\(\int \frac {e^{-\frac {2 (-2 x^3+2 x^4)}{-4-6 x^2+6 x^3+e^4 (-x^2+x^3)}} (-16-48 x^2+96 x^3-100 x^4+96 x^5-84 x^6+24 x^7+e^8 (-x^4+2 x^5-x^6)+e^4 (-8 x^2+8 x^3-12 x^4+28 x^5-20 x^6+4 x^7))}{16+48 x^2-48 x^3+36 x^4-72 x^5+36 x^6+e^8 (x^4-2 x^5+x^6)+e^4 (8 x^2-8 x^3+12 x^4-24 x^5+12 x^6)} \, dx\) [933]

Optimal result

Integrand size = 205, antiderivative size = 31 \[ \int \frac {e^{-\frac {2 \left (-2 x^3+2 x^4\right )}{-4-6 x^2+6 x^3+e^4 \left (-x^2+x^3\right )}} \left (-16-48 x^2+96 x^3-100 x^4+96 x^5-84 x^6+24 x^7+e^8 \left (-x^4+2 x^5-x^6\right )+e^4 \left (-8 x^2+8 x^3-12 x^4+28 x^5-20 x^6+4 x^7\right )\right )}{16+48 x^2-48 x^3+36 x^4-72 x^5+36 x^6+e^8 \left (x^4-2 x^5+x^6\right )+e^4 \left (8 x^2-8 x^3+12 x^4-24 x^5+12 x^6\right )} \, dx=3-e^{-\frac {4 x}{6+e^4+\frac {4}{x \left (x-x^2\right )}}} x \] Output:

3-x/exp(2*x/(exp(4)+6+4/(-x^2+x)/x))^2
 

Mathematica [A] (verified)

Time = 0.06 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.16 \[ \int \frac {e^{-\frac {2 \left (-2 x^3+2 x^4\right )}{-4-6 x^2+6 x^3+e^4 \left (-x^2+x^3\right )}} \left (-16-48 x^2+96 x^3-100 x^4+96 x^5-84 x^6+24 x^7+e^8 \left (-x^4+2 x^5-x^6\right )+e^4 \left (-8 x^2+8 x^3-12 x^4+28 x^5-20 x^6+4 x^7\right )\right )}{16+48 x^2-48 x^3+36 x^4-72 x^5+36 x^6+e^8 \left (x^4-2 x^5+x^6\right )+e^4 \left (8 x^2-8 x^3+12 x^4-24 x^5+12 x^6\right )} \, dx=-e^{-\frac {4 (-1+x) x^3}{-4-\left (6+e^4\right ) x^2+\left (6+e^4\right ) x^3}} x \] Input:

Integrate[(-16 - 48*x^2 + 96*x^3 - 100*x^4 + 96*x^5 - 84*x^6 + 24*x^7 + E^ 
8*(-x^4 + 2*x^5 - x^6) + E^4*(-8*x^2 + 8*x^3 - 12*x^4 + 28*x^5 - 20*x^6 + 
4*x^7))/(E^((2*(-2*x^3 + 2*x^4))/(-4 - 6*x^2 + 6*x^3 + E^4*(-x^2 + x^3)))* 
(16 + 48*x^2 - 48*x^3 + 36*x^4 - 72*x^5 + 36*x^6 + E^8*(x^4 - 2*x^5 + x^6) 
 + E^4*(8*x^2 - 8*x^3 + 12*x^4 - 24*x^5 + 12*x^6))),x]
 

Output:

-(x/E^((4*(-1 + x)*x^3)/(-4 - (6 + E^4)*x^2 + (6 + E^4)*x^3)))
 

Rubi [F]

Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.

