Integrand size = 339, antiderivative size = 28 \[ \int \frac {1332+e^{20+4 e^3} x^4+e^{10} \left (5751 x^2+1260 x^3+69 x^4\right )+e^{20+3 e^3} \left (-36 x^4-4 x^5\right )+e^{20} \left (6561 x^4+2916 x^5+486 x^6+36 x^7+x^8\right )+e^{2 e^3} \left (71 e^{10} x^2+e^{20} \left (486 x^4+108 x^5+6 x^6\right )\right )+e^{e^3} \left (e^{10} \left (-1278 x^2-140 x^3\right )+e^{20} \left (-2916 x^4-972 x^5-108 x^6-4 x^7\right )\right )}{1296+e^{20+4 e^3} x^4+e^{10} \left (5832 x^2+1296 x^3+72 x^4\right )+e^{20+3 e^3} \left (-36 x^4-4 x^5\right )+e^{20} \left (6561 x^4+2916 x^5+486 x^6+36 x^7+x^8\right )+e^{2 e^3} \left (72 e^{10} x^2+e^{20} \left (486 x^4+108 x^5+6 x^6\right )\right )+e^{e^3} \left (e^{10} \left (-1296 x^2-144 x^3\right )+e^{20} \left (-2916 x^4-972 x^5-108 x^6-4 x^7\right )\right )} \, dx=-1+x+\frac {x}{36+e^{10} \left (-9+e^{e^3}-x\right )^2 x^2} \]
Leaf count is larger than twice the leaf count of optimal. \(88\) vs. \(2(28)=56\).
Time = 0.62 (sec) , antiderivative size = 88, normalized size of antiderivative = 3.14 \[ \int \frac {1332+e^{20+4 e^3} x^4+e^{10} \left (5751 x^2+1260 x^3+69 x^4\right )+e^{20+3 e^3} \left (-36 x^4-4 x^5\right )+e^{20} \left (6561 x^4+2916 x^5+486 x^6+36 x^7+x^8\right )+e^{2 e^3} \left (71 e^{10} x^2+e^{20} \left (486 x^4+108 x^5+6 x^6\right )\right )+e^{e^3} \left (e^{10} \left (-1278 x^2-140 x^3\right )+e^{20} \left (-2916 x^4-972 x^5-108 x^6-4 x^7\right )\right )}{1296+e^{20+4 e^3} x^4+e^{10} \left (5832 x^2+1296 x^3+72 x^4\right )+e^{20+3 e^3} \left (-36 x^4-4 x^5\right )+e^{20} \left (6561 x^4+2916 x^5+486 x^6+36 x^7+x^8\right )+e^{2 e^3} \left (72 e^{10} x^2+e^{20} \left (486 x^4+108 x^5+6 x^6\right )\right )+e^{e^3} \left (e^{10} \left (-1296 x^2-144 x^3\right )+e^{20} \left (-2916 x^4-972 x^5-108 x^6-4 x^7\right )\right )} \, dx=\frac {x \left (37+e^{2 \left (5+e^3\right )} x^2-2 e^{10+e^3} x^2 (9+x)+e^{10} x^2 (9+x)^2\right )}{36+e^{2 \left (5+e^3\right )} x^2-2 e^{10+e^3} x^2 (9+x)+e^{10} x^2 (9+x)^2} \]
Integrate[(1332 + E^(20 + 4*E^3)*x^4 + E^10*(5751*x^2 + 1260*x^3 + 69*x^4) + E^(20 + 3*E^3)*(-36*x^4 - 4*x^5) + E^20*(6561*x^4 + 2916*x^5 + 486*x^6 + 36*x^7 + x^8) + E^(2*E^3)*(71*E^10*x^2 + E^20*(486*x^4 + 108*x^5 + 6*x^6 )) + E^E^3*(E^10*(-1278*x^2 - 140*x^3) + E^20*(-2916*x^4 - 972*x^5 - 108*x ^6 - 4*x^7)))/(1296 + E^(20 + 4*E^3)*x^4 + E^10*(5832*x^2 + 1296*x^3 + 72* x^4) + E^(20 + 3*E^3)*(-36*x^4 - 4*x^5) + E^20*(6561*x^4 + 2916*x^5 + 486* x^6 + 36*x^7 + x^8) + E^(2*E^3)*(72*E^10*x^2 + E^20*(486*x^4 + 108*x^5 + 6 *x^6)) + E^E^3*(E^10*(-1296*x^2 - 144*x^3) + E^20*(-2916*x^4 - 972*x^5 - 1 08*x^6 - 4*x^7))),x]
(x*(37 + E^(2*(5 + E^3))*x^2 - 2*E^(10 + E^3)*x^2*(9 + x) + E^10*x^2*(9 + x)^2))/(36 + E^(2*(5 + E^3))*x^2 - 2*E^(10 + E^3)*x^2*(9 + x) + E^10*x^2*( 9 + x)^2)
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.
