)/x^2 + 7*(x + 4)/x^2) - 2240*x^10*e^((x^2 + 3*x + 12)/x^2 + 5*(x + 4)/x^2) + 94208*x^10*e^(2*(x^2 + 2*x +
8)/x^2 + 16*(x + 4)/x^2) + 104448*x^10*e^(2*(x^2 + 2*x + 8)/x^2 + 14*(x + 4)/x^2) + 43008*x^10*e^(2*(x^2 + 2*x
+ 8)/x^2 + 12*(x + 4)/x^2) + 7808*x^10*e^(2*(x^2 + 2*x + 8)/x^2 + 10*(x + 4)/x^2) + 528*x^10*e^(2*(x^2 + 2*x
+ 8)/x^2 + 8*(x + 4)/x^2) + 262144*x^10*e^((x^2 + 2*x + 8)/x^2 + 18*(x + 4)/x^2) - 1056768*x^10*e^((x^2 + 2*x
+ 8)/x^2 + 16*(x + 4)/x^2) - 1261568*x^10*e^((x^2 + 2*x + 8)/x^2 + 14*(x + 4)/x^2) - 508928*x^10*e^((x^2 + 2*x
+ 8)/x^2 + 12*(x + 4)/x^2) - 89088*x^10*e^((x^2 + 2*x + 8)/x^2 + 10*(x + 4)/x^2) - 5792*x^10*e^((x^2 + 2*x +
8)/x^2 + 8*(x + 4)/x^2) + 15728640*x^10*e^(18*(x + 4)/x^2) + 27525120*x^10*e^(16*(x + 4)/x^2) + 19722240*x^10*
e^(14*(x + 4)/x^2) + 7434240*x^10*e^(12*(x + 4)/x^2) + 1559040*x^10*e^(10*(x + 4)/x^2) + 172800*x^10*e^(8*(x +
4)/x^2) + 7920*x^10*e^(6*(x + 4)/x^2) + 3072*x^9*e^(2*(x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 12*(x + 4)
/x^2) + 2304*x^9*e^(2*(x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 10*(x + 4)/x^2) + 576*x^9*e^(2*(x^2 + 3*x +
12)/x^2 + (x^2 + 2*x + 8)/x^2 + 8*(x + 4)/x^2) + 48*x^9*e^(2*(x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 6*(
x + 4)/x^2) + 65536*x^9*e^(2*(x^2 + 3*x + 12)/x^2 + 14*(x + 4)/x^2) + 129024*x^9*e^(2*(x^2 + 3*x + 12)/x^2 + 1
2*(x + 4)/x^2) + 138752*x^9*e^(2*(x^2 + 3*x + 12)/x^2 + 10*(x + 4)/x^2) + 67200*x^9*e^(2*(x^2 + 3*x + 12)/x^2
+ 8*(x + 4)/x^2) + 14368*x^9*e^(2*(x^2 + 3*x + 12)/x^2 + 6*(x + 4)/x^2) + 1120*x^9*e^(2*(x^2 + 3*x + 12)/x^2 +
4*(x + 4)/x^2) - 3072*x^9*e^((x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 13*(x + 4)/x^2) - 2304*x^9*e^((x^
2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 11*(x + 4)/x^2) - 576*x^9*e^((x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x +
8)/x^2 + 9*(x + 4)/x^2) - 48*x^9*e^((x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 7*(x + 4)/x^2) - 1048576*x
^9*e^((x^2 + 3*x + 12)/x^2 + 17*(x + 4)/x^2) - 3735552*x^9*e^((x^2 + 3*x + 12)/x^2 + 15*(x + 4)/x^2) - 5992448
*x^9*e^((x^2 + 3*x + 12)/x^2 + 13*(x + 4)/x^2) - 4260864*x^9*e^((x^2 + 3*x + 12)/x^2 + 11*(x + 4)/x^2) - 14732
80*x^9*e^((x^2 + 3*x + 12)/x^2 + 9*(x + 4)/x^2) - 245440*x^9*e^((x^2 + 3*x + 12)/x^2 + 7*(x + 4)/x^2) - 15840*
x^9*e^((x^2 + 3*x + 12)/x^2 + 5*(x + 4)/x^2) - 65536*x^9*e^(2*(x^2 + 2*x + 8)/x^2 + 16*(x + 4)/x^2) + 116736*x
^9*e^(2*(x^2 + 2*x + 8)/x^2 + 14*(x + 4)/x^2) + 117248*x^9*e^(2*(x^2 + 2*x + 8)/x^2 + 12*(x + 4)/x^2) + 32640*
x^9*e^(2*(x^2 + 2*x + 8)/x^2 + 10*(x + 4)/x^2) + 2912*x^9*e^(2*(x^2 + 2*x + 8)/x^2 + 8*(x + 4)/x^2) + 1048576*
x^9*e^((x^2 + 2*x + 8)/x^2 + 18*(x + 4)/x^2) - 4128768*x^9*e^((x^2 + 2*x + 8)/x^2 + 16*(x + 4)/x^2) - 5804032*
x^9*e^((x^2 + 2*x + 8)/x^2 + 14*(x + 4)/x^2) - 2651136*x^9*e^((x^2 + 2*x + 8)/x^2 + 12*(x + 4)/x^2) - 515840*x
^9*e^((x^2 + 2*x + 8)/x^2 + 10*(x + 4)/x^2) - 36800*x^9*e^((x^2 + 2*x + 8)/x^2 + 8*(x + 4)/x^2) + 31457280*x^9
*e^(16*(x + 4)/x^2) + 41287680*x^9*e^(14*(x + 4)/x^2) + 21639168*x^9*e^(12*(x + 4)/x^2) + 5661696*x^9*e^(10*(x
+ 4)/x^2) + 739584*x^9*e^(8*(x + 4)/x^2) + 38592*x^9*e^(6*(x + 4)/x^2) - 16384*x^8*e^(2*(x^2 + 3*x + 12)/x^2
+ (x^2 + 2*x + 8)/x^2 + 12*(x + 4)/x^2) - 7680*x^8*e^(2*(x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 10*(x + 4
)/x^2) - 768*x^8*e^(2*(x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 8*(x + 4)/x^2) + 32*x^8*e^(2*(x^2 + 3*x + 1
2)/x^2 + (x^2 + 2*x + 8)/x^2 + 6*(x + 4)/x^2) + 262144*x^8*e^(2*(x^2 + 3*x + 12)/x^2 + 14*(x + 4)/x^2) + 54067
2*x^8*e^(2*(x^2 + 3*x + 12)/x^2 + 12*(x + 4)/x^2) + 666624*x^8*e^(2*(x^2 + 3*x + 12)/x^2 + 10*(x + 4)/x^2) + 3
73760*x^8*e^(2*(x^2 + 3*x + 12)/x^2 + 8*(x + 4)/x^2) + 90880*x^8*e^(2*(x^2 + 3*x + 12)/x^2 + 6*(x + 4)/x^2) +
7920*x^8*e^(2*(x^2 + 3*x + 12)/x^2 + 4*(x + 4)/x^2) + 16384*x^8*e^((x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^
2 + 13*(x + 4)/x^2) + 7680*x^8*e^((x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 11*(x + 4)/x^2) + 768*x^8*e^(
(x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 9*(x + 4)/x^2) - 32*x^8*e^((x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x
+ 8)/x^2 + 7*(x + 4)/x^2) - 4718592*x^8*e^((x^2 + 3*x + 12)/x^2 + 15*(x + 4)/x^2) - 12189696*x^8*e^((x^2 + 3*x
+ 12)/x^2 + 13*(x + 4)/x^2) - 11954176*x^8*e^((x^2 + 3*x + 12)/x^2 + 11*(x + 4)/x^2) - 5220352*x^8*e^((x^2 +
3*x + 12)/x^2 + 9*(x + 4)/x^2) - 1038720*x^8*e^((x^2 + 3*x + 12)/x^2 + 7*(x + 4)/x^2) - 77184*x^8*e^((x^2 + 3*
x + 12)/x^2 + 5*(x + 4)/x^2) - 262144*x^8*e^(2*(x^2 + 2*x + 8)/x^2 + 16*(x + 4)/x^2) + 442368*x^8*e^(2*(x^2 +
2*x + 8)/x^2 + 14*(x + 4)/x^2) + 562176*x^8*e^(2*(x^2 + 2*x + 8)/x^2 + 12*(x + 4)/x^2) + 183040*x^8*e^(2*(x^2
+ 2*x + 8)/x^2 + 10*(x + 4)/x^2) + 18560*x^8*e^(2*(x^2 + 2*x + 8)/x^2 + 8*(x + 4)/x^2) + 4718592*x^8*e^((x^2 +
2*x + 8)/x^2 + 16*(x + 4)/x^2) - 3538944*x^8*e^((x^2 + 2*x + 8)/x^2 + 14*(x + 4)/x^2) - 4757504*x^8*e^((x^2 +
2*x + 8)/x^2 + 12*(x + 4)/x^2) - 1421312*x^8*e^((x^2 + 2*x + 8)/x^2 + 10*(x + 4)/x^2) - 131712*x^8*e^((x^2 +
2*x + 8)/x^2 + 8*(x + 4)/x^2) + 83886080*x^8*e^(16*(x + 4)/x^2) + 128450560*x^8*e^(14*(x + 4)/x^2) + 76513280*
x^8*e^(12*(x + 4)/x^2) + 22324224*x^8*e^(10*(x + 4)/x^2) + 3205632*x^8*e^(8*(x + 4)/x^2) + 181824*x^8*e^(6*(x
+ 4)/x^2) - 65536*x^7*e^(2*(x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 12*(x + 4)/x^2) - 36864*x^7*e^(2*(x^2
+ 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 10*(x + 4)/x^2) - 3840*x^7*e^(2*(x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)
/x^2 + 8*(x + 4)/x^2) + 320*x^7*e^(2*(x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 6*(x + 4)/x^2) + 1179648*x^7
*e^(2*(x^2 + 3*x + 12)/x^2 + 12*(x + 4)/x^2) + 1769472*x^7*e^(2*(x^2 + 3*x + 12)/x^2 + 10*(x + 4)/x^2) + 12354
56*x^7*e^(2*(x^2 + 3*x + 12)/x^2 + 8*(x + 4)/x^2) + 370944*x^7*e^(2*(x^2 + 3*x + 12)/x^2 + 6*(x + 4)/x^2) + 38
592*x^7*e^(2*(x^2 + 3*x + 12)/x^2 + 4*(x + 4)/x^2) + 65536*x^7*e^((x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2
+ 13*(x + 4)/x^2) + 36864*x^7*e^((x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 11*(x + 4)/x^2) + 3840*x^7*e^
((x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 9*(x + 4)/x^2) - 320*x^7*e^((x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*
x + 8)/x^2 + 7*(x + 4)/x^2) - 12582912*x^7*e^((x^2 + 3*x + 12)/x^2 + 15*(x + 4)/x^2) - 35127296*x^7*e^((x^2 +
3*x + 12)/x^2 + 13*(x + 4)/x^2) - 39862272*x^7*e^((x^2 + 3*x + 12)/x^2 + 11*(x + 4)/x^2) - 19906560*x^7*e^((x^
2 + 3*x + 12)/x^2 + 9*(x + 4)/x^2) - 4439552*x^7*e^((x^2 + 3*x + 12)/x^2 + 7*(x + 4)/x^2) - 363648*x^7*e^((x^2
+ 3*x + 12)/x^2 + 5*(x + 4)/x^2) - 1179648*x^7*e^(2*(x^2 + 2*x + 8)/x^2 + 14*(x + 4)/x^2) + 196608*x^7*e^(2*(
x^2 + 2*x + 8)/x^2 + 12*(x + 4)/x^2) + 361984*x^7*e^(2*(x^2 + 2*x + 8)/x^2 + 10*(x + 4)/x^2) + 59904*x^7*e^(2*
(x^2 + 2*x + 8)/x^2 + 8*(x + 4)/x^2) + 12582912*x^7*e^((x^2 + 2*x + 8)/x^2 + 16*(x + 4)/x^2) - 6815744*x^7*e^(
(x^2 + 2*x + 8)/x^2 + 14*(x + 4)/x^2) - 13877248*x^7*e^((x^2 + 2*x + 8)/x^2 + 12*(x + 4)/x^2) - 4915200*x^7*e^
((x^2 + 2*x + 8)/x^2 + 10*(x + 4)/x^2) - 517120*x^7*e^((x^2 + 2*x + 8)/x^2 + 8*(x + 4)/x^2) + 125829120*x^7*e^
(14*(x + 4)/x^2) + 133693440*x^7*e^(12*(x + 4)/x^2) + 53133312*x^7*e^(10*(x + 4)/x^2) + 9363456*x^7*e^(8*(x +
4)/x^2) + 617472*x^7*e^(6*(x + 4)/x^2) - 294912*x^6*e^(2*(x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 10*(x +
