Integrand size = 180, antiderivative size = 25 \[ \int \left (324 x^3+e^{9 e^{e^{e^x}}+3 x} \left (-750000 x^3-562500 x^4-1687500 e^{e^{e^x}+e^x+x} x^4\right )+e^{3 e^{e^{e^x}}+x} \left (-10800 x^3-2700 x^4-8100 e^{e^{e^x}+e^x+x} x^4\right )+e^{6 e^{e^{e^x}}+2 x} \left (135000 x^3+67500 x^4+202500 e^{e^{e^x}+e^x+x} x^4\right )+e^{12 e^{e^{e^x}}+4 x} \left (1562500 x^3+1562500 x^4+4687500 e^{e^{e^x}+e^x+x} x^4\right )\right ) \, dx=\left (-x+\left (4-25 e^{3 e^{e^{e^x}}+x}\right ) x\right )^4 \] Output:
((4-25*exp(3*exp(exp(exp(x)))+x))*x-x)^4
Time = 0.56 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.92 \[ \int \left (324 x^3+e^{9 e^{e^{e^x}}+3 x} \left (-750000 x^3-562500 x^4-1687500 e^{e^{e^x}+e^x+x} x^4\right )+e^{3 e^{e^{e^x}}+x} \left (-10800 x^3-2700 x^4-8100 e^{e^{e^x}+e^x+x} x^4\right )+e^{6 e^{e^{e^x}}+2 x} \left (135000 x^3+67500 x^4+202500 e^{e^{e^x}+e^x+x} x^4\right )+e^{12 e^{e^{e^x}}+4 x} \left (1562500 x^3+1562500 x^4+4687500 e^{e^{e^x}+e^x+x} x^4\right )\right ) \, dx=\left (3-25 e^{3 e^{e^{e^x}}+x}\right )^4 x^4 \] Input:
Integrate[324*x^3 + E^(9*E^E^E^x + 3*x)*(-750000*x^3 - 562500*x^4 - 168750 0*E^(E^E^x + E^x + x)*x^4) + E^(3*E^E^E^x + x)*(-10800*x^3 - 2700*x^4 - 81 00*E^(E^E^x + E^x + x)*x^4) + E^(6*E^E^E^x + 2*x)*(135000*x^3 + 67500*x^4 + 202500*E^(E^E^x + E^x + x)*x^4) + E^(12*E^E^E^x + 4*x)*(1562500*x^3 + 15 62500*x^4 + 4687500*E^(E^E^x + E^x + x)*x^4),x]
Output:
(3 - 25*E^(3*E^E^E^x + x))^4*x^4
Leaf count is larger than twice the leaf count of optimal. \(228\) vs. \(2(25)=50\).
Time = 0.75 (sec) , antiderivative size = 228, normalized size of antiderivative = 9.12, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.006, Rules used = {2009}
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.
| \(\displaystyle \int \left (324 x^3+e^{3 x+9 e^{e^{e^x}}} \left (-1687500 e^{x+e^{e^x}+e^x} x^4-562500 x^4-750000 x^3\right )+e^{x+3 e^{e^{e^x}}} \left (-8100 e^{x+e^{e^x}+e^x} x^4-2700 x^4-10800 x^3\right )+e^{2 x+6 e^{e^{e^x}}} \left (202500 e^{x+e^{e^x}+e^x} x^4+67500 x^4+135000 x^3\right )+e^{4 x+12 e^{e^{e^x}}} \left (4687500 e^{x+e^{e^x}+e^x} x^4+1562500 x^4+1562500 x^3\right )\right ) \, dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle 81 x^4-\frac {2700 e^{x+3 e^{e^{e^x}}} \left (3 e^{x+e^{e^x}+e^x} x^4+x^4\right )}{3 e^{x+e^{e^x}+e^x}+1}+\frac {33750 e^{2 x+6 e^{e^{e^x}}} \left (3 e^{x+e^{e^x}+e^x} x^4+x^4\right )}{3 e^{x+e^{e^x}+e^x}+1}-\frac {187500 e^{3 x+9 e^{e^{e^x}}} \left (3 e^{x+e^{e^x}+e^x} x^4+x^4\right )}{3 e^{x+e^{e^x}+e^x}+1}+\frac {390625 e^{4 x+12 e^{e^{e^x}}} \left (3 e^{x+e^{e^x}+e^x} x^4+x^4\right )}{3 e^{x+e^{e^x}+e^x}+1}\) |