\(\displaystyle \int \frac {\left (24 x^7-84 x^6+96 x^5-100 x^4+96 x^3-48 x^2+e^8 \left (-x^6+2 x^5-x^4\right )+e^4 \left (4 x^7-20 x^6+28 x^5-12 x^4+8 x^3-8 x^2\right )-16\right ) \exp \left (-\frac {2 \left (2 x^4-2 x^3\right )}{6 x^3-6 x^2+e^4 \left (x^3-x^2\right )-4}\right )}{36 x^6-72 x^5+36 x^4-48 x^3+48 x^2+e^8 \left (x^6-2 x^5+x^4\right )+e^4 \left (12 x^6-24 x^5+12 x^4-8 x^3+8 x^2\right )+16} \, dx\)

\(\Big \downarrow \) 2463

\(\displaystyle \int \frac {\left (24 x^7-84 x^6+96 x^5-100 x^4+96 x^3-48 x^2+e^8 \left (-x^6+2 x^5-x^4\right )+e^4 \left (4 x^7-20 x^6+28 x^5-12 x^4+8 x^3-8 x^2\right )-16\right ) \exp \left (-\frac {2 \left (2 x^4-2 x^3\right )}{6 x^3-6 x^2+e^4 \left (x^3-x^2\right )-4}\right )}{\left (e^4 x^3+6 x^3-e^4 x^2-6 x^2-4\right )^2}dx\)

\(\Big \downarrow \) 6

\(\displaystyle \int \frac {\left (24 x^7-84 x^6+96 x^5-100 x^4+96 x^3-48 x^2+e^8 \left (-x^6+2 x^5-x^4\right )+e^4 \left (4 x^7-20 x^6+28 x^5-12 x^4+8 x^3-8 x^2\right )-16\right ) \exp \left (-\frac {2 \left (2 x^4-2 x^3\right )}{6 x^3-6 x^2+e^4 \left (x^3-x^2\right )-4}\right )}{\left (e^4 x^3+6 x^3+\left (-6-e^4\right ) x^2-4\right )^2}dx\)

\(\Big \downarrow \) 6

\(\displaystyle \int \frac {\left (24 x^7-84 x^6+96 x^5-100 x^4+96 x^3-48 x^2+e^8 \left (-x^6+2 x^5-x^4\right )+e^4 \left (4 x^7-20 x^6+28 x^5-12 x^4+8 x^3-8 x^2\right )-16\right ) \exp \left (-\frac {2 \left (2 x^4-2 x^3\right )}{6 x^3-6 x^2+e^4 \left (x^3-x^2\right )-4}\right )}{\left (\left (6+e^4\right ) x^3+\left (-6-e^4\right ) x^2-4\right )^2}dx\)

\(\Big \downarrow \) 7292

\(\displaystyle \int \frac {\left (24 x^7-84 x^6+96 x^5-100 x^4+96 x^3-48 x^2+e^8 \left (-x^6+2 x^5-x^4\right )+e^4 \left (4 x^7-20 x^6+28 x^5-12 x^4+8 x^3-8 x^2\right )-16\right ) \exp \left (-\frac {2 x^3 (2 x-2)}{\left (6+e^4\right ) x^3-\left (6+e^4\right ) x^2-4}\right )}{\left (-\left (\left (6+e^4\right ) x^3\right )+\left (6+e^4\right ) x^2+4\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {4 x \exp \left (-\frac {2 x^3 (2 x-2)}{\left (6+e^4\right ) x^3-\left (6+e^4\right ) x^2-4}\right )}{6+e^4}-\exp \left (-\frac {2 x^3 (2 x-2)}{\left (6+e^4\right ) x^3-\left (6+e^4\right ) x^2-4}\right )+\frac {16 (2 x+1) \exp \left (-\frac {2 x^3 (2 x-2)}{\left (6+e^4\right ) x^3-\left (6+e^4\right ) x^2-4}\right )}{\left (6+e^4\right ) \left (-\left (\left (6+e^4\right ) x^3\right )+\left (6+e^4\right ) x^2+4\right )}+\frac {16 \left (-\left (\left (6+e^4\right ) x^2\right )-12 x-4\right ) \exp \left (-\frac {2 x^3 (2 x-2)}{\left (6+e^4\right ) x^3-\left (6+e^4\right ) x^2-4}\right )}{\left (6+e^4\right ) \left (-\left (\left (6+e^4\right ) x^3\right )+\left (6+e^4\right ) x^2+4\right )^2}\right )dx\)