4)/x^2) - 122880*x^6*e^(2*(x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 8*(x + 4)/x^2) - 11904*x^6*e^(2*(x^2 +
3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 6*(x + 4)/x^2) + 3145728*x^6*e^(2*(x^2 + 3*x + 12)/x^2 + 12*(x + 4)/x^2)
+ 5373952*x^6*e^(2*(x^2 + 3*x + 12)/x^2 + 10*(x + 4)/x^2) + 4362240*x^6*e^(2*(x^2 + 3*x + 12)/x^2 + 8*(x + 4)
/x^2) + 1525760*x^6*e^(2*(x^2 + 3*x + 12)/x^2 + 6*(x + 4)/x^2) + 181824*x^6*e^(2*(x^2 + 3*x + 12)/x^2 + 4*(x +
4)/x^2) + 294912*x^6*e^((x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 11*(x + 4)/x^2) + 122880*x^6*e^((x^2 +
3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 9*(x + 4)/x^2) + 11904*x^6*e^((x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8
)/x^2 + 7*(x + 4)/x^2) - 25165824*x^6*e^((x^2 + 3*x + 12)/x^2 + 13*(x + 4)/x^2) - 60555264*x^6*e^((x^2 + 3*x +
12)/x^2 + 11*(x + 4)/x^2) - 44564480*x^6*e^((x^2 + 3*x + 12)/x^2 + 9*(x + 4)/x^2) - 12689408*x^6*e^((x^2 + 3*
x + 12)/x^2 + 7*(x + 4)/x^2) - 1234944*x^6*e^((x^2 + 3*x + 12)/x^2 + 5*(x + 4)/x^2) - 3145728*x^6*e^(2*(x^2 +
2*x + 8)/x^2 + 14*(x + 4)/x^2) - 131072*x^6*e^(2*(x^2 + 2*x + 8)/x^2 + 12*(x + 4)/x^2) + 1044480*x^6*e^(2*(x^2
+ 2*x + 8)/x^2 + 10*(x + 4)/x^2) + 225280*x^6*e^(2*(x^2 + 2*x + 8)/x^2 + 8*(x + 4)/x^2) + 25165824*x^6*e^((x^
2 + 2*x + 8)/x^2 + 14*(x + 4)/x^2) - 2359296*x^6*e^((x^2 + 2*x + 8)/x^2 + 12*(x + 4)/x^2) - 6553600*x^6*e^((x^
2 + 2*x + 8)/x^2 + 10*(x + 4)/x^2) - 1097728*x^6*e^((x^2 + 2*x + 8)/x^2 + 8*(x + 4)/x^2) + 251658240*x^6*e^(14
*(x + 4)/x^2) + 314572800*x^6*e^(12*(x + 4)/x^2) + 142540800*x^6*e^(10*(x + 4)/x^2) + 28016640*x^6*e^(8*(x + 4
)/x^2) + 2027520*x^6*e^(6*(x + 4)/x^2) - 786432*x^5*e^(2*(x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 10*(x +
4)/x^2) - 491520*x^5*e^(2*(x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 8*(x + 4)/x^2) - 66560*x^5*e^(2*(x^2 +
3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 6*(x + 4)/x^2) + 6291456*x^5*e^(2*(x^2 + 3*x + 12)/x^2 + 10*(x + 4)/x^2)
+ 8323072*x^5*e^(2*(x^2 + 3*x + 12)/x^2 + 8*(x + 4)/x^2) + 4063232*x^5*e^(2*(x^2 + 3*x + 12)/x^2 + 6*(x + 4)/
x^2) + 617472*x^5*e^(2*(x^2 + 3*x + 12)/x^2 + 4*(x + 4)/x^2) + 786432*x^5*e^((x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2
*x + 8)/x^2 + 11*(x + 4)/x^2) + 491520*x^5*e^((x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 9*(x + 4)/x^2) +
66560*x^5*e^((x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 7*(x + 4)/x^2) - 50331648*x^5*e^((x^2 + 3*x + 12)/
x^2 + 13*(x + 4)/x^2) - 127926272*x^5*e^((x^2 + 3*x + 12)/x^2 + 11*(x + 4)/x^2) - 112197632*x^5*e^((x^2 + 3*x
+ 12)/x^2 + 9*(x + 4)/x^2) - 37060608*x^5*e^((x^2 + 3*x + 12)/x^2 + 7*(x + 4)/x^2) - 4055040*x^5*e^((x^2 + 3*x
+ 12)/x^2 + 5*(x + 4)/x^2) - 6291456*x^5*e^(2*(x^2 + 2*x + 8)/x^2 + 12*(x + 4)/x^2) - 458752*x^5*e^(2*(x^2 +
2*x + 8)/x^2 + 10*(x + 4)/x^2) + 360448*x^5*e^(2*(x^2 + 2*x + 8)/x^2 + 8*(x + 4)/x^2) + 50331648*x^5*e^((x^2 +
2*x + 8)/x^2 + 14*(x + 4)/x^2) + 2097152*x^5*e^((x^2 + 2*x + 8)/x^2 + 12*(x + 4)/x^2) - 13631488*x^5*e^((x^2
+ 2*x + 8)/x^2 + 10*(x + 4)/x^2) - 2752512*x^5*e^((x^2 + 2*x + 8)/x^2 + 8*(x + 4)/x^2) + 251658240*x^5*e^(12*(
x + 4)/x^2) + 199229440*x^5*e^(10*(x + 4)/x^2) + 52428800*x^5*e^(8*(x + 4)/x^2) + 4587520*x^5*e^(6*(x + 4)/x^2
) - 1572864*x^4*e^(2*(x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 8*(x + 4)/x^2) - 376832*x^4*e^(2*(x^2 + 3*x
+ 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 6*(x + 4)/x^2) + 12582912*x^4*e^(2*(x^2 + 3*x + 12)/x^2 + 10*(x + 4)/x^2) +
18350080*x^4*e^(2*(x^2 + 3*x + 12)/x^2 + 8*(x + 4)/x^2) + 11010048*x^4*e^(2*(x^2 + 3*x + 12)/x^2 + 6*(x + 4)/x
^2) + 2027520*x^4*e^(2*(x^2 + 3*x + 12)/x^2 + 4*(x + 4)/x^2) + 1572864*x^4*e^((x^2 + 3*x + 12)/x^2 + 2*(x^2 +
2*x + 8)/x^2 + 9*(x + 4)/x^2) + 376832*x^4*e^((x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 7*(x + 4)/x^2) -
41943040*x^4*e^((x^2 + 3*x + 12)/x^2 + 11*(x + 4)/x^2) - 125829120*x^4*e^((x^2 + 3*x + 12)/x^2 + 9*(x + 4)/x^2
) - 65536000*x^4*e^((x^2 + 3*x + 12)/x^2 + 7*(x + 4)/x^2) - 9175040*x^4*e^((x^2 + 3*x + 12)/x^2 + 5*(x + 4)/x^
2) - 12582912*x^4*e^(2*(x^2 + 2*x + 8)/x^2 + 12*(x + 4)/x^2) - 2621440*x^4*e^(2*(x^2 + 2*x + 8)/x^2 + 10*(x +
4)/x^2) + 786432*x^4*e^(2*(x^2 + 2*x + 8)/x^2 + 8*(x + 4)/x^2) + 41943040*x^4*e^((x^2 + 2*x + 8)/x^2 + 12*(x +
4)/x^2) - 2621440*x^4*e^((x^2 + 2*x + 8)/x^2 + 8*(x + 4)/x^2) + 402653184*x^4*e^(12*(x + 4)/x^2) + 364904448*
x^4*e^(10*(x + 4)/x^2) + 106954752*x^4*e^(8*(x + 4)/x^2) + 10223616*x^4*e^(6*(x + 4)/x^2) - 3145728*x^3*e^(2*(
x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 8*(x + 4)/x^2) - 1179648*x^3*e^(2*(x^2 + 3*x + 12)/x^2 + (x^2 + 2*
x + 8)/x^2 + 6*(x + 4)/x^2) + 10485760*x^3*e^(2*(x^2 + 3*x + 12)/x^2 + 8*(x + 4)/x^2) + 15728640*x^3*e^(2*(x^2
+ 3*x + 12)/x^2 + 6*(x + 4)/x^2) + 4587520*x^3*e^(2*(x^2 + 3*x + 12)/x^2 + 4*(x + 4)/x^2) + 3145728*x^3*e^((x
^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 9*(x + 4)/x^2) + 1179648*x^3*e^((x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2
*x + 8)/x^2 + 7*(x + 4)/x^2) - 67108864*x^3*e^((x^2 + 3*x + 12)/x^2 + 11*(x + 4)/x^2) - 201326592*x^3*e^((x^2
+ 3*x + 12)/x^2 + 9*(x + 4)/x^2) - 127926272*x^3*e^((x^2 + 3*x + 12)/x^2 + 7*(x + 4)/x^2) - 20447232*x^3*e^((x
^2 + 3*x + 12)/x^2 + 5*(x + 4)/x^2) - 10485760*x^3*e^(2*(x^2 + 2*x + 8)/x^2 + 10*(x + 4)/x^2) + 67108864*x^3*e
^((x^2 + 2*x + 8)/x^2 + 12*(x + 4)/x^2) - 4194304*x^3*e^((x^2 + 2*x + 8)/x^2 + 8*(x + 4)/x^2) + 201326592*x^3*
e^(10*(x + 4)/x^2) + 100663296*x^3*e^(8*(x + 4)/x^2) + 12582912*x^3*e^(6*(x + 4)/x^2) - 2621440*x^2*e^(2*(x^2
+ 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 6*(x + 4)/x^2) + 16777216*x^2*e^(2*(x^2 + 3*x + 12)/x^2 + 8*(x + 4)/x^
2) + 25165824*x^2*e^(2*(x^2 + 3*x + 12)/x^2 + 6*(x + 4)/x^2) + 10223616*x^2*e^(2*(x^2 + 3*x + 12)/x^2 + 4*(x +
4)/x^2) + 2621440*x^2*e^((x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 7*(x + 4)/x^2) - 100663296*x^2*e^((x^
2 + 3*x + 12)/x^2 + 7*(x + 4)/x^2) - 25165824*x^2*e^((x^2 + 3*x + 12)/x^2 + 5*(x + 4)/x^2) - 16777216*x^2*e^(2
*(x^2 + 2*x + 8)/x^2 + 10*(x + 4)/x^2) + 268435456*x^2*e^(10*(x + 4)/x^2) + 134217728*x^2*e^(8*(x + 4)/x^2) +
16777216*x^2*e^(6*(x + 4)/x^2) - 4194304*x*e^(2*(x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 6*(x + 4)/x^2) +
12582912*x*e^(2*(x^2 + 3*x + 12)/x^2 + 4*(x + 4)/x^2) + 4194304*x*e^((x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/
x^2 + 7*(x + 4)/x^2) - 134217728*x*e^((x^2 + 3*x + 12)/x^2 + 7*(x + 4)/x^2) - 33554432*x*e^((x^2 + 3*x + 12)/x
^2 + 5*(x + 4)/x^2) + 16777216*e^(2*(x^2 + 3*x + 12)/x^2 + 4*(x + 4)/x^2))/(1048576*x^16*e^(22*(x + 4)/x^2) +
2621440*x^16*e^(20*(x + 4)/x^2) + 2949120*x^16*e^(18*(x + 4)/x^2) + 1966080*x^16*e^(16*(x + 4)/x^2) + 860160*x
^16*e^(14*(x + 4)/x^2) + 258048*x^16*e^(12*(x + 4)/x^2) + 53760*x^16*e^(10*(x + 4)/x^2) + 7680*x^16*e^(8*(x +
4)/x^2) + 720*x^16*e^(6*(x + 4)/x^2) + 40*x^16*e^(4*(x + 4)/x^2) + x^16*e^(2*(x + 4)/x^2) - 524288*x^15*e^((x^
2 + 3*x + 12)/x^2 + 19*(x + 4)/x^2) - 1179648*x^15*e^((x^2 + 3*x + 12)/x^2 + 17*(x + 4)/x^2) - 1179648*x^15*e^
((x^2 + 3*x + 12)/x^2 + 15*(x + 4)/x^2) - 688128*x^15*e^((x^2 + 3*x + 12)/x^2 + 13*(x + 4)/x^2) - 258048*x^15*
e^((x^2 + 3*x + 12)/x^2 + 11*(x + 4)/x^2) - 64512*x^15*e^((x^2 + 3*x + 12)/x^2 + 9*(x + 4)/x^2) - 10752*x^15*e
^((x^2 + 3*x + 12)/x^2 + 7*(x + 4)/x^2) - 1152*x^15*e^((x^2 + 3*x + 12)/x^2 + 5*(x + 4)/x^2) - 72*x^15*e^((x^2