Input:
Int[324*x^3 + E^(9*E^E^E^x + 3*x)*(-750000*x^3 - 562500*x^4 - 1687500*E^(E ^E^x + E^x + x)*x^4) + E^(3*E^E^E^x + x)*(-10800*x^3 - 2700*x^4 - 8100*E^( E^E^x + E^x + x)*x^4) + E^(6*E^E^E^x + 2*x)*(135000*x^3 + 67500*x^4 + 2025 00*E^(E^E^x + E^x + x)*x^4) + E^(12*E^E^E^x + 4*x)*(1562500*x^3 + 1562500* x^4 + 4687500*E^(E^E^x + E^x + x)*x^4),x]
Output:
81*x^4 - (2700*E^(3*E^E^E^x + x)*(x^4 + 3*E^(E^E^x + E^x + x)*x^4))/(1 + 3 *E^(E^E^x + E^x + x)) + (33750*E^(6*E^E^E^x + 2*x)*(x^4 + 3*E^(E^E^x + E^x + x)*x^4))/(1 + 3*E^(E^E^x + E^x + x)) - (187500*E^(9*E^E^E^x + 3*x)*(x^4 + 3*E^(E^E^x + E^x + x)*x^4))/(1 + 3*E^(E^E^x + E^x + x)) + (390625*E^(12 *E^E^E^x + 4*x)*(x^4 + 3*E^(E^E^x + E^x + x)*x^4))/(1 + 3*E^(E^E^x + E^x + x))
Leaf count of result is larger than twice the leaf count of optimal. \(68\) vs. \(2(21)=42\).
Time = 4.81 (sec) , antiderivative size = 69, normalized size of antiderivative = 2.76
| method | result | size |
| risch | \(390625 \,{\mathrm e}^{12 \,{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x}}}+4 x} x^{4}-187500 \,{\mathrm e}^{9 \,{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x}}}+3 x} x^{4}+33750 \,{\mathrm e}^{6 \,{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x}}}+2 x} x^{4}-2700 \,{\mathrm e}^{3 \,{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x}}}+x} x^{4}+81 x^{4}\) | \(69\) |
| parallelrisch | \(390625 \,{\mathrm e}^{12 \,{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x}}}+4 x} x^{4}-187500 \,{\mathrm e}^{9 \,{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x}}}+3 x} x^{4}+33750 \,{\mathrm e}^{6 \,{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x}}}+2 x} x^{4}-2700 \,{\mathrm e}^{3 \,{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x}}}+x} x^{4}+81 x^{4}\) | \(69\) |
Input:
int((4687500*x^4*exp(x)*exp(exp(x))*exp(exp(exp(x)))+1562500*x^4+1562500*x ^3)*exp(3*exp(exp(exp(x)))+x)^4+(-1687500*x^4*exp(x)*exp(exp(x))*exp(exp(e xp(x)))-562500*x^4-750000*x^3)*exp(3*exp(exp(exp(x)))+x)^3+(202500*x^4*exp (x)*exp(exp(x))*exp(exp(exp(x)))+67500*x^4+135000*x^3)*exp(3*exp(exp(exp(x )))+x)^2+(-8100*x^4*exp(x)*exp(exp(x))*exp(exp(exp(x)))-2700*x^4-10800*x^3 )*exp(3*exp(exp(exp(x)))+x)+324*x^3,x,method=_RETURNVERBOSE)
Output:
390625*exp(3*exp(exp(exp(x)))+x)^4*x^4-187500*exp(3*exp(exp(exp(x)))+x)^3* x^4+33750*exp(3*exp(exp(exp(x)))+x)^2*x^4-2700*exp(3*exp(exp(exp(x)))+x)*x ^4+81*x^4
Leaf count of result is larger than twice the leaf count of optimal. 145 vs. \(2 (19) = 38\).