\(\Big \downarrow \) 2009

\(\displaystyle -\int \exp \left (-\frac {2 x^3 (2 x-2)}{\left (6+e^4\right ) x^3-\left (6+e^4\right ) x^2-4}\right )dx+\frac {4 \int \exp \left (-\frac {2 x^3 (2 x-2)}{\left (6+e^4\right ) x^3-\left (6+e^4\right ) x^2-4}\right ) xdx}{6+e^4}-\frac {64 \int \frac {\exp \left (-\frac {2 x^3 (2 x-2)}{\left (6+e^4\right ) x^3-\left (6+e^4\right ) x^2-4}\right )}{\left (-\left (\left (6+e^4\right ) x^3\right )+\left (6+e^4\right ) x^2+4\right )^2}dx}{6+e^4}-\frac {192 \int \frac {\exp \left (-\frac {2 x^3 (2 x-2)}{\left (6+e^4\right ) x^3-\left (6+e^4\right ) x^2-4}\right ) x}{\left (-\left (\left (6+e^4\right ) x^3\right )+\left (6+e^4\right ) x^2+4\right )^2}dx}{6+e^4}-16 \int \frac {\exp \left (-\frac {2 x^3 (2 x-2)}{\left (6+e^4\right ) x^3-\left (6+e^4\right ) x^2-4}\right ) x^2}{\left (-\left (\left (6+e^4\right ) x^3\right )+\left (6+e^4\right ) x^2+4\right )^2}dx+\frac {16 \int \frac {\exp \left (-\frac {2 x^3 (2 x-2)}{\left (6+e^4\right ) x^3-\left (6+e^4\right ) x^2-4}\right )}{-\left (\left (6+e^4\right ) x^3\right )+\left (6+e^4\right ) x^2+4}dx}{6+e^4}+\frac {32 \int \frac {\exp \left (-\frac {2 x^3 (2 x-2)}{\left (6+e^4\right ) x^3-\left (6+e^4\right ) x^2-4}\right ) x}{-\left (\left (6+e^4\right ) x^3\right )+\left (6+e^4\right ) x^2+4}dx}{6+e^4}\)

Input:

Int[(-16 - 48*x^2 + 96*x^3 - 100*x^4 + 96*x^5 - 84*x^6 + 24*x^7 + E^8*(-x^ 
4 + 2*x^5 - x^6) + E^4*(-8*x^2 + 8*x^3 - 12*x^4 + 28*x^5 - 20*x^6 + 4*x^7) 
)/(E^((2*(-2*x^3 + 2*x^4))/(-4 - 6*x^2 + 6*x^3 + E^4*(-x^2 + x^3)))*(16 + 
48*x^2 - 48*x^3 + 36*x^4 - 72*x^5 + 36*x^6 + E^8*(x^4 - 2*x^5 + x^6) + E^4 
*(8*x^2 - 8*x^3 + 12*x^4 - 24*x^5 + 12*x^6))),x]
 

Output:

$Aborted
 

Maple [A] (verified)

Time = 1.45 (sec) , antiderivative size = 40, normalized size of antiderivative = 1.29

method	result	size
risch	\(-x \,{\mathrm e}^{-\frac {4 x^{3} \left (-1+x \right )}{x^{3} {\mathrm e}^{4}-x^{2} {\mathrm e}^{4}+6 x^{3}-6 x^{2}-4}}\)	\(40\)
gosper	\(-x \,{\mathrm e}^{-\frac {4 x^{3} \left (-1+x \right )}{x^{3} {\mathrm e}^{4}-x^{2} {\mathrm e}^{4}+6 x^{3}-6 x^{2}-4}}\)	\(42\)
norman	\(\frac {\left (\left (-{\mathrm e}^{4}-6\right ) x^{4}+\left ({\mathrm e}^{4}+6\right ) x^{3}+4 x \right ) {\mathrm e}^{-\frac {2 \left (2 x^{4}-2 x^{3}\right )}{\left (x^{3}-x^{2}\right ) {\mathrm e}^{4}+6 x^{3}-6 x^{2}-4}}}{x^{3} {\mathrm e}^{4}-x^{2} {\mathrm e}^{4}+6 x^{3}-6 x^{2}-4}\)	\(92\)
parallelrisch	\(\frac {\left (-256 x^{4} {\mathrm e}^{4}+256 x^{3} {\mathrm e}^{4}-1536 x^{4}+1536 x^{3}+1024 x \right ) {\mathrm e}^{-\frac {4 x^{3} \left (-1+x \right )}{x^{3} {\mathrm e}^{4}-x^{2} {\mathrm e}^{4}+6 x^{3}-6 x^{2}-4}}}{256 x^{3} {\mathrm e}^{4}-256 x^{2} {\mathrm e}^{4}+1536 x^{3}-1536 x^{2}-1024}\)	\(96\)