+ 3*x + 12)/x^2 + 3*(x + 4)/x^2) - 2*x^15*e^((x^2 + 3*x + 12)/x^2 + (x + 4)/x^2) - 524288*x^15*e^((x^2 + 2*x
+ 8)/x^2 + 20*(x + 4)/x^2) - 1179648*x^15*e^((x^2 + 2*x + 8)/x^2 + 18*(x + 4)/x^2) - 1179648*x^15*e^((x^2 + 2*
x + 8)/x^2 + 16*(x + 4)/x^2) - 688128*x^15*e^((x^2 + 2*x + 8)/x^2 + 14*(x + 4)/x^2) - 258048*x^15*e^((x^2 + 2*
x + 8)/x^2 + 12*(x + 4)/x^2) - 64512*x^15*e^((x^2 + 2*x + 8)/x^2 + 10*(x + 4)/x^2) - 10752*x^15*e^((x^2 + 2*x
+ 8)/x^2 + 8*(x + 4)/x^2) - 1152*x^15*e^((x^2 + 2*x + 8)/x^2 + 6*(x + 4)/x^2) - 72*x^15*e^((x^2 + 2*x + 8)/x^2
+ 4*(x + 4)/x^2) - 2*x^15*e^((x^2 + 2*x + 8)/x^2 + 2*(x + 4)/x^2) + 3145728*x^15*e^(20*(x + 4)/x^2) + 7077888
*x^15*e^(18*(x + 4)/x^2) + 7077888*x^15*e^(16*(x + 4)/x^2) + 4128768*x^15*e^(14*(x + 4)/x^2) + 1548288*x^15*e^
(12*(x + 4)/x^2) + 387072*x^15*e^(10*(x + 4)/x^2) + 64512*x^15*e^(8*(x + 4)/x^2) + 6912*x^15*e^(6*(x + 4)/x^2)
+ 432*x^15*e^(4*(x + 4)/x^2) + 12*x^15*e^(2*(x + 4)/x^2) + x^14*e^(2*(x^2 + 3*x + 12)/x^2) + 65536*x^14*e^(2*
(x^2 + 3*x + 12)/x^2 + 16*(x + 4)/x^2) + 131072*x^14*e^(2*(x^2 + 3*x + 12)/x^2 + 14*(x + 4)/x^2) + 114688*x^14
*e^(2*(x^2 + 3*x + 12)/x^2 + 12*(x + 4)/x^2) + 57344*x^14*e^(2*(x^2 + 3*x + 12)/x^2 + 10*(x + 4)/x^2) + 17920*
x^14*e^(2*(x^2 + 3*x + 12)/x^2 + 8*(x + 4)/x^2) + 3584*x^14*e^(2*(x^2 + 3*x + 12)/x^2 + 6*(x + 4)/x^2) + 448*x
^14*e^(2*(x^2 + 3*x + 12)/x^2 + 4*(x + 4)/x^2) + 32*x^14*e^(2*(x^2 + 3*x + 12)/x^2 + 2*(x + 4)/x^2) + 262144*x
^14*e^((x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 17*(x + 4)/x^2) + 524288*x^14*e^((x^2 + 3*x + 12)/x^2 + (x
^2 + 2*x + 8)/x^2 + 15*(x + 4)/x^2) + 458752*x^14*e^((x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 13*(x + 4)/x
^2) + 229376*x^14*e^((x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 11*(x + 4)/x^2) + 71680*x^14*e^((x^2 + 3*x +
12)/x^2 + (x^2 + 2*x + 8)/x^2 + 9*(x + 4)/x^2) + 14336*x^14*e^((x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 7
*(x + 4)/x^2) + 1792*x^14*e^((x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 5*(x + 4)/x^2) + 128*x^14*e^((x^2 +
3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 3*(x + 4)/x^2) + 4*x^14*e^((x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 +
(x + 4)/x^2) - 1572864*x^14*e^((x^2 + 3*x + 12)/x^2 + 17*(x + 4)/x^2) - 3145728*x^14*e^((x^2 + 3*x + 12)/x^2 +
15*(x + 4)/x^2) - 2752512*x^14*e^((x^2 + 3*x + 12)/x^2 + 13*(x + 4)/x^2) - 1376256*x^14*e^((x^2 + 3*x + 12)/x
^2 + 11*(x + 4)/x^2) - 430080*x^14*e^((x^2 + 3*x + 12)/x^2 + 9*(x + 4)/x^2) - 86016*x^14*e^((x^2 + 3*x + 12)/x
^2 + 7*(x + 4)/x^2) - 10752*x^14*e^((x^2 + 3*x + 12)/x^2 + 5*(x + 4)/x^2) - 768*x^14*e^((x^2 + 3*x + 12)/x^2 +
3*(x + 4)/x^2) - 24*x^14*e^((x^2 + 3*x + 12)/x^2 + (x + 4)/x^2) + 65536*x^14*e^(2*(x^2 + 2*x + 8)/x^2 + 18*(x
+ 4)/x^2) + 131072*x^14*e^(2*(x^2 + 2*x + 8)/x^2 + 16*(x + 4)/x^2) + 114688*x^14*e^(2*(x^2 + 2*x + 8)/x^2 + 1
4*(x + 4)/x^2) + 57344*x^14*e^(2*(x^2 + 2*x + 8)/x^2 + 12*(x + 4)/x^2) + 17920*x^14*e^(2*(x^2 + 2*x + 8)/x^2 +
10*(x + 4)/x^2) + 3584*x^14*e^(2*(x^2 + 2*x + 8)/x^2 + 8*(x + 4)/x^2) + 448*x^14*e^(2*(x^2 + 2*x + 8)/x^2 + 6
*(x + 4)/x^2) + 32*x^14*e^(2*(x^2 + 2*x + 8)/x^2 + 4*(x + 4)/x^2) + x^14*e^(2*(x^2 + 2*x + 8)/x^2 + 2*(x + 4)/
x^2) - 1572864*x^14*e^((x^2 + 2*x + 8)/x^2 + 18*(x + 4)/x^2) - 3145728*x^14*e^((x^2 + 2*x + 8)/x^2 + 16*(x + 4
)/x^2) - 2752512*x^14*e^((x^2 + 2*x + 8)/x^2 + 14*(x + 4)/x^2) - 1376256*x^14*e^((x^2 + 2*x + 8)/x^2 + 12*(x +
4)/x^2) - 430080*x^14*e^((x^2 + 2*x + 8)/x^2 + 10*(x + 4)/x^2) - 86016*x^14*e^((x^2 + 2*x + 8)/x^2 + 8*(x + 4
)/x^2) - 10752*x^14*e^((x^2 + 2*x + 8)/x^2 + 6*(x + 4)/x^2) - 768*x^14*e^((x^2 + 2*x + 8)/x^2 + 4*(x + 4)/x^2)
- 24*x^14*e^((x^2 + 2*x + 8)/x^2 + 2*(x + 4)/x^2) + 25165824*x^14*e^(20*(x + 4)/x^2) + 60555264*x^14*e^(18*(x
+ 4)/x^2) + 64487424*x^14*e^(16*(x + 4)/x^2) + 39911424*x^14*e^(14*(x + 4)/x^2) + 15826944*x^14*e^(12*(x + 4)
/x^2) + 4171776*x^14*e^(10*(x + 4)/x^2) + 731136*x^14*e^(8*(x + 4)/x^2) + 82176*x^14*e^(6*(x + 4)/x^2) + 5376*
x^14*e^(4*(x + 4)/x^2) + 156*x^14*e^(2*(x + 4)/x^2) + 12*x^13*e^(2*(x^2 + 3*x + 12)/x^2) - 32768*x^13*e^(2*(x^
2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 14*(x + 4)/x^2) - 57344*x^13*e^(2*(x^2 + 3*x + 12)/x^2 + (x^2 + 2*x
+ 8)/x^2 + 12*(x + 4)/x^2) - 43008*x^13*e^(2*(x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 10*(x + 4)/x^2) - 17
920*x^13*e^(2*(x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 8*(x + 4)/x^2) - 4480*x^13*e^(2*(x^2 + 3*x + 12)/x^
2 + (x^2 + 2*x + 8)/x^2 + 6*(x + 4)/x^2) - 672*x^13*e^(2*(x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 4*(x + 4
)/x^2) - 56*x^13*e^(2*(x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 2*(x + 4)/x^2) - 2*x^13*e^(2*(x^2 + 3*x + 1
2)/x^2 + (x^2 + 2*x + 8)/x^2) + 196608*x^13*e^(2*(x^2 + 3*x + 12)/x^2 + 14*(x + 4)/x^2) + 344064*x^13*e^(2*(x^
2 + 3*x + 12)/x^2 + 12*(x + 4)/x^2) + 258048*x^13*e^(2*(x^2 + 3*x + 12)/x^2 + 10*(x + 4)/x^2) + 107520*x^13*e^
(2*(x^2 + 3*x + 12)/x^2 + 8*(x + 4)/x^2) + 26880*x^13*e^(2*(x^2 + 3*x + 12)/x^2 + 6*(x + 4)/x^2) + 4032*x^13*e
^(2*(x^2 + 3*x + 12)/x^2 + 4*(x + 4)/x^2) + 336*x^13*e^(2*(x^2 + 3*x + 12)/x^2 + 2*(x + 4)/x^2) - 32768*x^13*e
^((x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 15*(x + 4)/x^2) - 57344*x^13*e^((x^2 + 3*x + 12)/x^2 + 2*(x^2
+ 2*x + 8)/x^2 + 13*(x + 4)/x^2) - 43008*x^13*e^((x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 11*(x + 4)/x^
2) - 17920*x^13*e^((x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 9*(x + 4)/x^2) - 4480*x^13*e^((x^2 + 3*x + 1
2)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 7*(x + 4)/x^2) - 672*x^13*e^((x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 5
*(x + 4)/x^2) - 56*x^13*e^((x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 3*(x + 4)/x^2) - 2*x^13*e^((x^2 + 3*
x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + (x + 4)/x^2) + 786432*x^13*e^((x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2
+ 15*(x + 4)/x^2) + 1376256*x^13*e^((x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 13*(x + 4)/x^2) + 1032192*x^
13*e^((x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 11*(x + 4)/x^2) + 430080*x^13*e^((x^2 + 3*x + 12)/x^2 + (x^
2 + 2*x + 8)/x^2 + 9*(x + 4)/x^2) + 107520*x^13*e^((x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 7*(x + 4)/x^2)
+ 16128*x^13*e^((x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 5*(x + 4)/x^2) + 1344*x^13*e^((x^2 + 3*x + 12)/x
^2 + (x^2 + 2*x + 8)/x^2 + 3*(x + 4)/x^2) + 48*x^13*e^((x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + (x + 4)/x^
2) - 12582912*x^13*e^((x^2 + 3*x + 12)/x^2 + 17*(x + 4)/x^2) - 27131904*x^13*e^((x^2 + 3*x + 12)/x^2 + 15*(x +
4)/x^2) - 25460736*x^13*e^((x^2 + 3*x + 12)/x^2 + 13*(x + 4)/x^2) - 13590528*x^13*e^((x^2 + 3*x + 12)/x^2 + 1
1*(x + 4)/x^2) - 4515840*x^13*e^((x^2 + 3*x + 12)/x^2 + 9*(x + 4)/x^2) - 956928*x^13*e^((x^2 + 3*x + 12)/x^2 +
7*(x + 4)/x^2) - 126336*x^13*e^((x^2 + 3*x + 12)/x^2 + 5*(x + 4)/x^2) - 9504*x^13*e^((x^2 + 3*x + 12)/x^2 + 3
*(x + 4)/x^2) - 312*x^13*e^((x^2 + 3*x + 12)/x^2 + (x + 4)/x^2) + 196608*x^13*e^(2*(x^2 + 2*x + 8)/x^2 + 16*(x
+ 4)/x^2) + 344064*x^13*e^(2*(x^2 + 2*x + 8)/x^2 + 14*(x + 4)/x^2) + 258048*x^13*e^(2*(x^2 + 2*x + 8)/x^2 + 1
2*(x + 4)/x^2) + 107520*x^13*e^(2*(x^2 + 2*x + 8)/x^2 + 10*(x + 4)/x^2) + 26880*x^13*e^(2*(x^2 + 2*x + 8)/x^2