| \(\displaystyle \int \frac {e^{20+4 e^3} x^4+e^{20+3 e^3} \left (-4 x^5-36 x^4\right )+e^{10} \left (69 x^4+1260 x^3+5751 x^2\right )+e^{2 e^3} \left (71 e^{10} x^2+e^{20} \left (6 x^6+108 x^5+486 x^4\right )\right )+e^{20} \left (x^8+36 x^7+486 x^6+2916 x^5+6561 x^4\right )+e^{e^3} \left (e^{10} \left (-140 x^3-1278 x^2\right )+e^{20} \left (-4 x^7-108 x^6-972 x^5-2916 x^4\right )\right )+1332}{e^{20+4 e^3} x^4+e^{20+3 e^3} \left (-4 x^5-36 x^4\right )+e^{10} \left (72 x^4+1296 x^3+5832 x^2\right )+e^{2 e^3} \left (72 e^{10} x^2+e^{20} \left (6 x^6+108 x^5+486 x^4\right )\right )+e^{20} \left (x^8+36 x^7+486 x^6+2916 x^5+6561 x^4\right )+e^{e^3} \left (e^{10} \left (-144 x^3-1296 x^2\right )+e^{20} \left (-4 x^7-108 x^6-972 x^5-2916 x^4\right )\right )+1296} \, dx\) |
| \(\Big \downarrow \) 2462 |
| \(\displaystyle \int \left (\frac {2 \left (e^{10} \left (9-e^{e^3}\right ) x^3+e^{10} \left (9-e^{e^3}\right )^2 x^2+72\right )}{\left (e^{10} x^4+2 e^{10} \left (9-e^{e^3}\right ) x^3+e^{10} \left (9-e^{e^3}\right )^2 x^2+36\right )^2}+\frac {3}{-e^{10} x^4-2 e^{10} \left (9-e^{e^3}\right ) x^3-e^{10} \left (9-e^{e^3}\right )^2 x^2-36}+1\right )dx\) |
| \(\Big \downarrow \) 7299 |
| \(\displaystyle \int \left (\frac {2 \left (e^{10} \left (9-e^{e^3}\right ) x^3+e^{10} \left (9-e^{e^3}\right )^2 x^2+72\right )}{\left (e^{10} x^4+2 e^{10} \left (9-e^{e^3}\right ) x^3+e^{10} \left (9-e^{e^3}\right )^2 x^2+36\right )^2}+\frac {3}{-e^{10} x^4-2 e^{10} \left (9-e^{e^3}\right ) x^3-e^{10} \left (9-e^{e^3}\right )^2 x^2-36}+1\right )dx\) |
Int[(1332 + E^(20 + 4*E^3)*x^4 + E^10*(5751*x^2 + 1260*x^3 + 69*x^4) + E^( 20 + 3*E^3)*(-36*x^4 - 4*x^5) + E^20*(6561*x^4 + 2916*x^5 + 486*x^6 + 36*x ^7 + x^8) + E^(2*E^3)*(71*E^10*x^2 + E^20*(486*x^4 + 108*x^5 + 6*x^6)) + E ^E^3*(E^10*(-1278*x^2 - 140*x^3) + E^20*(-2916*x^4 - 972*x^5 - 108*x^6 - 4 *x^7)))/(1296 + E^(20 + 4*E^3)*x^4 + E^10*(5832*x^2 + 1296*x^3 + 72*x^4) + E^(20 + 3*E^3)*(-36*x^4 - 4*x^5) + E^20*(6561*x^4 + 2916*x^5 + 486*x^6 + 36*x^7 + x^8) + E^(2*E^3)*(72*E^10*x^2 + E^20*(486*x^4 + 108*x^5 + 6*x^6)) + E^E^3*(E^10*(-1296*x^2 - 144*x^3) + E^20*(-2916*x^4 - 972*x^5 - 108*x^6 - 4*x^7))),x]
3.19.61.3.1 Defintions of rubi rules used
Int[(u_.)*(Px_)^(p_), x_Symbol] :> With[{Qx = Factor[Px]}, Int[ExpandIntegr and[u*Qx^p, x], x] /; !SumQ[NonfreeFactors[Qx, x]]] /; PolyQ[Px, x] && GtQ [Expon[Px, x], 2] && !BinomialQ[Px, x] && !TrinomialQ[Px, x] && ILtQ[p, 0 ] && RationalFunctionQ[u, x]
Leaf count of result is larger than twice the leaf count of optimal. \(59\) vs. \(2(27)=54\).