Input:

int(((-x^6+2*x^5-x^4)*exp(4)^2+(4*x^7-20*x^6+28*x^5-12*x^4+8*x^3-8*x^2)*ex 
p(4)+24*x^7-84*x^6+96*x^5-100*x^4+96*x^3-48*x^2-16)/((x^6-2*x^5+x^4)*exp(4 
)^2+(12*x^6-24*x^5+12*x^4-8*x^3+8*x^2)*exp(4)+36*x^6-72*x^5+36*x^4-48*x^3+ 
48*x^2+16)/exp((2*x^4-2*x^3)/((x^3-x^2)*exp(4)+6*x^3-6*x^2-4))^2,x,method= 
_RETURNVERBOSE)
 

Output:

-x*exp(-4*x^3*(-1+x)/(x^3*exp(4)-x^2*exp(4)+6*x^3-6*x^2-4))
 

Fricas [A] (verification not implemented)

Time = 0.08 (sec) , antiderivative size = 41, normalized size of antiderivative = 1.32 \[ \int \frac {e^{-\frac {2 \left (-2 x^3+2 x^4\right )}{-4-6 x^2+6 x^3+e^4 \left (-x^2+x^3\right )}} \left (-16-48 x^2+96 x^3-100 x^4+96 x^5-84 x^6+24 x^7+e^8 \left (-x^4+2 x^5-x^6\right )+e^4 \left (-8 x^2+8 x^3-12 x^4+28 x^5-20 x^6+4 x^7\right )\right )}{16+48 x^2-48 x^3+36 x^4-72 x^5+36 x^6+e^8 \left (x^4-2 x^5+x^6\right )+e^4 \left (8 x^2-8 x^3+12 x^4-24 x^5+12 x^6\right )} \, dx=-x e^{\left (-\frac {4 \, {\left (x^{4} - x^{3}\right )}}{6 \, x^{3} - 6 \, x^{2} + {\left (x^{3} - x^{2}\right )} e^{4} - 4}\right )} \] Input:

integrate(((-x^6+2*x^5-x^4)*exp(4)^2+(4*x^7-20*x^6+28*x^5-12*x^4+8*x^3-8*x 
^2)*exp(4)+24*x^7-84*x^6+96*x^5-100*x^4+96*x^3-48*x^2-16)/((x^6-2*x^5+x^4) 
*exp(4)^2+(12*x^6-24*x^5+12*x^4-8*x^3+8*x^2)*exp(4)+36*x^6-72*x^5+36*x^4-4 
8*x^3+48*x^2+16)/exp((2*x^4-2*x^3)/((x^3-x^2)*exp(4)+6*x^3-6*x^2-4))^2,x, 
algorithm="fricas")
 

Output:

-x*e^(-4*(x^4 - x^3)/(6*x^3 - 6*x^2 + (x^3 - x^2)*e^4 - 4))
 

Sympy [F(-1)]

Timed out. \[ \int \frac {e^{-\frac {2 \left (-2 x^3+2 x^4\right )}{-4-6 x^2+6 x^3+e^4 \left (-x^2+x^3\right )}} \left (-16-48 x^2+96 x^3-100 x^4+96 x^5-84 x^6+24 x^7+e^8 \left (-x^4+2 x^5-x^6\right )+e^4 \left (-8 x^2+8 x^3-12 x^4+28 x^5-20 x^6+4 x^7\right )\right )}{16+48 x^2-48 x^3+36 x^4-72 x^5+36 x^6+e^8 \left (x^4-2 x^5+x^6\right )+e^4 \left (8 x^2-8 x^3+12 x^4-24 x^5+12 x^6\right )} \, dx=\text {Timed out} \] Input:

integrate(((-x**6+2*x**5-x**4)*exp(4)**2+(4*x**7-20*x**6+28*x**5-12*x**4+8 
*x**3-8*x**2)*exp(4)+24*x**7-84*x**6+96*x**5-100*x**4+96*x**3-48*x**2-16)/ 
((x**6-2*x**5+x**4)*exp(4)**2+(12*x**6-24*x**5+12*x**4-8*x**3+8*x**2)*exp( 
4)+36*x**6-72*x**5+36*x**4-48*x**3+48*x**2+16)/exp((2*x**4-2*x**3)/((x**3- 
x**2)*exp(4)+6*x**3-6*x**2-4))**2,x)
 