+ 8*(x + 4)/x^2) + 4032*x^13*e^(2*(x^2 + 2*x + 8)/x^2 + 6*(x + 4)/x^2) + 336*x^13*e^(2*(x^2 + 2*x + 8)/x^2 + 4
*(x + 4)/x^2) + 12*x^13*e^(2*(x^2 + 2*x + 8)/x^2 + 2*(x + 4)/x^2) - 12582912*x^13*e^((x^2 + 2*x + 8)/x^2 + 18*
(x + 4)/x^2) - 27131904*x^13*e^((x^2 + 2*x + 8)/x^2 + 16*(x + 4)/x^2) - 25460736*x^13*e^((x^2 + 2*x + 8)/x^2 +
14*(x + 4)/x^2) - 13590528*x^13*e^((x^2 + 2*x + 8)/x^2 + 12*(x + 4)/x^2) - 4515840*x^13*e^((x^2 + 2*x + 8)/x^
2 + 10*(x + 4)/x^2) - 956928*x^13*e^((x^2 + 2*x + 8)/x^2 + 8*(x + 4)/x^2) - 126336*x^13*e^((x^2 + 2*x + 8)/x^2
+ 6*(x + 4)/x^2) - 9504*x^13*e^((x^2 + 2*x + 8)/x^2 + 4*(x + 4)/x^2) - 312*x^13*e^((x^2 + 2*x + 8)/x^2 + 2*(x
+ 4)/x^2) + 62914560*x^13*e^(18*(x + 4)/x^2) + 128450560*x^13*e^(16*(x + 4)/x^2) + 114688000*x^13*e^(14*(x +
4)/x^2) + 58490880*x^13*e^(12*(x + 4)/x^2) + 18636800*x^13*e^(10*(x + 4)/x^2) + 3799040*x^13*e^(8*(x + 4)/x^2)
+ 483840*x^13*e^(6*(x + 4)/x^2) + 35200*x^13*e^(4*(x + 4)/x^2) + 1120*x^13*e^(2*(x + 4)/x^2) + 156*x^12*e^(2*
(x^2 + 3*x + 12)/x^2) + 4096*x^12*e^(2*(x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 12*(x + 4)/x^2) + 6144*x
^12*e^(2*(x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 10*(x + 4)/x^2) + 3840*x^12*e^(2*(x^2 + 3*x + 12)/x^2
+ 2*(x^2 + 2*x + 8)/x^2 + 8*(x + 4)/x^2) + 1280*x^12*e^(2*(x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 6*(x
+ 4)/x^2) + 240*x^12*e^(2*(x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 4*(x + 4)/x^2) + 24*x^12*e^(2*(x^2 +
3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 2*(x + 4)/x^2) + x^12*e^(2*(x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^
2) - 98304*x^12*e^(2*(x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 12*(x + 4)/x^2) - 147456*x^12*e^(2*(x^2 + 3*
x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 10*(x + 4)/x^2) - 92160*x^12*e^(2*(x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x
^2 + 8*(x + 4)/x^2) - 30720*x^12*e^(2*(x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 6*(x + 4)/x^2) - 5760*x^12*
e^(2*(x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 4*(x + 4)/x^2) - 576*x^12*e^(2*(x^2 + 3*x + 12)/x^2 + (x^2 +
2*x + 8)/x^2 + 2*(x + 4)/x^2) - 24*x^12*e^(2*(x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2) + 1572864*x^12*e^(2*
(x^2 + 3*x + 12)/x^2 + 14*(x + 4)/x^2) + 2998272*x^12*e^(2*(x^2 + 3*x + 12)/x^2 + 12*(x + 4)/x^2) + 2433024*x^
12*e^(2*(x^2 + 3*x + 12)/x^2 + 10*(x + 4)/x^2) + 1090560*x^12*e^(2*(x^2 + 3*x + 12)/x^2 + 8*(x + 4)/x^2) + 291
840*x^12*e^(2*(x^2 + 3*x + 12)/x^2 + 6*(x + 4)/x^2) + 46656*x^12*e^(2*(x^2 + 3*x + 12)/x^2 + 4*(x + 4)/x^2) +
4128*x^12*e^(2*(x^2 + 3*x + 12)/x^2 + 2*(x + 4)/x^2) - 98304*x^12*e^((x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/
x^2 + 13*(x + 4)/x^2) - 147456*x^12*e^((x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 11*(x + 4)/x^2) - 92160*
x^12*e^((x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 9*(x + 4)/x^2) - 30720*x^12*e^((x^2 + 3*x + 12)/x^2 + 2
*(x^2 + 2*x + 8)/x^2 + 7*(x + 4)/x^2) - 5760*x^12*e^((x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 5*(x + 4)/
x^2) - 576*x^12*e^((x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 3*(x + 4)/x^2) - 24*x^12*e^((x^2 + 3*x + 12)
/x^2 + 2*(x^2 + 2*x + 8)/x^2 + (x + 4)/x^2) + 6291456*x^12*e^((x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 15*
(x + 4)/x^2) + 11993088*x^12*e^((x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 13*(x + 4)/x^2) + 9732096*x^12*e^
((x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 11*(x + 4)/x^2) + 4362240*x^12*e^((x^2 + 3*x + 12)/x^2 + (x^2 +
2*x + 8)/x^2 + 9*(x + 4)/x^2) + 1167360*x^12*e^((x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 7*(x + 4)/x^2) +
186624*x^12*e^((x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 5*(x + 4)/x^2) + 16512*x^12*e^((x^2 + 3*x + 12)/x^
2 + (x^2 + 2*x + 8)/x^2 + 3*(x + 4)/x^2) + 624*x^12*e^((x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + (x + 4)/x^
2) - 31457280*x^12*e^((x^2 + 3*x + 12)/x^2 + 15*(x + 4)/x^2) - 56360960*x^12*e^((x^2 + 3*x + 12)/x^2 + 13*(x +
4)/x^2) - 43253760*x^12*e^((x^2 + 3*x + 12)/x^2 + 11*(x + 4)/x^2) - 18432000*x^12*e^((x^2 + 3*x + 12)/x^2 + 9
*(x + 4)/x^2) - 4710400*x^12*e^((x^2 + 3*x + 12)/x^2 + 7*(x + 4)/x^2) - 721920*x^12*e^((x^2 + 3*x + 12)/x^2 +
5*(x + 4)/x^2) - 61440*x^12*e^((x^2 + 3*x + 12)/x^2 + 3*(x + 4)/x^2) - 2240*x^12*e^((x^2 + 3*x + 12)/x^2 + (x
+ 4)/x^2) + 1572864*x^12*e^(2*(x^2 + 2*x + 8)/x^2 + 16*(x + 4)/x^2) + 2998272*x^12*e^(2*(x^2 + 2*x + 8)/x^2 +
14*(x + 4)/x^2) + 2433024*x^12*e^(2*(x^2 + 2*x + 8)/x^2 + 12*(x + 4)/x^2) + 1090560*x^12*e^(2*(x^2 + 2*x + 8)/
x^2 + 10*(x + 4)/x^2) + 291840*x^12*e^(2*(x^2 + 2*x + 8)/x^2 + 8*(x + 4)/x^2) + 46656*x^12*e^(2*(x^2 + 2*x + 8
)/x^2 + 6*(x + 4)/x^2) + 4128*x^12*e^(2*(x^2 + 2*x + 8)/x^2 + 4*(x + 4)/x^2) + 156*x^12*e^(2*(x^2 + 2*x + 8)/x
^2 + 2*(x + 4)/x^2) - 31457280*x^12*e^((x^2 + 2*x + 8)/x^2 + 16*(x + 4)/x^2) - 56360960*x^12*e^((x^2 + 2*x + 8
)/x^2 + 14*(x + 4)/x^2) - 43253760*x^12*e^((x^2 + 2*x + 8)/x^2 + 12*(x + 4)/x^2) - 18432000*x^12*e^((x^2 + 2*x
+ 8)/x^2 + 10*(x + 4)/x^2) - 4710400*x^12*e^((x^2 + 2*x + 8)/x^2 + 8*(x + 4)/x^2) - 721920*x^12*e^((x^2 + 2*x
+ 8)/x^2 + 6*(x + 4)/x^2) - 61440*x^12*e^((x^2 + 2*x + 8)/x^2 + 4*(x + 4)/x^2) - 2240*x^12*e^((x^2 + 2*x + 8)
/x^2 + 2*(x + 4)/x^2) + 251658240*x^12*e^(18*(x + 4)/x^2) + 566231040*x^12*e^(16*(x + 4)/x^2) + 551485440*x^12
*e^(14*(x + 4)/x^2) + 304250880*x^12*e^(12*(x + 4)/x^2) + 104140800*x^12*e^(10*(x + 4)/x^2) + 22671360*x^12*e^
(8*(x + 4)/x^2) + 3068160*x^12*e^(6*(x + 4)/x^2) + 236160*x^12*e^(4*(x + 4)/x^2) + 7920*x^12*e^(2*(x + 4)/x^2)
+ 1120*x^11*e^(2*(x^2 + 3*x + 12)/x^2) + 12288*x^11*e^(2*(x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 10*(x
+ 4)/x^2) + 15360*x^11*e^(2*(x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 8*(x + 4)/x^2) + 7680*x^11*e^(2*(x
^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 6*(x + 4)/x^2) + 1920*x^11*e^(2*(x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2
*x + 8)/x^2 + 4*(x + 4)/x^2) + 240*x^11*e^(2*(x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 2*(x + 4)/x^2) + 1
2*x^11*e^(2*(x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2) - 786432*x^11*e^(2*(x^2 + 3*x + 12)/x^2 + (x^2 + 2*x
+ 8)/x^2 + 12*(x + 4)/x^2) - 1302528*x^11*e^(2*(x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 10*(x + 4)/x^2) -
890880*x^11*e^(2*(x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 8*(x + 4)/x^2) - 322560*x^11*e^(2*(x^2 + 3*x +
12)/x^2 + (x^2 + 2*x + 8)/x^2 + 6*(x + 4)/x^2) - 65280*x^11*e^(2*(x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 +
4*(x + 4)/x^2) - 7008*x^11*e^(2*(x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 2*(x + 4)/x^2) - 312*x^11*e^(2*(x
^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2) + 3932160*x^11*e^(2*(x^2 + 3*x + 12)/x^2 + 12*(x + 4)/x^2) + 6062080
*x^11*e^(2*(x^2 + 3*x + 12)/x^2 + 10*(x + 4)/x^2) + 3891200*x^11*e^(2*(x^2 + 3*x + 12)/x^2 + 8*(x + 4)/x^2) +
1331200*x^11*e^(2*(x^2 + 3*x + 12)/x^2 + 6*(x + 4)/x^2) + 256000*x^11*e^(2*(x^2 + 3*x + 12)/x^2 + 4*(x + 4)/x^
2) + 26240*x^11*e^(2*(x^2 + 3*x + 12)/x^2 + 2*(x + 4)/x^2) - 786432*x^11*e^((x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*
x + 8)/x^2 + 13*(x + 4)/x^2) - 1302528*x^11*e^((x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 11*(x + 4)/x^2)
- 890880*x^11*e^((x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 9*(x + 4)/x^2) - 322560*x^11*e^((x^2 + 3*x + 1