Time = 0.09 (sec) , antiderivative size = 145, normalized size of antiderivative = 5.80 \[ \int \left (324 x^3+e^{9 e^{e^{e^x}}+3 x} \left (-750000 x^3-562500 x^4-1687500 e^{e^{e^x}+e^x+x} x^4\right )+e^{3 e^{e^{e^x}}+x} \left (-10800 x^3-2700 x^4-8100 e^{e^{e^x}+e^x+x} x^4\right )+e^{6 e^{e^{e^x}}+2 x} \left (135000 x^3+67500 x^4+202500 e^{e^{e^x}+e^x+x} x^4\right )+e^{12 e^{e^{e^x}}+4 x} \left (1562500 x^3+1562500 x^4+4687500 e^{e^{e^x}+e^x+x} x^4\right )\right ) \, dx=390625 \, x^{4} e^{\left (4 \, {\left (x e^{\left (x + e^{x}\right )} + 3 \, e^{\left (x + e^{x} + e^{\left (e^{x}\right )}\right )}\right )} e^{\left (-x - e^{x}\right )}\right )} - 187500 \, x^{4} e^{\left (3 \, {\left (x e^{\left (x + e^{x}\right )} + 3 \, e^{\left (x + e^{x} + e^{\left (e^{x}\right )}\right )}\right )} e^{\left (-x - e^{x}\right )}\right )} + 33750 \, x^{4} e^{\left (2 \, {\left (x e^{\left (x + e^{x}\right )} + 3 \, e^{\left (x + e^{x} + e^{\left (e^{x}\right )}\right )}\right )} e^{\left (-x - e^{x}\right )}\right )} - 2700 \, x^{4} e^{\left ({\left (x e^{\left (x + e^{x}\right )} + 3 \, e^{\left (x + e^{x} + e^{\left (e^{x}\right )}\right )}\right )} e^{\left (-x - e^{x}\right )}\right )} + 81 \, x^{4} \] Input:
integrate((4687500*x^4*exp(x)*exp(exp(x))*exp(exp(exp(x)))+1562500*x^4+156 2500*x^3)*exp(3*exp(exp(exp(x)))+x)^4+(-1687500*x^4*exp(x)*exp(exp(x))*exp (exp(exp(x)))-562500*x^4-750000*x^3)*exp(3*exp(exp(exp(x)))+x)^3+(202500*x ^4*exp(x)*exp(exp(x))*exp(exp(exp(x)))+67500*x^4+135000*x^3)*exp(3*exp(exp (exp(x)))+x)^2+(-8100*x^4*exp(x)*exp(exp(x))*exp(exp(exp(x)))-2700*x^4-108 00*x^3)*exp(3*exp(exp(exp(x)))+x)+324*x^3,x, algorithm="fricas")
Output:
390625*x^4*e^(4*(x*e^(x + e^x) + 3*e^(x + e^x + e^(e^x)))*e^(-x - e^x)) - 187500*x^4*e^(3*(x*e^(x + e^x) + 3*e^(x + e^x + e^(e^x)))*e^(-x - e^x)) + 33750*x^4*e^(2*(x*e^(x + e^x) + 3*e^(x + e^x + e^(e^x)))*e^(-x - e^x)) - 2 700*x^4*e^((x*e^(x + e^x) + 3*e^(x + e^x + e^(e^x)))*e^(-x - e^x)) + 81*x^ 4
Leaf count of result is larger than twice the leaf count of optimal. 76 vs. \(2 (19) = 38\).