Output:

Timed out
 

Maxima [A] (verification not implemented)

Time = 0.32 (sec) , antiderivative size = 50, normalized size of antiderivative = 1.61 \[ \int \frac {e^{-\frac {2 \left (-2 x^3+2 x^4\right )}{-4-6 x^2+6 x^3+e^4 \left (-x^2+x^3\right )}} \left (-16-48 x^2+96 x^3-100 x^4+96 x^5-84 x^6+24 x^7+e^8 \left (-x^4+2 x^5-x^6\right )+e^4 \left (-8 x^2+8 x^3-12 x^4+28 x^5-20 x^6+4 x^7\right )\right )}{16+48 x^2-48 x^3+36 x^4-72 x^5+36 x^6+e^8 \left (x^4-2 x^5+x^6\right )+e^4 \left (8 x^2-8 x^3+12 x^4-24 x^5+12 x^6\right )} \, dx=-x e^{\left (-\frac {16 \, x}{x^{3} {\left (e^{8} + 12 \, e^{4} + 36\right )} - x^{2} {\left (e^{8} + 12 \, e^{4} + 36\right )} - 4 \, e^{4} - 24} - \frac {4 \, x}{e^{4} + 6}\right )} \] Input:

integrate(((-x^6+2*x^5-x^4)*exp(4)^2+(4*x^7-20*x^6+28*x^5-12*x^4+8*x^3-8*x 
^2)*exp(4)+24*x^7-84*x^6+96*x^5-100*x^4+96*x^3-48*x^2-16)/((x^6-2*x^5+x^4) 
*exp(4)^2+(12*x^6-24*x^5+12*x^4-8*x^3+8*x^2)*exp(4)+36*x^6-72*x^5+36*x^4-4 
8*x^3+48*x^2+16)/exp((2*x^4-2*x^3)/((x^3-x^2)*exp(4)+6*x^3-6*x^2-4))^2,x, 
algorithm="maxima")
 

Output:

-x*e^(-16*x/(x^3*(e^8 + 12*e^4 + 36) - x^2*(e^8 + 12*e^4 + 36) - 4*e^4 - 2 
4) - 4*x/(e^4 + 6))
 

Giac [A] (verification not implemented)

Time = 0.41 (sec) , antiderivative size = 42, normalized size of antiderivative = 1.35 \[ \int \frac {e^{-\frac {2 \left (-2 x^3+2 x^4\right )}{-4-6 x^2+6 x^3+e^4 \left (-x^2+x^3\right )}} \left (-16-48 x^2+96 x^3-100 x^4+96 x^5-84 x^6+24 x^7+e^8 \left (-x^4+2 x^5-x^6\right )+e^4 \left (-8 x^2+8 x^3-12 x^4+28 x^5-20 x^6+4 x^7\right )\right )}{16+48 x^2-48 x^3+36 x^4-72 x^5+36 x^6+e^8 \left (x^4-2 x^5+x^6\right )+e^4 \left (8 x^2-8 x^3+12 x^4-24 x^5+12 x^6\right )} \, dx=-x e^{\left (-\frac {4 \, {\left (x^{4} - x^{3}\right )}}{x^{3} e^{4} + 6 \, x^{3} - x^{2} e^{4} - 6 \, x^{2} - 4}\right )} \] Input:

integrate(((-x^6+2*x^5-x^4)*exp(4)^2+(4*x^7-20*x^6+28*x^5-12*x^4+8*x^3-8*x 
^2)*exp(4)+24*x^7-84*x^6+96*x^5-100*x^4+96*x^3-48*x^2-16)/((x^6-2*x^5+x^4) 
*exp(4)^2+(12*x^6-24*x^5+12*x^4-8*x^3+8*x^2)*exp(4)+36*x^6-72*x^5+36*x^4-4 
8*x^3+48*x^2+16)/exp((2*x^4-2*x^3)/((x^3-x^2)*exp(4)+6*x^3-6*x^2-4))^2,x, 
algorithm="giac")
 

Output:

-x*e^(-4*(x^4 - x^3)/(x^3*e^4 + 6*x^3 - x^2*e^4 - 6*x^2 - 4))
 