2)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 7*(x + 4)/x^2) - 65280*x^11*e^((x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 +
5*(x + 4)/x^2) - 7008*x^11*e^((x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 3*(x + 4)/x^2) - 312*x^11*e^((x^
2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + (x + 4)/x^2) + 15728640*x^11*e^((x^2 + 3*x + 12)/x^2 + (x^2 + 2*x
+ 8)/x^2 + 13*(x + 4)/x^2) + 24248320*x^11*e^((x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 11*(x + 4)/x^2) + 1
5564800*x^11*e^((x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 9*(x + 4)/x^2) + 5324800*x^11*e^((x^2 + 3*x + 12)
/x^2 + (x^2 + 2*x + 8)/x^2 + 7*(x + 4)/x^2) + 1024000*x^11*e^((x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 5*(
x + 4)/x^2) + 104960*x^11*e^((x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 3*(x + 4)/x^2) + 4480*x^11*e^((x^2 +
3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + (x + 4)/x^2) - 125829120*x^11*e^((x^2 + 3*x + 12)/x^2 + 15*(x + 4)/x^2)
- 251658240*x^11*e^((x^2 + 3*x + 12)/x^2 + 13*(x + 4)/x^2) - 212828160*x^11*e^((x^2 + 3*x + 12)/x^2 + 11*(x +
4)/x^2) - 98918400*x^11*e^((x^2 + 3*x + 12)/x^2 + 9*(x + 4)/x^2) - 27340800*x^11*e^((x^2 + 3*x + 12)/x^2 + 7*
(x + 4)/x^2) - 4500480*x^11*e^((x^2 + 3*x + 12)/x^2 + 5*(x + 4)/x^2) - 408960*x^11*e^((x^2 + 3*x + 12)/x^2 + 3
*(x + 4)/x^2) - 15840*x^11*e^((x^2 + 3*x + 12)/x^2 + (x + 4)/x^2) + 3932160*x^11*e^(2*(x^2 + 2*x + 8)/x^2 + 14
*(x + 4)/x^2) + 6062080*x^11*e^(2*(x^2 + 2*x + 8)/x^2 + 12*(x + 4)/x^2) + 3891200*x^11*e^(2*(x^2 + 2*x + 8)/x^
2 + 10*(x + 4)/x^2) + 1331200*x^11*e^(2*(x^2 + 2*x + 8)/x^2 + 8*(x + 4)/x^2) + 256000*x^11*e^(2*(x^2 + 2*x + 8
)/x^2 + 6*(x + 4)/x^2) + 26240*x^11*e^(2*(x^2 + 2*x + 8)/x^2 + 4*(x + 4)/x^2) + 1120*x^11*e^(2*(x^2 + 2*x + 8)
/x^2 + 2*(x + 4)/x^2) - 125829120*x^11*e^((x^2 + 2*x + 8)/x^2 + 16*(x + 4)/x^2) - 251658240*x^11*e^((x^2 + 2*x
+ 8)/x^2 + 14*(x + 4)/x^2) - 212828160*x^11*e^((x^2 + 2*x + 8)/x^2 + 12*(x + 4)/x^2) - 98918400*x^11*e^((x^2
+ 2*x + 8)/x^2 + 10*(x + 4)/x^2) - 27340800*x^11*e^((x^2 + 2*x + 8)/x^2 + 8*(x + 4)/x^2) - 4500480*x^11*e^((x^
2 + 2*x + 8)/x^2 + 6*(x + 4)/x^2) - 408960*x^11*e^((x^2 + 2*x + 8)/x^2 + 4*(x + 4)/x^2) - 15840*x^11*e^((x^2 +
2*x + 8)/x^2 + 2*(x + 4)/x^2) + 503316480*x^11*e^(16*(x + 4)/x^2) + 912261120*x^11*e^(14*(x + 4)/x^2) + 70798
5408*x^11*e^(12*(x + 4)/x^2) + 304988160*x^11*e^(10*(x + 4)/x^2) + 78766080*x^11*e^(8*(x + 4)/x^2) + 12195840*
x^11*e^(6*(x + 4)/x^2) + 1048320*x^11*e^(4*(x + 4)/x^2) + 38592*x^11*e^(2*(x + 4)/x^2) + 7920*x^10*e^(2*(x^2 +
3*x + 12)/x^2) + 98304*x^10*e^(2*(x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 10*(x + 4)/x^2) + 138240*x^10
*e^(2*(x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 8*(x + 4)/x^2) + 76800*x^10*e^(2*(x^2 + 3*x + 12)/x^2 + 2
*(x^2 + 2*x + 8)/x^2 + 6*(x + 4)/x^2) + 21120*x^10*e^(2*(x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 4*(x +
4)/x^2) + 2880*x^10*e^(2*(x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 2*(x + 4)/x^2) + 156*x^10*e^(2*(x^2 +
3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2) - 1966080*x^10*e^(2*(x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 10*(x
+ 4)/x^2) - 2539520*x^10*e^(2*(x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 8*(x + 4)/x^2) - 1310720*x^10*e^(2*
(x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 6*(x + 4)/x^2) - 337920*x^10*e^(2*(x^2 + 3*x + 12)/x^2 + (x^2 + 2
*x + 8)/x^2 + 4*(x + 4)/x^2) - 43520*x^10*e^(2*(x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 2*(x + 4)/x^2) - 2
240*x^10*e^(2*(x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2) + 15728640*x^10*e^(2*(x^2 + 3*x + 12)/x^2 + 12*(x +
4)/x^2) + 27525120*x^10*e^(2*(x^2 + 3*x + 12)/x^2 + 10*(x + 4)/x^2) + 19722240*x^10*e^(2*(x^2 + 3*x + 12)/x^2
+ 8*(x + 4)/x^2) + 7434240*x^10*e^(2*(x^2 + 3*x + 12)/x^2 + 6*(x + 4)/x^2) + 1559040*x^10*e^(2*(x^2 + 3*x + 12
)/x^2 + 4*(x + 4)/x^2) + 172800*x^10*e^(2*(x^2 + 3*x + 12)/x^2 + 2*(x + 4)/x^2) - 1966080*x^10*e^((x^2 + 3*x +
12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 11*(x + 4)/x^2) - 2539520*x^10*e^((x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/
x^2 + 9*(x + 4)/x^2) - 1310720*x^10*e^((x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 7*(x + 4)/x^2) - 337920*
x^10*e^((x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 5*(x + 4)/x^2) - 43520*x^10*e^((x^2 + 3*x + 12)/x^2 + 2
*(x^2 + 2*x + 8)/x^2 + 3*(x + 4)/x^2) - 2240*x^10*e^((x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + (x + 4)/x^
2) + 62914560*x^10*e^((x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 13*(x + 4)/x^2) + 110100480*x^10*e^((x^2 +
3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 11*(x + 4)/x^2) + 78888960*x^10*e^((x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8
)/x^2 + 9*(x + 4)/x^2) + 29736960*x^10*e^((x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 7*(x + 4)/x^2) + 623616
0*x^10*e^((x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 5*(x + 4)/x^2) + 691200*x^10*e^((x^2 + 3*x + 12)/x^2 +
(x^2 + 2*x + 8)/x^2 + 3*(x + 4)/x^2) + 31680*x^10*e^((x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + (x + 4)/x^2)
- 251658240*x^10*e^((x^2 + 3*x + 12)/x^2 + 13*(x + 4)/x^2) - 393216000*x^10*e^((x^2 + 3*x + 12)/x^2 + 11*(x +
4)/x^2) - 255688704*x^10*e^((x^2 + 3*x + 12)/x^2 + 9*(x + 4)/x^2) - 88571904*x^10*e^((x^2 + 3*x + 12)/x^2 + 7
*(x + 4)/x^2) - 17240064*x^10*e^((x^2 + 3*x + 12)/x^2 + 5*(x + 4)/x^2) - 1787904*x^10*e^((x^2 + 3*x + 12)/x^2
+ 3*(x + 4)/x^2) - 77184*x^10*e^((x^2 + 3*x + 12)/x^2 + (x + 4)/x^2) + 15728640*x^10*e^(2*(x^2 + 2*x + 8)/x^2
+ 14*(x + 4)/x^2) + 27525120*x^10*e^(2*(x^2 + 2*x + 8)/x^2 + 12*(x + 4)/x^2) + 19722240*x^10*e^(2*(x^2 + 2*x +
8)/x^2 + 10*(x + 4)/x^2) + 7434240*x^10*e^(2*(x^2 + 2*x + 8)/x^2 + 8*(x + 4)/x^2) + 1559040*x^10*e^(2*(x^2 +
2*x + 8)/x^2 + 6*(x + 4)/x^2) + 172800*x^10*e^(2*(x^2 + 2*x + 8)/x^2 + 4*(x + 4)/x^2) + 7920*x^10*e^(2*(x^2 +
2*x + 8)/x^2 + 2*(x + 4)/x^2) - 251658240*x^10*e^((x^2 + 2*x + 8)/x^2 + 14*(x + 4)/x^2) - 393216000*x^10*e^((x
^2 + 2*x + 8)/x^2 + 12*(x + 4)/x^2) - 255688704*x^10*e^((x^2 + 2*x + 8)/x^2 + 10*(x + 4)/x^2) - 88571904*x^10*
e^((x^2 + 2*x + 8)/x^2 + 8*(x + 4)/x^2) - 17240064*x^10*e^((x^2 + 2*x + 8)/x^2 + 6*(x + 4)/x^2) - 1787904*x^10
*e^((x^2 + 2*x + 8)/x^2 + 4*(x + 4)/x^2) - 77184*x^10*e^((x^2 + 2*x + 8)/x^2 + 2*(x + 4)/x^2) + 1342177280*x^1
0*e^(16*(x + 4)/x^2) + 2726297600*x^10*e^(14*(x + 4)/x^2) + 2335703040*x^10*e^(12*(x + 4)/x^2) + 1097744384*x^
10*e^(10*(x + 4)/x^2) + 306397184*x^10*e^(8*(x + 4)/x^2) + 50878464*x^10*e^(6*(x + 4)/x^2) + 4660224*x^10*e^(4
*(x + 4)/x^2) + 181824*x^10*e^(2*(x + 4)/x^2) + 38592*x^9*e^(2*(x^2 + 3*x + 12)/x^2) + 245760*x^9*e^(2*(x^2 +
3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 8*(x + 4)/x^2) + 256000*x^9*e^(2*(x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x +
8)/x^2 + 6*(x + 4)/x^2) + 99840*x^9*e^(2*(x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 4*(x + 4)/x^2) + 1728
0*x^9*e^(2*(x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 2*(x + 4)/x^2) + 1120*x^9*e^(2*(x^2 + 3*x + 12)/x^2
+ 2*(x^2 + 2*x + 8)/x^2) - 7864320*x^9*e^(2*(x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 10*(x + 4)/x^2) - 117
96480*x^9*e^(2*(x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 8*(x + 4)/x^2) - 6912000*x^9*e^(2*(x^2 + 3*x + 12)
