\(\int \frac {e^{2 e^x} (-4+12 x^2-4 x^3)+e^6 (12 x^2-4 x^3)+e^{e^x} (4 e^{3+x} x+e^3 (-4+24 x^2-8 x^3))}{e^{2 e^x} (4-20 x+49 x^2-64 x^3+46 x^4-12 x^5+x^6)+e^6 (25 x^2-60 x^3+46 x^4-12 x^5+x^6)+e^{3+e^x} (-20 x+74 x^2-124 x^3+92 x^4-24 x^5+2 x^6)} \, dx\) [400]

Optimal result

Integrand size = 172, antiderivative size = 32 \[ \int \frac {e^{2 e^x} \left (-4+12 x^2-4 x^3\right )+e^6 \left (12 x^2-4 x^3\right )+e^{e^x} \left (4 e^{3+x} x+e^3 \left (-4+24 x^2-8 x^3\right )\right )}{e^{2 e^x} \left (4-20 x+49 x^2-64 x^3+46 x^4-12 x^5+x^6\right )+e^6 \left (25 x^2-60 x^3+46 x^4-12 x^5+x^6\right )+e^{3+e^x} \left (-20 x+74 x^2-124 x^3+92 x^4-24 x^5+2 x^6\right )} \, dx=\frac {2}{(-5+x) (-1+x)+\frac {2}{-x-e^{3-e^x} x}} \] Output:

2/((-1+x)*(-5+x)+2/(-x-exp(3)/exp(exp(x))*x))
                                                                                    
                                                                                    
 

Mathematica [A] (verified)

Time = 0.06 (sec) , antiderivative size = 47, normalized size of antiderivative = 1.47 \[ \int \frac {e^{2 e^x} \left (-4+12 x^2-4 x^3\right )+e^6 \left (12 x^2-4 x^3\right )+e^{e^x} \left (4 e^{3+x} x+e^3 \left (-4+24 x^2-8 x^3\right )\right )}{e^{2 e^x} \left (4-20 x+49 x^2-64 x^3+46 x^4-12 x^5+x^6\right )+e^6 \left (25 x^2-60 x^3+46 x^4-12 x^5+x^6\right )+e^{3+e^x} \left (-20 x+74 x^2-124 x^3+92 x^4-24 x^5+2 x^6\right )} \, dx=\frac {2 \left (e^3+e^{e^x}\right ) x}{e^3 x \left (5-6 x+x^2\right )+e^{e^x} \left (-2+5 x-6 x^2+x^3\right )} \] Input:

Integrate[(E^(2*E^x)*(-4 + 12*x^2 - 4*x^3) + E^6*(12*x^2 - 4*x^3) + E^E^x* 
(4*E^(3 + x)*x + E^3*(-4 + 24*x^2 - 8*x^3)))/(E^(2*E^x)*(4 - 20*x + 49*x^2 
 - 64*x^3 + 46*x^4 - 12*x^5 + x^6) + E^6*(25*x^2 - 60*x^3 + 46*x^4 - 12*x^ 
5 + x^6) + E^(3 + E^x)*(-20*x + 74*x^2 - 124*x^3 + 92*x^4 - 24*x^5 + 2*x^6 
)),x]
 

Output:

(2*(E^3 + E^E^x)*x)/(E^3*x*(5 - 6*x + x^2) + E^E^x*(-2 + 5*x - 6*x^2 + 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.

\(\displaystyle \int \frac {e^{2 e^x} \left (-4 x^3+12 x^2-4\right )+e^6 \left (12 x^2-4 x^3\right )+e^{e^x} \left (e^3 \left (-8 x^3+24 x^2-4\right )+4 e^{x+3} x\right )}{e^{2 e^x} \left (x^6-12 x^5+46 x^4-64 x^3+49 x^2-20 x+4\right )+e^6 \left (x^6-12 x^5+46 x^4-60 x^3+25 x^2\right )+e^{e^x+3} \left (2 x^6-24 x^5+92 x^4-124 x^3+74 x^2-20 x\right )} \, dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {4 \left (-e^6 (x-3) x^2-e^{2 e^x} \left (x^3-3 x^2+1\right )-e^{e^x+3} \left (2 x^3-6 x^2+1\right )+e^{x+e^x+3} x\right )}{\left (e^3 x \left (x^2-6 x+5\right )+e^{e^x} \left (x^3-6 x^2+5 x-2\right )\right )^2}dx\)