Mupad [B] (verification not implemented)

Time = 5.54 (sec) , antiderivative size = 44, normalized size of antiderivative = 1.42 \[ \int \frac {e^{-\frac {2 \left (-2 x^3+2 x^4\right )}{-4-6 x^2+6 x^3+e^4 \left (-x^2+x^3\right )}} \left (-16-48 x^2+96 x^3-100 x^4+96 x^5-84 x^6+24 x^7+e^8 \left (-x^4+2 x^5-x^6\right )+e^4 \left (-8 x^2+8 x^3-12 x^4+28 x^5-20 x^6+4 x^7\right )\right )}{16+48 x^2-48 x^3+36 x^4-72 x^5+36 x^6+e^8 \left (x^4-2 x^5+x^6\right )+e^4 \left (8 x^2-8 x^3+12 x^4-24 x^5+12 x^6\right )} \, dx=-x\,{\mathrm {e}}^{-\frac {4\,x^3-4\,x^4}{x^2\,{\mathrm {e}}^4-x^3\,{\mathrm {e}}^4+6\,x^2-6\,x^3+4}} \] Input:

int(-(exp(-(2*(2*x^3 - 2*x^4))/(exp(4)*(x^2 - x^3) + 6*x^2 - 6*x^3 + 4))*( 
exp(8)*(x^4 - 2*x^5 + x^6) + exp(4)*(8*x^2 - 8*x^3 + 12*x^4 - 28*x^5 + 20* 
x^6 - 4*x^7) + 48*x^2 - 96*x^3 + 100*x^4 - 96*x^5 + 84*x^6 - 24*x^7 + 16)) 
/(exp(8)*(x^4 - 2*x^5 + x^6) + exp(4)*(8*x^2 - 8*x^3 + 12*x^4 - 24*x^5 + 1 
2*x^6) + 48*x^2 - 48*x^3 + 36*x^4 - 72*x^5 + 36*x^6 + 16),x)
 

Output:

-x*exp(-(4*x^3 - 4*x^4)/(x^2*exp(4) - x^3*exp(4) + 6*x^2 - 6*x^3 + 4))
 

Reduce [B] (verification not implemented)

Time = 0.20 (sec) , antiderivative size = 77, normalized size of antiderivative = 2.48 \[ \int \frac {e^{-\frac {2 \left (-2 x^3+2 x^4\right )}{-4-6 x^2+6 x^3+e^4 \left (-x^2+x^3\right )}} \left (-16-48 x^2+96 x^3-100 x^4+96 x^5-84 x^6+24 x^7+e^8 \left (-x^4+2 x^5-x^6\right )+e^4 \left (-8 x^2+8 x^3-12 x^4+28 x^5-20 x^6+4 x^7\right )\right )}{16+48 x^2-48 x^3+36 x^4-72 x^5+36 x^6+e^8 \left (x^4-2 x^5+x^6\right )+e^4 \left (8 x^2-8 x^3+12 x^4-24 x^5+12 x^6\right )} \, dx=-\frac {e^{\frac {4 x^{3}}{e^{4} x^{3}-e^{4} x^{2}+6 x^{3}-6 x^{2}-4}} x}{e^{\frac {4 x^{4}}{e^{4} x^{3}-e^{4} x^{2}+6 x^{3}-6 x^{2}-4}}} \] Input:

int(((-x^6+2*x^5-x^4)*exp(4)^2+(4*x^7-20*x^6+28*x^5-12*x^4+8*x^3-8*x^2)*ex 
p(4)+24*x^7-84*x^6+96*x^5-100*x^4+96*x^3-48*x^2-16)/((x^6-2*x^5+x^4)*exp(4 
)^2+(12*x^6-24*x^5+12*x^4-8*x^3+8*x^2)*exp(4)+36*x^6-72*x^5+36*x^4-48*x^3+ 
48*x^2+16)/exp((2*x^4-2*x^3)/((x^3-x^2)*exp(4)+6*x^3-6*x^2-4))^2,x)
 

Output:

( - e**((4*x**3)/(e**4*x**3 - e**4*x**2 + 6*x**3 - 6*x**2 - 4))*x)/e**((4* 
x**4)/(e**4*x**3 - e**4*x**2 + 6*x**3 - 6*x**2 - 4))