/x^2 + (x^2 + 2*x + 8)/x^2 + 6*(x + 4)/x^2) - 1989120*x^9*e^(2*(x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 4*
(x + 4)/x^2) - 282240*x^9*e^(2*(x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 2*(x + 4)/x^2) - 15840*x^9*e^(2*(x
^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2) + 31457280*x^9*e^(2*(x^2 + 3*x + 12)/x^2 + 10*(x + 4)/x^2) + 4128768
0*x^9*e^(2*(x^2 + 3*x + 12)/x^2 + 8*(x + 4)/x^2) + 21639168*x^9*e^(2*(x^2 + 3*x + 12)/x^2 + 6*(x + 4)/x^2) + 5
661696*x^9*e^(2*(x^2 + 3*x + 12)/x^2 + 4*(x + 4)/x^2) + 739584*x^9*e^(2*(x^2 + 3*x + 12)/x^2 + 2*(x + 4)/x^2)
- 7864320*x^9*e^((x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 11*(x + 4)/x^2) - 11796480*x^9*e^((x^2 + 3*x +
12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 9*(x + 4)/x^2) - 6912000*x^9*e^((x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^
2 + 7*(x + 4)/x^2) - 1989120*x^9*e^((x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 5*(x + 4)/x^2) - 282240*x^9
*e^((x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 3*(x + 4)/x^2) - 15840*x^9*e^((x^2 + 3*x + 12)/x^2 + 2*(x^2
+ 2*x + 8)/x^2 + (x + 4)/x^2) + 125829120*x^9*e^((x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 11*(x + 4)/x^2)
+ 165150720*x^9*e^((x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 9*(x + 4)/x^2) + 86556672*x^9*e^((x^2 + 3*x +
12)/x^2 + (x^2 + 2*x + 8)/x^2 + 7*(x + 4)/x^2) + 22646784*x^9*e^((x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 +
5*(x + 4)/x^2) + 2958336*x^9*e^((x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 3*(x + 4)/x^2) + 154368*x^9*e^((
x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + (x + 4)/x^2) - 671088640*x^9*e^((x^2 + 3*x + 12)/x^2 + 13*(x + 4)/
x^2) - 1195376640*x^9*e^((x^2 + 3*x + 12)/x^2 + 11*(x + 4)/x^2) - 869007360*x^9*e^((x^2 + 3*x + 12)/x^2 + 9*(x
+ 4)/x^2) - 331620352*x^9*e^((x^2 + 3*x + 12)/x^2 + 7*(x + 4)/x^2) - 70293504*x^9*e^((x^2 + 3*x + 12)/x^2 + 5
*(x + 4)/x^2) - 7865856*x^9*e^((x^2 + 3*x + 12)/x^2 + 3*(x + 4)/x^2) - 363648*x^9*e^((x^2 + 3*x + 12)/x^2 + (x
+ 4)/x^2) + 31457280*x^9*e^(2*(x^2 + 2*x + 8)/x^2 + 12*(x + 4)/x^2) + 41287680*x^9*e^(2*(x^2 + 2*x + 8)/x^2 +
10*(x + 4)/x^2) + 21639168*x^9*e^(2*(x^2 + 2*x + 8)/x^2 + 8*(x + 4)/x^2) + 5661696*x^9*e^(2*(x^2 + 2*x + 8)/x
^2 + 6*(x + 4)/x^2) + 739584*x^9*e^(2*(x^2 + 2*x + 8)/x^2 + 4*(x + 4)/x^2) + 38592*x^9*e^(2*(x^2 + 2*x + 8)/x^
2 + 2*(x + 4)/x^2) - 671088640*x^9*e^((x^2 + 2*x + 8)/x^2 + 14*(x + 4)/x^2) - 1195376640*x^9*e^((x^2 + 2*x + 8
)/x^2 + 12*(x + 4)/x^2) - 869007360*x^9*e^((x^2 + 2*x + 8)/x^2 + 10*(x + 4)/x^2) - 331620352*x^9*e^((x^2 + 2*x
+ 8)/x^2 + 8*(x + 4)/x^2) - 70293504*x^9*e^((x^2 + 2*x + 8)/x^2 + 6*(x + 4)/x^2) - 7865856*x^9*e^((x^2 + 2*x
+ 8)/x^2 + 4*(x + 4)/x^2) - 363648*x^9*e^((x^2 + 2*x + 8)/x^2 + 2*(x + 4)/x^2) + 2013265920*x^9*e^(14*(x + 4)/
x^2) + 3145728000*x^9*e^(12*(x + 4)/x^2) + 2045509632*x^9*e^(10*(x + 4)/x^2) + 708575232*x^9*e^(8*(x + 4)/x^2)
+ 137920512*x^9*e^(6*(x + 4)/x^2) + 14303232*x^9*e^(4*(x + 4)/x^2) + 617472*x^9*e^(2*(x + 4)/x^2) + 181824*x^
8*e^(2*(x^2 + 3*x + 12)/x^2) + 983040*x^8*e^(2*(x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 8*(x + 4)/x^2) +
1228800*x^8*e^(2*(x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 6*(x + 4)/x^2) + 556800*x^8*e^(2*(x^2 + 3*x +
12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 4*(x + 4)/x^2) + 109440*x^8*e^(2*(x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x
^2 + 2*(x + 4)/x^2) + 7920*x^8*e^(2*(x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2) - 15728640*x^8*e^(2*(x^2 + 3
*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 8*(x + 4)/x^2) - 16711680*x^8*e^(2*(x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)
/x^2 + 6*(x + 4)/x^2) - 6641664*x^8*e^(2*(x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 4*(x + 4)/x^2) - 1170432
*x^8*e^(2*(x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 2*(x + 4)/x^2) - 77184*x^8*e^(2*(x^2 + 3*x + 12)/x^2 +
(x^2 + 2*x + 8)/x^2) + 83886080*x^8*e^(2*(x^2 + 3*x + 12)/x^2 + 10*(x + 4)/x^2) + 128450560*x^8*e^(2*(x^2 + 3*
x + 12)/x^2 + 8*(x + 4)/x^2) + 76513280*x^8*e^(2*(x^2 + 3*x + 12)/x^2 + 6*(x + 4)/x^2) + 22324224*x^8*e^(2*(x^
2 + 3*x + 12)/x^2 + 4*(x + 4)/x^2) + 3205632*x^8*e^(2*(x^2 + 3*x + 12)/x^2 + 2*(x + 4)/x^2) - 15728640*x^8*e^(
(x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 9*(x + 4)/x^2) - 16711680*x^8*e^((x^2 + 3*x + 12)/x^2 + 2*(x^2
+ 2*x + 8)/x^2 + 7*(x + 4)/x^2) - 6641664*x^8*e^((x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 5*(x + 4)/x^2)
- 1170432*x^8*e^((x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 3*(x + 4)/x^2) - 77184*x^8*e^((x^2 + 3*x + 12
)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + (x + 4)/x^2) + 335544320*x^8*e^((x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 1
1*(x + 4)/x^2) + 513802240*x^8*e^((x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 9*(x + 4)/x^2) + 306053120*x^8*
e^((x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 7*(x + 4)/x^2) + 89296896*x^8*e^((x^2 + 3*x + 12)/x^2 + (x^2 +
2*x + 8)/x^2 + 5*(x + 4)/x^2) + 12822528*x^8*e^((x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 3*(x + 4)/x^2) +
727296*x^8*e^((x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + (x + 4)/x^2) - 1006632960*x^8*e^((x^2 + 3*x + 12)/
x^2 + 11*(x + 4)/x^2) - 1321205760*x^8*e^((x^2 + 3*x + 12)/x^2 + 9*(x + 4)/x^2) - 692453376*x^8*e^((x^2 + 3*x
+ 12)/x^2 + 7*(x + 4)/x^2) - 181174272*x^8*e^((x^2 + 3*x + 12)/x^2 + 5*(x + 4)/x^2) - 23666688*x^8*e^((x^2 + 3
*x + 12)/x^2 + 3*(x + 4)/x^2) - 1234944*x^8*e^((x^2 + 3*x + 12)/x^2 + (x + 4)/x^2) + 83886080*x^8*e^(2*(x^2 +
2*x + 8)/x^2 + 12*(x + 4)/x^2) + 128450560*x^8*e^(2*(x^2 + 2*x + 8)/x^2 + 10*(x + 4)/x^2) + 76513280*x^8*e^(2*
(x^2 + 2*x + 8)/x^2 + 8*(x + 4)/x^2) + 22324224*x^8*e^(2*(x^2 + 2*x + 8)/x^2 + 6*(x + 4)/x^2) + 3205632*x^8*e^
(2*(x^2 + 2*x + 8)/x^2 + 4*(x + 4)/x^2) + 181824*x^8*e^(2*(x^2 + 2*x + 8)/x^2 + 2*(x + 4)/x^2) - 1006632960*x^
8*e^((x^2 + 2*x + 8)/x^2 + 12*(x + 4)/x^2) - 1321205760*x^8*e^((x^2 + 2*x + 8)/x^2 + 10*(x + 4)/x^2) - 6924533
76*x^8*e^((x^2 + 2*x + 8)/x^2 + 8*(x + 4)/x^2) - 181174272*x^8*e^((x^2 + 2*x + 8)/x^2 + 6*(x + 4)/x^2) - 23666
688*x^8*e^((x^2 + 2*x + 8)/x^2 + 4*(x + 4)/x^2) - 1234944*x^8*e^((x^2 + 2*x + 8)/x^2 + 2*(x + 4)/x^2) + 402653
1840*x^8*e^(14*(x + 4)/x^2) + 7046430720*x^8*e^(12*(x + 4)/x^2) + 5048893440*x^8*e^(10*(x + 4)/x^2) + 19031654
40*x^8*e^(8*(x + 4)/x^2) + 399114240*x^8*e^(6*(x + 4)/x^2) + 44236800*x^8*e^(4*(x + 4)/x^2) + 2027520*x^8*e^(2
*(x + 4)/x^2) + 617472*x^7*e^(2*(x^2 + 3*x + 12)/x^2) + 1966080*x^7*e^(2*(x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x +
8)/x^2 + 6*(x + 4)/x^2) + 1597440*x^7*e^(2*(x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 4*(x + 4)/x^2) + 43
0848*x^7*e^(2*(x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 2*(x + 4)/x^2) + 38592*x^7*e^(2*(x^2 + 3*x + 12)/
x^2 + 2*(x^2 + 2*x + 8)/x^2) - 41943040*x^7*e^(2*(x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 8*(x + 4)/x^2) -
53739520*x^7*e^(2*(x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 6*(x + 4)/x^2) - 24821760*x^7*e^(2*(x^2 + 3*x
+ 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 4*(x + 4)/x^2) - 4956672*x^7*e^(2*(x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2
+ 2*(x + 4)/x^2) - 363648*x^7*e^(2*(x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2) + 125829120*x^7*e^(2*(x^2 + 3*