Time = 4.30 (sec) , antiderivative size = 76, normalized size of antiderivative = 3.04 \[ \int \left (324 x^3+e^{9 e^{e^{e^x}}+3 x} \left (-750000 x^3-562500 x^4-1687500 e^{e^{e^x}+e^x+x} x^4\right )+e^{3 e^{e^{e^x}}+x} \left (-10800 x^3-2700 x^4-8100 e^{e^{e^x}+e^x+x} x^4\right )+e^{6 e^{e^{e^x}}+2 x} \left (135000 x^3+67500 x^4+202500 e^{e^{e^x}+e^x+x} x^4\right )+e^{12 e^{e^{e^x}}+4 x} \left (1562500 x^3+1562500 x^4+4687500 e^{e^{e^x}+e^x+x} x^4\right )\right ) \, dx=- 2700 x^{4} e^{x + 3 e^{e^{e^{x}}}} + 33750 x^{4} e^{2 x + 6 e^{e^{e^{x}}}} - 187500 x^{4} e^{3 x + 9 e^{e^{e^{x}}}} + 390625 x^{4} e^{4 x + 12 e^{e^{e^{x}}}} + 81 x^{4} \] Input:
integrate((4687500*x**4*exp(x)*exp(exp(x))*exp(exp(exp(x)))+1562500*x**4+1 562500*x**3)*exp(3*exp(exp(exp(x)))+x)**4+(-1687500*x**4*exp(x)*exp(exp(x) )*exp(exp(exp(x)))-562500*x**4-750000*x**3)*exp(3*exp(exp(exp(x)))+x)**3+( 202500*x**4*exp(x)*exp(exp(x))*exp(exp(exp(x)))+67500*x**4+135000*x**3)*ex p(3*exp(exp(exp(x)))+x)**2+(-8100*x**4*exp(x)*exp(exp(x))*exp(exp(exp(x))) -2700*x**4-10800*x**3)*exp(3*exp(exp(exp(x)))+x)+324*x**3,x)
Output:
-2700*x**4*exp(x + 3*exp(exp(exp(x)))) + 33750*x**4*exp(2*x + 6*exp(exp(ex p(x)))) - 187500*x**4*exp(3*x + 9*exp(exp(exp(x)))) + 390625*x**4*exp(4*x + 12*exp(exp(exp(x)))) + 81*x**4
Leaf count of result is larger than twice the leaf count of optimal. 68 vs. \(2 (19) = 38\).
Time = 0.15 (sec) , antiderivative size = 68, normalized size of antiderivative = 2.72 \[ \int \left (324 x^3+e^{9 e^{e^{e^x}}+3 x} \left (-750000 x^3-562500 x^4-1687500 e^{e^{e^x}+e^x+x} x^4\right )+e^{3 e^{e^{e^x}}+x} \left (-10800 x^3-2700 x^4-8100 e^{e^{e^x}+e^x+x} x^4\right )+e^{6 e^{e^{e^x}}+2 x} \left (135000 x^3+67500 x^4+202500 e^{e^{e^x}+e^x+x} x^4\right )+e^{12 e^{e^{e^x}}+4 x} \left (1562500 x^3+1562500 x^4+4687500 e^{e^{e^x}+e^x+x} x^4\right )\right ) \, dx=390625 \, x^{4} e^{\left (4 \, x + 12 \, e^{\left (e^{\left (e^{x}\right )}\right )}\right )} - 187500 \, x^{4} e^{\left (3 \, x + 9 \, e^{\left (e^{\left (e^{x}\right )}\right )}\right )} + 33750 \, x^{4} e^{\left (2 \, x + 6 \, e^{\left (e^{\left (e^{x}\right )}\right )}\right )} - 2700 \, x^{4} e^{\left (x + 3 \, e^{\left (e^{\left (e^{x}\right )}\right )}\right )} + 81 \, x^{4} \] Input:
integrate((4687500*x^4*exp(x)*exp(exp(x))*exp(exp(exp(x)))+1562500*x^4+156 2500*x^3)*exp(3*exp(exp(exp(x)))+x)^4+(-1687500*x^4*exp(x)*exp(exp(x))*exp (exp(exp(x)))-562500*x^4-750000*x^3)*exp(3*exp(exp(exp(x)))+x)^3+(202500*x ^4*exp(x)*exp(exp(x))*exp(exp(exp(x)))+67500*x^4+135000*x^3)*exp(3*exp(exp (exp(x)))+x)^2+(-8100*x^4*exp(x)*exp(exp(x))*exp(exp(exp(x)))-2700*x^4-108 00*x^3)*exp(3*exp(exp(exp(x)))+x)+324*x^3,x, algorithm="maxima")