\(\Big \downarrow \) 27

\(\displaystyle 4 \int \frac {e^6 (3-x) x^2+e^{x+e^x+3} x-e^{2 e^x} \left (x^3-3 x^2+1\right )-e^{3+e^x} \left (2 x^3-6 x^2+1\right )}{\left (e^3 x \left (x^2-6 x+5\right )-e^{e^x} \left (-x^3+6 x^2-5 x+2\right )\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle 4 \int \left (-\frac {e^6 (x-3) x^2}{\left (e^{e^x} x^3+e^3 x^3-6 e^{e^x} x^2-6 e^3 x^2+5 e^{e^x} x+5 e^3 x-2 e^{e^x}\right )^2}+\frac {e^{x+e^x+3} x}{\left (e^{e^x} x^3+e^3 x^3-6 e^{e^x} x^2-6 e^3 x^2+5 e^{e^x} x+5 e^3 x-2 e^{e^x}\right )^2}-\frac {e^{2 e^x} \left (x^3-3 x^2+1\right )}{\left (e^{e^x} x^3+e^3 x^3-6 e^{e^x} x^2-6 e^3 x^2+5 e^{e^x} x+5 e^3 x-2 e^{e^x}\right )^2}-\frac {e^{3+e^x} \left (2 x^3-6 x^2+1\right )}{\left (e^{e^x} x^3+e^3 x^3-6 e^{e^x} x^2-6 e^3 x^2+5 e^{e^x} x+5 e^3 x-2 e^{e^x}\right )^2}\right )dx\)

\(\Big \downarrow \) 2009

\(\displaystyle 4 \left (-\int \frac {e^{2 e^x}}{\left (e^{e^x} x^3+e^3 x^3-6 e^{e^x} x^2-6 e^3 x^2+5 e^{e^x} x+5 e^3 x-2 e^{e^x}\right )^2}dx-\int \frac {e^{3+e^x}}{\left (e^{e^x} x^3+e^3 x^3-6 e^{e^x} x^2-6 e^3 x^2+5 e^{e^x} x+5 e^3 x-2 e^{e^x}\right )^2}dx+\int \frac {e^{x+e^x+3} x}{\left (e^{e^x} x^3+e^3 x^3-6 e^{e^x} x^2-6 e^3 x^2+5 e^{e^x} x+5 e^3 x-2 e^{e^x}\right )^2}dx+3 e^6 \int \frac {x^2}{\left (e^{e^x} x^3+e^3 x^3-6 e^{e^x} x^2-6 e^3 x^2+5 e^{e^x} x+5 e^3 x-2 e^{e^x}\right )^2}dx+3 \int \frac {e^{2 e^x} x^2}{\left (e^{e^x} x^3+e^3 x^3-6 e^{e^x} x^2-6 e^3 x^2+5 e^{e^x} x+5 e^3 x-2 e^{e^x}\right )^2}dx+6 \int \frac {e^{3+e^x} x^2}{\left (e^{e^x} x^3+e^3 x^3-6 e^{e^x} x^2-6 e^3 x^2+5 e^{e^x} x+5 e^3 x-2 e^{e^x}\right )^2}dx-e^6 \int \frac {x^3}{\left (e^{e^x} x^3+e^3 x^3-6 e^{e^x} x^2-6 e^3 x^2+5 e^{e^x} x+5 e^3 x-2 e^{e^x}\right )^2}dx-\int \frac {e^{2 e^x} x^3}{\left (e^{e^x} x^3+e^3 x^3-6 e^{e^x} x^2-6 e^3 x^2+5 e^{e^x} x+5 e^3 x-2 e^{e^x}\right )^2}dx-2 \int \frac {e^{3+e^x} x^3}{\left (e^{e^x} x^3+e^3 x^3-6 e^{e^x} x^2-6 e^3 x^2+5 e^{e^x} x+5 e^3 x-2 e^{e^x}\right )^2}dx\right )\)

Input:

Int[(E^(2*E^x)*(-4 + 12*x^2 - 4*x^3) + E^6*(12*x^2 - 4*x^3) + E^E^x*(4*E^( 
3 + x)*x + E^3*(-4 + 24*x^2 - 8*x^3)))/(E^(2*E^x)*(4 - 20*x + 49*x^2 - 64* 
x^3 + 46*x^4 - 12*x^5 + x^6) + E^6*(25*x^2 - 60*x^3 + 46*x^4 - 12*x^5 + x^ 
6) + E^(3 + E^x)*(-20*x + 74*x^2 - 124*x^3 + 92*x^4 - 24*x^5 + 2*x^6)),x]
 

Output:

$Aborted
 

Maple [A] (verified)

Time = 1.83 (sec) , antiderivative size = 61, normalized size of antiderivative = 1.91

method	result	size
parallelrisch	\(\frac {2 x \,{\mathrm e}^{3}+2 x \,{\mathrm e}^{{\mathrm e}^{x}}}{x^{3} {\mathrm e}^{{\mathrm e}^{x}}+x^{3} {\mathrm e}^{3}-6 \,{\mathrm e}^{{\mathrm e}^{x}} x^{2}-6 x^{2} {\mathrm e}^{3}+5 x \,{\mathrm e}^{{\mathrm e}^{x}}+5 x \,{\mathrm e}^{3}-2 \,{\mathrm e}^{{\mathrm e}^{x}}}\)	\(61\)
risch	\(\frac {2 x}{x^{3}-6 x^{2}+5 x -2}-\frac {4 x \,{\mathrm e}^{3}}{\left (x^{3}-6 x^{2}+5 x -2\right ) \left (x^{3} {\mathrm e}^{{\mathrm e}^{x}}+x^{3} {\mathrm e}^{3}-6 \,{\mathrm e}^{{\mathrm e}^{x}} x^{2}-6 x^{2} {\mathrm e}^{3}+5 x \,{\mathrm e}^{{\mathrm e}^{x}}+5 x \,{\mathrm e}^{3}-2 \,{\mathrm e}^{{\mathrm e}^{x}}\right )}\)	\(87\)

Input:

int(((-4*x^3+12*x^2-4)*exp(exp(x))^2+(4*x*exp(3)*exp(x)+(-8*x^3+24*x^2-4)* 
exp(3))*exp(exp(x))+(-4*x^3+12*x^2)*exp(3)^2)/((x^6-12*x^5+46*x^4-64*x^3+4 
9*x^2-20*x+4)*exp(exp(x))^2+(2*x^6-24*x^5+92*x^4-124*x^3+74*x^2-20*x)*exp( 
3)*exp(exp(x))+(x^6-12*x^5+46*x^4-60*x^3+25*x^2)*exp(3)^2),x,method=_RETUR 
NVERBOSE)
 

Output:

(2*x*exp(3)+2*x*exp(exp(x)))/(x^3*exp(exp(x))+x^3*exp(3)-6*exp(exp(x))*x^2 
-6*x^2*exp(3)+5*x*exp(exp(x))+5*x*exp(3)-2*exp(exp(x)))
 

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 67 vs. \(2 (27) = 54\).

Time = 0.08 (sec) , antiderivative size = 67, normalized size of antiderivative = 2.09 \[ \int \frac {e^{2 e^x} \left (-4+12 x^2-4 x^3\right )+e^6 \left (12 x^2-4 x^3\right )+e^{e^x} \left (4 e^{3+x} x+e^3 \left (-4+24 x^2-8 x^3\right )\right )}{e^{2 e^x} \left (4-20 x+49 x^2-64 x^3+46 x^4-12 x^5+x^6\right )+e^6 \left (25 x^2-60 x^3+46 x^4-12 x^5+x^6\right )+e^{3+e^x} \left (-20 x+74 x^2-124 x^3+92 x^4-24 x^5+2 x^6\right )} \, dx=\frac {2 \, {\left (x e^{6} + x e^{\left ({\left (3 \, e^{3} + e^{\left (x + 3\right )}\right )} e^{\left (-3\right )}\right )}\right )}}{{\left (x^{3} - 6 \, x^{2} + 5 \, x\right )} e^{6} + {\left (x^{3} - 6 \, x^{2} + 5 \, x - 2\right )} e^{\left ({\left (3 \, e^{3} + e^{\left (x + 3\right )}\right )} e^{\left (-3\right )}\right )}} \] Input:

integrate(((-4*x^3+12*x^2-4)*exp(exp(x))^2+(4*x*exp(3)*exp(x)+(-8*x^3+24*x 
^2-4)*exp(3))*exp(exp(x))+(-4*x^3+12*x^2)*exp(3)^2)/((x^6-12*x^5+46*x^4-64 
*x^3+49*x^2-20*x+4)*exp(exp(x))^2+(2*x^6-24*x^5+92*x^4-124*x^3+74*x^2-20*x 
)*exp(3)*exp(exp(x))+(x^6-12*x^5+46*x^4-60*x^3+25*x^2)*exp(3)^2),x, algori 
thm="fricas")
 

Output:

2*(x*e^6 + x*e^((3*e^3 + e^(x + 3))*e^(-3)))/((x^3 - 6*x^2 + 5*x)*e^6 + (x 
^3 - 6*x^2 + 5*x - 2)*e^((3*e^3 + e^(x + 3))*e^(-3)))
 

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 104 vs. \(2 (22) = 44\).

Time = 0.35 (sec) , antiderivative size = 104, normalized size of antiderivative = 3.25 \[ \int \frac {e^{2 e^x} \left (-4+12 x^2-4 x^3\right )+e^6 \left (12 x^2-4 x^3\right )+e^{e^x} \left (4 e^{3+x} x+e^3 \left (-4+24 x^2-8 x^3\right )\right )}{e^{2 e^x} \left (4-20 x+49 x^2-64 x^3+46 x^4-12 x^5+x^6\right )+e^6 \left (25 x^2-60 x^3+46 x^4-12 x^5+x^6\right )+e^{3+e^x} \left (-20 x+74 x^2-124 x^3+92 x^4-24 x^5+2 x^6\right )} \, dx=- \frac {4 x e^{3}}{x^{6} e^{3} - 12 x^{5} e^{3} + 46 x^{4} e^{3} - 62 x^{3} e^{3} + 37 x^{2} e^{3} - 10 x e^{3} + \left (x^{6} - 12 x^{5} + 46 x^{4} - 64 x^{3} + 49 x^{2} - 20 x + 4\right ) e^{e^{x}}} + \frac {2 x}{x^{3} - 6 x^{2} + 5 x - 2} \] Input:

integrate(((-4*x**3+12*x**2-4)*exp(exp(x))**2+(4*x*exp(3)*exp(x)+(-8*x**3+ 
24*x**2-4)*exp(3))*exp(exp(x))+(-4*x**3+12*x**2)*exp(3)**2)/((x**6-12*x**5 
+46*x**4-64*x**3+49*x**2-20*x+4)*exp(exp(x))**2+(2*x**6-24*x**5+92*x**4-12 
4*x**3+74*x**2-20*x)*exp(3)*exp(exp(x))+(x**6-12*x**5+46*x**4-60*x**3+25*x 
**2)*exp(3)**2),x)
 

Output:

-4*x*exp(3)/(x**6*exp(3) - 12*x**5*exp(3) + 46*x**4*exp(3) - 62*x**3*exp(3 
) + 37*x**2*exp(3) - 10*x*exp(3) + (x**6 - 12*x**5 + 46*x**4 - 64*x**3 + 4 
9*x**2 - 20*x + 4)*exp(exp(x))) + 2*x/(x**3 - 6*x**2 + 5*x - 2)
 

Maxima [A] (verification not implemented)

Time = 0.22 (sec) , antiderivative size = 50, normalized size of antiderivative = 1.56 \[ \int \frac {e^{2 e^x} \left (-4+12 x^2-4 x^3\right )+e^6 \left (12 x^2-4 x^3\right )+e^{e^x} \left (4 e^{3+x} x+e^3 \left (-4+24 x^2-8 x^3\right )\right )}{e^{2 e^x} \left (4-20 x+49 x^2-64 x^3+46 x^4-12 x^5+x^6\right )+e^6 \left (25 x^2-60 x^3+46 x^4-12 x^5+x^6\right )+e^{3+e^x} \left (-20 x+74 x^2-124 x^3+92 x^4-24 x^5+2 x^6\right )} \, dx=\frac {2 \, {\left (x e^{3} + x e^{\left (e^{x}\right )}\right )}}{x^{3} e^{3} - 6 \, x^{2} e^{3} + 5 \, x e^{3} + {\left (x^{3} - 6 \, x^{2} + 5 \, x - 2\right )} e^{\left (e^{x}\right )}} \] Input:

integrate(((-4*x^3+12*x^2-4)*exp(exp(x))^2+(4*x*exp(3)*exp(x)+(-8*x^3+24*x 
^2-4)*exp(3))*exp(exp(x))+(-4*x^3+12*x^2)*exp(3)^2)/((x^6-12*x^5+46*x^4-64 
*x^3+49*x^2-20*x+4)*exp(exp(x))^2+(2*x^6-24*x^5+92*x^4-124*x^3+74*x^2-20*x 
)*exp(3)*exp(exp(x))+(x^6-12*x^5+46*x^4-60*x^3+25*x^2)*exp(3)^2),x, algori 
thm="maxima")
 

Output:

2*(x*e^3 + x*e^(e^x))/(x^3*e^3 - 6*x^2*e^3 + 5*x*e^3 + (x^3 - 6*x^2 + 5*x 
- 2)*e^(e^x))
 

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 59 vs. \(2 (27) = 54\).

Time = 0.20 (sec) , antiderivative size = 59, normalized size of antiderivative = 1.84 \[ \int \frac {e^{2 e^x} \left (-4+12 x^2-4 x^3\right )+e^6 \left (12 x^2-4 x^3\right )+e^{e^x} \left (4 e^{3+x} x+e^3 \left (-4+24 x^2-8 x^3\right )\right )}{e^{2 e^x} \left (4-20 x+49 x^2-64 x^3+46 x^4-12 x^5+x^6\right )+e^6 \left (25 x^2-60 x^3+46 x^4-12 x^5+x^6\right )+e^{3+e^x} \left (-20 x+74 x^2-124 x^3+92 x^4-24 x^5+2 x^6\right )} \, dx=\frac {2 \, {\left (x e^{3} + x e^{\left (e^{x}\right )}\right )}}{x^{3} e^{3} + x^{3} e^{\left (e^{x}\right )} - 6 \, x^{2} e^{3} - 6 \, x^{2} e^{\left (e^{x}\right )} + 5 \, x e^{3} + 5 \, x e^{\left (e^{x}\right )} - 2 \, e^{\left (e^{x}\right )}} \] Input:

integrate(((-4*x^3+12*x^2-4)*exp(exp(x))^2+(4*x*exp(3)*exp(x)+(-8*x^3+24*x 
^2-4)*exp(3))*exp(exp(x))+(-4*x^3+12*x^2)*exp(3)^2)/((x^6-12*x^5+46*x^4-64 
*x^3+49*x^2-20*x+4)*exp(exp(x))^2+(2*x^6-24*x^5+92*x^4-124*x^3+74*x^2-20*x 
)*exp(3)*exp(exp(x))+(x^6-12*x^5+46*x^4-60*x^3+25*x^2)*exp(3)^2),x, algori 
thm="giac")
 

Output:

2*(x*e^3 + x*e^(e^x))/(x^3*e^3 + x^3*e^(e^x) - 6*x^2*e^3 - 6*x^2*e^(e^x) + 
 5*x*e^3 + 5*x*e^(e^x) - 2*e^(e^x))
 

Mupad [F(-1)]

Timed out. \[ \int \frac {e^{2 e^x} \left (-4+12 x^2-4 x^3\right )+e^6 \left (12 x^2-4 x^3\right )+e^{e^x} \left (4 e^{3+x} x+e^3 \left (-4+24 x^2-8 x^3\right )\right )}{e^{2 e^x} \left (4-20 x+49 x^2-64 x^3+46 x^4-12 x^5+x^6\right )+e^6 \left (25 x^2-60 x^3+46 x^4-12 x^5+x^6\right )+e^{3+e^x} \left (-20 x+74 x^2-124 x^3+92 x^4-24 x^5+2 x^6\right )} \, dx=\int -\frac {{\mathrm {e}}^{{\mathrm {e}}^x}\,\left ({\mathrm {e}}^3\,\left (8\,x^3-24\,x^2+4\right )-4\,x\,{\mathrm {e}}^3\,{\mathrm {e}}^x\right )-{\mathrm {e}}^6\,\left (12\,x^2-4\,x^3\right )+{\mathrm {e}}^{2\,{\mathrm {e}}^x}\,\left (4\,x^3-12\,x^2+4\right )}{{\mathrm {e}}^6\,\left (x^6-12\,x^5+46\,x^4-60\,x^3+25\,x^2\right )+{\mathrm {e}}^{2\,{\mathrm {e}}^x}\,\left (x^6-12\,x^5+46\,x^4-64\,x^3+49\,x^2-20\,x+4\right )-{\mathrm {e}}^{{\mathrm {e}}^x}\,{\mathrm {e}}^3\,\left (-2\,x^6+24\,x^5-92\,x^4+124\,x^3-74\,x^2+20\,x\right )} \,d x \] Input:

int(-(exp(exp(x))*(exp(3)*(8*x^3 - 24*x^2 + 4) - 4*x*exp(3)*exp(x)) - exp( 
6)*(12*x^2 - 4*x^3) + exp(2*exp(x))*(4*x^3 - 12*x^2 + 4))/(exp(6)*(25*x^2 
- 60*x^3 + 46*x^4 - 12*x^5 + x^6) + exp(2*exp(x))*(49*x^2 - 20*x - 64*x^3 
+ 46*x^4 - 12*x^5 + x^6 + 4) - exp(exp(x))*exp(3)*(20*x - 74*x^2 + 124*x^3 
 - 92*x^4 + 24*x^5 - 2*x^6)),x)
 

Output:

int(-(exp(exp(x))*(exp(3)*(8*x^3 - 24*x^2 + 4) - 4*x*exp(3)*exp(x)) - exp( 
6)*(12*x^2 - 4*x^3) + exp(2*exp(x))*(4*x^3 - 12*x^2 + 4))/(exp(6)*(25*x^2 
- 60*x^3 + 46*x^4 - 12*x^5 + x^6) + exp(2*exp(x))*(49*x^2 - 20*x - 64*x^3 
+ 46*x^4 - 12*x^5 + x^6 + 4) - exp(exp(x))*exp(3)*(20*x - 74*x^2 + 124*x^3 
 - 92*x^4 + 24*x^5 - 2*x^6)), x)
 

Reduce [B] (verification not implemented)

Time = 0.23 (sec) , antiderivative size = 70, normalized size of antiderivative = 2.19 \[ \int \frac {e^{2 e^x} \left (-4+12 x^2-4 x^3\right )+e^6 \left (12 x^2-4 x^3\right )+e^{e^x} \left (4 e^{3+x} x+e^3 \left (-4+24 x^2-8 x^3\right )\right )}{e^{2 e^x} \left (4-20 x+49 x^2-64 x^3+46 x^4-12 x^5+x^6\right )+e^6 \left (25 x^2-60 x^3+46 x^4-12 x^5+x^6\right )+e^{3+e^x} \left (-20 x+74 x^2-124 x^3+92 x^4-24 x^5+2 x^6\right )} \, dx=\frac {2 x \left (e^{e^{x}}+e^{3}\right )}{e^{e^{x}} x^{3}-6 e^{e^{x}} x^{2}+5 e^{e^{x}} x -2 e^{e^{x}}+e^{3} x^{3}-6 e^{3} x^{2}+5 e^{3} x} \] Input:

int(((-4*x^3+12*x^2-4)*exp(exp(x))^2+(4*x*exp(3)*exp(x)+(-8*x^3+24*x^2-4)* 
exp(3))*exp(exp(x))+(-4*x^3+12*x^2)*exp(3)^2)/((x^6-12*x^5+46*x^4-64*x^3+4 
9*x^2-20*x+4)*exp(exp(x))^2+(2*x^6-24*x^5+92*x^4-124*x^3+74*x^2-20*x)*exp( 
3)*exp(exp(x))+(x^6-12*x^5+46*x^4-60*x^3+25*x^2)*exp(3)^2),x)
 

Output:

(2*x*(e**(e**x) + e**3))/(e**(e**x)*x**3 - 6*e**(e**x)*x**2 + 5*e**(e**x)* 
x - 2*e**(e**x) + e**3*x**3 - 6*e**3*x**2 + 5*e**3*x)