x + 12)/x^2 + 8*(x + 4)/x^2) + 133693440*x^7*e^(2*(x^2 + 3*x + 12)/x^2 + 6*(x + 4)/x^2) + 53133312*x^7*e^(2*(x
^2 + 3*x + 12)/x^2 + 4*(x + 4)/x^2) + 9363456*x^7*e^(2*(x^2 + 3*x + 12)/x^2 + 2*(x + 4)/x^2) - 41943040*x^7*e^
((x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 9*(x + 4)/x^2) - 53739520*x^7*e^((x^2 + 3*x + 12)/x^2 + 2*(x^2
+ 2*x + 8)/x^2 + 7*(x + 4)/x^2) - 24821760*x^7*e^((x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 5*(x + 4)/x^
2) - 4956672*x^7*e^((x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 3*(x + 4)/x^2) - 363648*x^7*e^((x^2 + 3*x +
12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + (x + 4)/x^2) + 503316480*x^7*e^((x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2
+ 9*(x + 4)/x^2) + 534773760*x^7*e^((x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 7*(x + 4)/x^2) + 212533248*x^
7*e^((x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 5*(x + 4)/x^2) + 37453824*x^7*e^((x^2 + 3*x + 12)/x^2 + (x^2
+ 2*x + 8)/x^2 + 3*(x + 4)/x^2) + 2469888*x^7*e^((x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + (x + 4)/x^2) -
2013265920*x^7*e^((x^2 + 3*x + 12)/x^2 + 11*(x + 4)/x^2) - 3019898880*x^7*e^((x^2 + 3*x + 12)/x^2 + 9*(x + 4)/
x^2) - 1769472000*x^7*e^((x^2 + 3*x + 12)/x^2 + 7*(x + 4)/x^2) - 509214720*x^7*e^((x^2 + 3*x + 12)/x^2 + 5*(x
+ 4)/x^2) - 72253440*x^7*e^((x^2 + 3*x + 12)/x^2 + 3*(x + 4)/x^2) - 4055040*x^7*e^((x^2 + 3*x + 12)/x^2 + (x +
4)/x^2) + 125829120*x^7*e^(2*(x^2 + 2*x + 8)/x^2 + 10*(x + 4)/x^2) + 133693440*x^7*e^(2*(x^2 + 2*x + 8)/x^2 +
8*(x + 4)/x^2) + 53133312*x^7*e^(2*(x^2 + 2*x + 8)/x^2 + 6*(x + 4)/x^2) + 9363456*x^7*e^(2*(x^2 + 2*x + 8)/x^
2 + 4*(x + 4)/x^2) + 617472*x^7*e^(2*(x^2 + 2*x + 8)/x^2 + 2*(x + 4)/x^2) - 2013265920*x^7*e^((x^2 + 2*x + 8)/
x^2 + 12*(x + 4)/x^2) - 3019898880*x^7*e^((x^2 + 2*x + 8)/x^2 + 10*(x + 4)/x^2) - 1769472000*x^7*e^((x^2 + 2*x
+ 8)/x^2 + 8*(x + 4)/x^2) - 509214720*x^7*e^((x^2 + 2*x + 8)/x^2 + 6*(x + 4)/x^2) - 72253440*x^7*e^((x^2 + 2*
x + 8)/x^2 + 4*(x + 4)/x^2) - 4055040*x^7*e^((x^2 + 2*x + 8)/x^2 + 2*(x + 4)/x^2) + 4026531840*x^7*e^(12*(x +
4)/x^2) + 5200936960*x^7*e^(10*(x + 4)/x^2) + 2684354560*x^7*e^(8*(x + 4)/x^2) + 692060160*x^7*e^(6*(x + 4)/x^
2) + 89128960*x^7*e^(4*(x + 4)/x^2) + 4587520*x^7*e^(2*(x + 4)/x^2) + 2027520*x^6*e^(2*(x^2 + 3*x + 12)/x^2) +
5242880*x^6*e^(2*(x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 6*(x + 4)/x^2) + 5406720*x^6*e^(2*(x^2 + 3*x
+ 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 4*(x + 4)/x^2) + 1751040*x^6*e^(2*(x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)
/x^2 + 2*(x + 4)/x^2) + 181824*x^6*e^(2*(x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2) - 62914560*x^6*e^(2*(x^2
+ 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 6*(x + 4)/x^2) - 51118080*x^6*e^(2*(x^2 + 3*x + 12)/x^2 + (x^2 + 2*x
+ 8)/x^2 + 4*(x + 4)/x^2) - 13787136*x^6*e^(2*(x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 2*(x + 4)/x^2) - 12
34944*x^6*e^(2*(x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2) + 251658240*x^6*e^(2*(x^2 + 3*x + 12)/x^2 + 8*(x +
4)/x^2) + 314572800*x^6*e^(2*(x^2 + 3*x + 12)/x^2 + 6*(x + 4)/x^2) + 142540800*x^6*e^(2*(x^2 + 3*x + 12)/x^2 +
4*(x + 4)/x^2) + 28016640*x^6*e^(2*(x^2 + 3*x + 12)/x^2 + 2*(x + 4)/x^2) - 62914560*x^6*e^((x^2 + 3*x + 12)/x
^2 + 2*(x^2 + 2*x + 8)/x^2 + 7*(x + 4)/x^2) - 51118080*x^6*e^((x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 5
*(x + 4)/x^2) - 13787136*x^6*e^((x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 3*(x + 4)/x^2) - 1234944*x^6*e^
((x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + (x + 4)/x^2) + 1006632960*x^6*e^((x^2 + 3*x + 12)/x^2 + (x^2 +
2*x + 8)/x^2 + 9*(x + 4)/x^2) + 1258291200*x^6*e^((x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 7*(x + 4)/x^2)
+ 570163200*x^6*e^((x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 5*(x + 4)/x^2) + 112066560*x^6*e^((x^2 + 3*x
+ 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 3*(x + 4)/x^2) + 8110080*x^6*e^((x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 +
(x + 4)/x^2) - 2013265920*x^6*e^((x^2 + 3*x + 12)/x^2 + 9*(x + 4)/x^2) - 2097152000*x^6*e^((x^2 + 3*x + 12)/x
^2 + 7*(x + 4)/x^2) - 817889280*x^6*e^((x^2 + 3*x + 12)/x^2 + 5*(x + 4)/x^2) - 141557760*x^6*e^((x^2 + 3*x + 1
2)/x^2 + 3*(x + 4)/x^2) - 9175040*x^6*e^((x^2 + 3*x + 12)/x^2 + (x + 4)/x^2) + 251658240*x^6*e^(2*(x^2 + 2*x +
8)/x^2 + 10*(x + 4)/x^2) + 314572800*x^6*e^(2*(x^2 + 2*x + 8)/x^2 + 8*(x + 4)/x^2) + 142540800*x^6*e^(2*(x^2
+ 2*x + 8)/x^2 + 6*(x + 4)/x^2) + 28016640*x^6*e^(2*(x^2 + 2*x + 8)/x^2 + 4*(x + 4)/x^2) + 2027520*x^6*e^(2*(x
^2 + 2*x + 8)/x^2 + 2*(x + 4)/x^2) - 2013265920*x^6*e^((x^2 + 2*x + 8)/x^2 + 10*(x + 4)/x^2) - 2097152000*x^6*
e^((x^2 + 2*x + 8)/x^2 + 8*(x + 4)/x^2) - 817889280*x^6*e^((x^2 + 2*x + 8)/x^2 + 6*(x + 4)/x^2) - 141557760*x^
6*e^((x^2 + 2*x + 8)/x^2 + 4*(x + 4)/x^2) - 9175040*x^6*e^((x^2 + 2*x + 8)/x^2 + 2*(x + 4)/x^2) + 6442450944*x
^6*e^(12*(x + 4)/x^2) + 9059696640*x^6*e^(10*(x + 4)/x^2) + 5033164800*x^6*e^(8*(x + 4)/x^2) + 1384120320*x^6*
e^(6*(x + 4)/x^2) + 188743680*x^6*e^(4*(x + 4)/x^2) + 10223616*x^6*e^(2*(x + 4)/x^2) + 4587520*x^5*e^(2*(x^2 +
3*x + 12)/x^2) + 7864320*x^5*e^(2*(x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 4*(x + 4)/x^2) + 4423680*x^5
*e^(2*(x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 2*(x + 4)/x^2) + 617472*x^5*e^(2*(x^2 + 3*x + 12)/x^2 + 2
*(x^2 + 2*x + 8)/x^2) - 125829120*x^5*e^(2*(x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 6*(x + 4)/x^2) - 12582
9120*x^5*e^(2*(x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 4*(x + 4)/x^2) - 39813120*x^5*e^(2*(x^2 + 3*x + 12)
/x^2 + (x^2 + 2*x + 8)/x^2 + 2*(x + 4)/x^2) - 4055040*x^5*e^(2*(x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2) + 2
51658240*x^5*e^(2*(x^2 + 3*x + 12)/x^2 + 6*(x + 4)/x^2) + 199229440*x^5*e^(2*(x^2 + 3*x + 12)/x^2 + 4*(x + 4)/
x^2) + 52428800*x^5*e^(2*(x^2 + 3*x + 12)/x^2 + 2*(x + 4)/x^2) - 125829120*x^5*e^((x^2 + 3*x + 12)/x^2 + 2*(x^
2 + 2*x + 8)/x^2 + 7*(x + 4)/x^2) - 125829120*x^5*e^((x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 5*(x + 4)/
x^2) - 39813120*x^5*e^((x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 3*(x + 4)/x^2) - 4055040*x^5*e^((x^2 + 3
*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + (x + 4)/x^2) + 1006632960*x^5*e^((x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)
/x^2 + 7*(x + 4)/x^2) + 796917760*x^5*e^((x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 5*(x + 4)/x^2) + 2097152
00*x^5*e^((x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 3*(x + 4)/x^2) + 18350080*x^5*e^((x^2 + 3*x + 12)/x^2 +
(x^2 + 2*x + 8)/x^2 + (x + 4)/x^2) - 3221225472*x^5*e^((x^2 + 3*x + 12)/x^2 + 9*(x + 4)/x^2) - 3724541952*x^5
*e^((x^2 + 3*x + 12)/x^2 + 7*(x + 4)/x^2) - 1585446912*x^5*e^((x^2 + 3*x + 12)/x^2 + 5*(x + 4)/x^2) - 29569843
2*x^5*e^((x^2 + 3*x + 12)/x^2 + 3*(x + 4)/x^2) - 20447232*x^5*e^((x^2 + 3*x + 12)/x^2 + (x + 4)/x^2) + 2516582
40*x^5*e^(2*(x^2 + 2*x + 8)/x^2 + 8*(x + 4)/x^2) + 199229440*x^5*e^(2*(x^2 + 2*x + 8)/x^2 + 6*(x + 4)/x^2) + 5
2428800*x^5*e^(2*(x^2 + 2*x + 8)/x^2 + 4*(x + 4)/x^2) + 4587520*x^5*e^(2*(x^2 + 2*x + 8)/x^2 + 2*(x + 4)/x^2)
- 3221225472*x^5*e^((x^2 + 2*x + 8)/x^2 + 10*(x + 4)/x^2) - 3724541952*x^5*e^((x^2 + 2*x + 8)/x^2 + 8*(x + 4)/
x^2) - 1585446912*x^5*e^((x^2 + 2*x + 8)/x^2 + 6*(x + 4)/x^2) - 295698432*x^5*e^((x^2 + 2*x + 8)/x^2 + 4*(x +