Output:
390625*x^4*e^(4*x + 12*e^(e^(e^x))) - 187500*x^4*e^(3*x + 9*e^(e^(e^x))) + 33750*x^4*e^(2*x + 6*e^(e^(e^x))) - 2700*x^4*e^(x + 3*e^(e^(e^x))) + 81*x ^4
\[ \int \left (324 x^3+e^{9 e^{e^{e^x}}+3 x} \left (-750000 x^3-562500 x^4-1687500 e^{e^{e^x}+e^x+x} x^4\right )+e^{3 e^{e^{e^x}}+x} \left (-10800 x^3-2700 x^4-8100 e^{e^{e^x}+e^x+x} x^4\right )+e^{6 e^{e^{e^x}}+2 x} \left (135000 x^3+67500 x^4+202500 e^{e^{e^x}+e^x+x} x^4\right )+e^{12 e^{e^{e^x}}+4 x} \left (1562500 x^3+1562500 x^4+4687500 e^{e^{e^x}+e^x+x} x^4\right )\right ) \, dx=\int { 324 \, x^{3} + 1562500 \, {\left (3 \, x^{4} e^{\left (x + e^{x} + e^{\left (e^{x}\right )}\right )} + x^{4} + x^{3}\right )} e^{\left (4 \, x + 12 \, e^{\left (e^{\left (e^{x}\right )}\right )}\right )} - 187500 \, {\left (9 \, x^{4} e^{\left (x + e^{x} + e^{\left (e^{x}\right )}\right )} + 3 \, x^{4} + 4 \, x^{3}\right )} e^{\left (3 \, x + 9 \, e^{\left (e^{\left (e^{x}\right )}\right )}\right )} + 67500 \, {\left (3 \, x^{4} e^{\left (x + e^{x} + e^{\left (e^{x}\right )}\right )} + x^{4} + 2 \, x^{3}\right )} e^{\left (2 \, x + 6 \, e^{\left (e^{\left (e^{x}\right )}\right )}\right )} - 2700 \, {\left (3 \, x^{4} e^{\left (x + e^{x} + e^{\left (e^{x}\right )}\right )} + x^{4} + 4 \, x^{3}\right )} e^{\left (x + 3 \, e^{\left (e^{\left (e^{x}\right )}\right )}\right )} \,d x } \] Input:
integrate((4687500*x^4*exp(x)*exp(exp(x))*exp(exp(exp(x)))+1562500*x^4+156 2500*x^3)*exp(3*exp(exp(exp(x)))+x)^4+(-1687500*x^4*exp(x)*exp(exp(x))*exp (exp(exp(x)))-562500*x^4-750000*x^3)*exp(3*exp(exp(exp(x)))+x)^3+(202500*x ^4*exp(x)*exp(exp(x))*exp(exp(exp(x)))+67500*x^4+135000*x^3)*exp(3*exp(exp (exp(x)))+x)^2+(-8100*x^4*exp(x)*exp(exp(x))*exp(exp(exp(x)))-2700*x^4-108 00*x^3)*exp(3*exp(exp(exp(x)))+x)+324*x^3,x, algorithm="giac")
Output:
integrate(324*x^3 + 1562500*(3*x^4*e^(x + e^x + e^(e^x)) + x^4 + x^3)*e^(4 *x + 12*e^(e^(e^x))) - 187500*(9*x^4*e^(x + e^x + e^(e^x)) + 3*x^4 + 4*x^3 )*e^(3*x + 9*e^(e^(e^x))) + 67500*(3*x^4*e^(x + e^x + e^(e^x)) + x^4 + 2*x ^3)*e^(2*x + 6*e^(e^(e^x))) - 2700*(3*x^4*e^(x + e^x + e^(e^x)) + x^4 + 4* x^3)*e^(x + 3*e^(e^(e^x))), x)