4)/x^2) - 20447232*x^5*e^((x^2 + 2*x + 8)/x^2 + 2*(x + 4)/x^2) + 3221225472*x^5*e^(10*(x + 4)/x^2) + 322122547
2*x^5*e^(8*(x + 4)/x^2) + 1207959552*x^5*e^(6*(x + 4)/x^2) + 201326592*x^5*e^(4*(x + 4)/x^2) + 12582912*x^5*e^
(2*(x + 4)/x^2) + 10223616*x^4*e^(2*(x^2 + 3*x + 12)/x^2) + 15728640*x^4*e^(2*(x^2 + 3*x + 12)/x^2 + 2*(x^2 +
2*x + 8)/x^2 + 4*(x + 4)/x^2) + 11796480*x^4*e^(2*(x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 2*(x + 4)/x^2
) + 2027520*x^4*e^(2*(x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2) - 125829120*x^4*e^(2*(x^2 + 3*x + 12)/x^2 +
(x^2 + 2*x + 8)/x^2 + 4*(x + 4)/x^2) - 68157440*x^4*e^(2*(x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 2*(x +
4)/x^2) - 9175040*x^4*e^(2*(x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2) + 402653184*x^4*e^(2*(x^2 + 3*x + 12)/x
^2 + 6*(x + 4)/x^2) + 364904448*x^4*e^(2*(x^2 + 3*x + 12)/x^2 + 4*(x + 4)/x^2) + 106954752*x^4*e^(2*(x^2 + 3*x
+ 12)/x^2 + 2*(x + 4)/x^2) - 125829120*x^4*e^((x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 5*(x + 4)/x^2) -
68157440*x^4*e^((x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 3*(x + 4)/x^2) - 9175040*x^4*e^((x^2 + 3*x + 1
2)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + (x + 4)/x^2) + 1610612736*x^4*e^((x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 +
7*(x + 4)/x^2) + 1459617792*x^4*e^((x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 5*(x + 4)/x^2) + 427819008*x^
4*e^((x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 3*(x + 4)/x^2) + 40894464*x^4*e^((x^2 + 3*x + 12)/x^2 + (x^2
+ 2*x + 8)/x^2 + (x + 4)/x^2) - 1610612736*x^4*e^((x^2 + 3*x + 12)/x^2 + 7*(x + 4)/x^2) - 1207959552*x^4*e^((
x^2 + 3*x + 12)/x^2 + 5*(x + 4)/x^2) - 301989888*x^4*e^((x^2 + 3*x + 12)/x^2 + 3*(x + 4)/x^2) - 25165824*x^4*e
^((x^2 + 3*x + 12)/x^2 + (x + 4)/x^2) + 402653184*x^4*e^(2*(x^2 + 2*x + 8)/x^2 + 8*(x + 4)/x^2) + 364904448*x^
4*e^(2*(x^2 + 2*x + 8)/x^2 + 6*(x + 4)/x^2) + 106954752*x^4*e^(2*(x^2 + 2*x + 8)/x^2 + 4*(x + 4)/x^2) + 102236
16*x^4*e^(2*(x^2 + 2*x + 8)/x^2 + 2*(x + 4)/x^2) - 1610612736*x^4*e^((x^2 + 2*x + 8)/x^2 + 8*(x + 4)/x^2) - 12
07959552*x^4*e^((x^2 + 2*x + 8)/x^2 + 6*(x + 4)/x^2) - 301989888*x^4*e^((x^2 + 2*x + 8)/x^2 + 4*(x + 4)/x^2) -
25165824*x^4*e^((x^2 + 2*x + 8)/x^2 + 2*(x + 4)/x^2) + 4294967296*x^4*e^(10*(x + 4)/x^2) + 4294967296*x^4*e^(
8*(x + 4)/x^2) + 1610612736*x^4*e^(6*(x + 4)/x^2) + 268435456*x^4*e^(4*(x + 4)/x^2) + 16777216*x^4*e^(2*(x + 4
)/x^2) + 12582912*x^3*e^(2*(x^2 + 3*x + 12)/x^2) + 15728640*x^3*e^(2*(x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/
x^2 + 2*(x + 4)/x^2) + 4587520*x^3*e^(2*(x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2) - 201326592*x^3*e^(2*(x^
2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 4*(x + 4)/x^2) - 132120576*x^3*e^(2*(x^2 + 3*x + 12)/x^2 + (x^2 + 2*
x + 8)/x^2 + 2*(x + 4)/x^2) - 20447232*x^3*e^(2*(x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2) + 201326592*x^3*e^
(2*(x^2 + 3*x + 12)/x^2 + 4*(x + 4)/x^2) + 100663296*x^3*e^(2*(x^2 + 3*x + 12)/x^2 + 2*(x + 4)/x^2) - 20132659
2*x^3*e^((x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 5*(x + 4)/x^2) - 132120576*x^3*e^((x^2 + 3*x + 12)/x^2
+ 2*(x^2 + 2*x + 8)/x^2 + 3*(x + 4)/x^2) - 20447232*x^3*e^((x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + (x
+ 4)/x^2) + 805306368*x^3*e^((x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 5*(x + 4)/x^2) + 402653184*x^3*e^((x
^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 3*(x + 4)/x^2) + 50331648*x^3*e^((x^2 + 3*x + 12)/x^2 + (x^2 + 2*x
+ 8)/x^2 + (x + 4)/x^2) - 2147483648*x^3*e^((x^2 + 3*x + 12)/x^2 + 7*(x + 4)/x^2) - 1610612736*x^3*e^((x^2 + 3
*x + 12)/x^2 + 5*(x + 4)/x^2) - 402653184*x^3*e^((x^2 + 3*x + 12)/x^2 + 3*(x + 4)/x^2) - 33554432*x^3*e^((x^2
+ 3*x + 12)/x^2 + (x + 4)/x^2) + 201326592*x^3*e^(2*(x^2 + 2*x + 8)/x^2 + 6*(x + 4)/x^2) + 100663296*x^3*e^(2*
(x^2 + 2*x + 8)/x^2 + 4*(x + 4)/x^2) + 12582912*x^3*e^(2*(x^2 + 2*x + 8)/x^2 + 2*(x + 4)/x^2) - 2147483648*x^3
*e^((x^2 + 2*x + 8)/x^2 + 8*(x + 4)/x^2) - 1610612736*x^3*e^((x^2 + 2*x + 8)/x^2 + 6*(x + 4)/x^2) - 402653184*
x^3*e^((x^2 + 2*x + 8)/x^2 + 4*(x + 4)/x^2) - 33554432*x^3*e^((x^2 + 2*x + 8)/x^2 + 2*(x + 4)/x^2) + 16777216*
x^2*e^(2*(x^2 + 3*x + 12)/x^2) + 25165824*x^2*e^(2*(x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 2*(x + 4)/x^
2) + 10223616*x^2*e^(2*(x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2) - 100663296*x^2*e^(2*(x^2 + 3*x + 12)/x^2
+ (x^2 + 2*x + 8)/x^2 + 2*(x + 4)/x^2) - 25165824*x^2*e^(2*(x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2) + 2684
35456*x^2*e^(2*(x^2 + 3*x + 12)/x^2 + 4*(x + 4)/x^2) + 134217728*x^2*e^(2*(x^2 + 3*x + 12)/x^2 + 2*(x + 4)/x^2
) - 100663296*x^2*e^((x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 3*(x + 4)/x^2) - 25165824*x^2*e^((x^2 + 3*
x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + (x + 4)/x^2) + 1073741824*x^2*e^((x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/
x^2 + 5*(x + 4)/x^2) + 536870912*x^2*e^((x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 3*(x + 4)/x^2) + 67108864
*x^2*e^((x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + (x + 4)/x^2) + 268435456*x^2*e^(2*(x^2 + 2*x + 8)/x^2 + 6
*(x + 4)/x^2) + 134217728*x^2*e^(2*(x^2 + 2*x + 8)/x^2 + 4*(x + 4)/x^2) + 16777216*x^2*e^(2*(x^2 + 2*x + 8)/x^
2 + 2*(x + 4)/x^2) + 12582912*x*e^(2*(x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2) - 134217728*x*e^(2*(x^2 + 3
*x + 12)/x^2 + (x^2 + 2*x + 8)/x^2 + 2*(x + 4)/x^2) - 33554432*x*e^(2*(x^2 + 3*x + 12)/x^2 + (x^2 + 2*x + 8)/x
^2) - 134217728*x*e^((x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + 3*(x + 4)/x^2) - 33554432*x*e^((x^2 + 3*x
+ 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2 + (x + 4)/x^2) + 16777216*e^(2*(x^2 + 3*x + 12)/x^2 + 2*(x^2 + 2*x + 8)/x^2)
)
Mupad [F(-1)]
Timed out. \[
\int \frac {100 e^{\frac {3 (8+2 x)}{x^2}} x^2+e^{\frac {2 (8+2 x)}{x^2}} \left (400+50 x+25 x^2\right )}{-8 x^5+e^{\frac {3 (8+2 x)}{x^2}} \left (8 e^3 x^2-96 e^2 x^3+384 e x^4-512 x^5\right )+e^{\frac {2 (8+2 x)}{x^2}} \left (-24 e^2 x^3+192 e x^4-384 x^5\right )+e^{\frac {8+2 x}{x^2}} \left (24 e x^4-96 x^5\right )} \, dx=\int -\frac {100\,x^2\,{\mathrm {e}}^{\frac {3\,\left (2\,x+8\right )}{x^2}}+{\mathrm {e}}^{\frac {2\,\left (2\,x+8\right )}{x^2}}\,\left (25\,x^2+50\,x+400\right )}{{\mathrm {e}}^{\frac {2\,\left (2\,x+8\right )}{x^2}}\,\left (384\,x^5-192\,\mathrm {e}\,x^4+24\,{\mathrm {e}}^2\,x^3\right )-{\mathrm {e}}^{\frac {2\,x+8}{x^2}}\,\left (24\,x^4\,\mathrm {e}-96\,x^5\right )-{\mathrm {e}}^{\frac {3\,\left (2\,x+8\right )}{x^2}}\,\left (-512\,x^5+384\,\mathrm {e}\,x^4-96\,{\mathrm {e}}^2\,x^3+8\,{\mathrm {e}}^3\,x^2\right )+8\,x^5} \,d x
\]
[In]
int(-(100*x^2*exp((3*(2*x + 8))/x^2) + exp((2*(2*x + 8))/x^2)*(50*x + 25*x^2 + 400))/(exp((2*(2*x + 8))/x^2)*(
24*x^3*exp(2) - 192*x^4*exp(1) + 384*x^5) - exp((2*x + 8)/x^2)*(24*x^4*exp(1) - 96*x^5) - exp((3*(2*x + 8))/x^
2)*(8*x^2*exp(3) - 96*x^3*exp(2) + 384*x^4*exp(1) - 512*x^5) + 8*x^5),x)
[Out]
int(-(100*x^2*exp((3*(2*x + 8))/x^2) + exp((2*(2*x + 8))/x^2)*(50*x + 25*x^2 + 400))/(exp((2*(2*x + 8))/x^2)*(
24*x^3*exp(2) - 192*x^4*exp(1) + 384*x^5) - exp((2*x + 8)/x^2)*(24*x^4*exp(1) - 96*x^5) - exp((3*(2*x + 8))/x^
2)*(8*x^2*exp(3) - 96*x^3*exp(2) + 384*x^4*exp(1) - 512*x^5) + 8*x^5), x)