Time = 0.32 (sec) , antiderivative size = 68, normalized size of antiderivative = 2.72 \[ \int \left (324 x^3+e^{9 e^{e^{e^x}}+3 x} \left (-750000 x^3-562500 x^4-1687500 e^{e^{e^x}+e^x+x} x^4\right )+e^{3 e^{e^{e^x}}+x} \left (-10800 x^3-2700 x^4-8100 e^{e^{e^x}+e^x+x} x^4\right )+e^{6 e^{e^{e^x}}+2 x} \left (135000 x^3+67500 x^4+202500 e^{e^{e^x}+e^x+x} x^4\right )+e^{12 e^{e^{e^x}}+4 x} \left (1562500 x^3+1562500 x^4+4687500 e^{e^{e^x}+e^x+x} x^4\right )\right ) \, dx=81\,x^4-2700\,x^4\,{\mathrm {e}}^{x+3\,{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^x}}}+33750\,x^4\,{\mathrm {e}}^{2\,x+6\,{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^x}}}-187500\,x^4\,{\mathrm {e}}^{3\,x+9\,{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^x}}}+390625\,x^4\,{\mathrm {e}}^{4\,x+12\,{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^x}}} \] Input:
int(exp(2*x + 6*exp(exp(exp(x))))*(135000*x^3 + 67500*x^4 + 202500*x^4*exp (exp(x))*exp(exp(exp(x)))*exp(x)) - exp(x + 3*exp(exp(exp(x))))*(10800*x^3 + 2700*x^4 + 8100*x^4*exp(exp(x))*exp(exp(exp(x)))*exp(x)) - exp(3*x + 9* exp(exp(exp(x))))*(750000*x^3 + 562500*x^4 + 1687500*x^4*exp(exp(x))*exp(e xp(exp(x)))*exp(x)) + exp(4*x + 12*exp(exp(exp(x))))*(1562500*x^3 + 156250 0*x^4 + 4687500*x^4*exp(exp(x))*exp(exp(exp(x)))*exp(x)) + 324*x^3,x)
Output:
81*x^4 - 2700*x^4*exp(x + 3*exp(exp(exp(x)))) + 33750*x^4*exp(2*x + 6*exp( exp(exp(x)))) - 187500*x^4*exp(3*x + 9*exp(exp(exp(x)))) + 390625*x^4*exp( 4*x + 12*exp(exp(exp(x))))
Time = 0.20 (sec) , antiderivative size = 72, normalized size of antiderivative = 2.88 \[ \int \left (324 x^3+e^{9 e^{e^{e^x}}+3 x} \left (-750000 x^3-562500 x^4-1687500 e^{e^{e^x}+e^x+x} x^4\right )+e^{3 e^{e^{e^x}}+x} \left (-10800 x^3-2700 x^4-8100 e^{e^{e^x}+e^x+x} x^4\right )+e^{6 e^{e^{e^x}}+2 x} \left (135000 x^3+67500 x^4+202500 e^{e^{e^x}+e^x+x} x^4\right )+e^{12 e^{e^{e^x}}+4 x} \left (1562500 x^3+1562500 x^4+4687500 e^{e^{e^x}+e^x+x} x^4\right )\right ) \, dx=x^{4} \left (390625 e^{12 e^{e^{e^{x}}}+4 x}-187500 e^{9 e^{e^{e^{x}}}+3 x}+33750 e^{6 e^{e^{e^{x}}}+2 x}-2700 e^{3 e^{e^{e^{x}}}+x}+81\right ) \] Input:
int((4687500*x^4*exp(x)*exp(exp(x))*exp(exp(exp(x)))+1562500*x^4+1562500*x ^3)*exp(3*exp(exp(exp(x)))+x)^4+(-1687500*x^4*exp(x)*exp(exp(x))*exp(exp(e xp(x)))-562500*x^4-750000*x^3)*exp(3*exp(exp(exp(x)))+x)^3+(202500*x^4*exp (x)*exp(exp(x))*exp(exp(exp(x)))+67500*x^4+135000*x^3)*exp(3*exp(exp(exp(x )))+x)^2+(-8100*x^4*exp(x)*exp(exp(x))*exp(exp(exp(x)))-2700*x^4-10800*x^3 )*exp(3*exp(exp(exp(x)))+x)+324*x^3,x)
Output:
x**4*(390625*e**(12*e**(e**(e**x)) + 4*x) - 187500*e**(9*e**(e**(e**x)) + 3*x) + 33750*e**(6*e**(e**(e**x)) + 2*x) - 2700*e**(3*e**(e**(e**x)) + x) + 81)