Time = 0.53 (sec) , antiderivative size = 60, normalized size of antiderivative = 2.14
| method | result | size |
| risch | \(x +\frac {x}{x^{2} {\mathrm e}^{2 \,{\mathrm e}^{3}+10}-2 x^{3} {\mathrm e}^{{\mathrm e}^{3}+10}+x^{4} {\mathrm e}^{10}-18 x^{2} {\mathrm e}^{{\mathrm e}^{3}+10}+18 x^{3} {\mathrm e}^{10}+81 x^{2} {\mathrm e}^{10}+36}\) | \(60\) |
| norman | \(\frac {x^{5} {\mathrm e}^{10}+{\mathrm e}^{10} \left ({\mathrm e}^{2 \,{\mathrm e}^{3}}-18 \,{\mathrm e}^{{\mathrm e}^{3}}+81\right ) x^{3}+\left (-2 \,{\mathrm e}^{{\mathrm e}^{3}} {\mathrm e}^{10}+18 \,{\mathrm e}^{10}\right ) x^{4}+37 x}{{\mathrm e}^{2 \,{\mathrm e}^{3}} {\mathrm e}^{10} x^{2}-2 \,{\mathrm e}^{{\mathrm e}^{3}} {\mathrm e}^{10} x^{3}+x^{4} {\mathrm e}^{10}-18 \,{\mathrm e}^{{\mathrm e}^{3}} {\mathrm e}^{10} x^{2}+18 x^{3} {\mathrm e}^{10}+81 x^{2} {\mathrm e}^{10}+36}\) | \(121\) |
| gosper | \(\frac {x \left ({\mathrm e}^{2 \,{\mathrm e}^{3}} {\mathrm e}^{10} x^{2}-2 \,{\mathrm e}^{{\mathrm e}^{3}} {\mathrm e}^{10} x^{3}+x^{4} {\mathrm e}^{10}-18 \,{\mathrm e}^{{\mathrm e}^{3}} {\mathrm e}^{10} x^{2}+18 x^{3} {\mathrm e}^{10}+81 x^{2} {\mathrm e}^{10}+37\right )}{{\mathrm e}^{2 \,{\mathrm e}^{3}} {\mathrm e}^{10} x^{2}-2 \,{\mathrm e}^{{\mathrm e}^{3}} {\mathrm e}^{10} x^{3}+x^{4} {\mathrm e}^{10}-18 \,{\mathrm e}^{{\mathrm e}^{3}} {\mathrm e}^{10} x^{2}+18 x^{3} {\mathrm e}^{10}+81 x^{2} {\mathrm e}^{10}+36}\) | \(135\) |
| parallelrisch | \(\frac {36 \,{\mathrm e}^{2 \,{\mathrm e}^{3}} {\mathrm e}^{10} x^{3}-72 \,{\mathrm e}^{{\mathrm e}^{3}} {\mathrm e}^{10} x^{4}+36 x^{5} {\mathrm e}^{10}-648 \,{\mathrm e}^{{\mathrm e}^{3}} {\mathrm e}^{10} x^{3}+648 x^{4} {\mathrm e}^{10}+2916 x^{3} {\mathrm e}^{10}+1332 x}{36 \,{\mathrm e}^{2 \,{\mathrm e}^{3}} {\mathrm e}^{10} x^{2}-72 \,{\mathrm e}^{{\mathrm e}^{3}} {\mathrm e}^{10} x^{3}+36 x^{4} {\mathrm e}^{10}-648 \,{\mathrm e}^{{\mathrm e}^{3}} {\mathrm e}^{10} x^{2}+648 x^{3} {\mathrm e}^{10}+2916 x^{2} {\mathrm e}^{10}+1296}\) | \(139\) |
int((x^4*exp(5)^4*exp(exp(3))^4+(-4*x^5-36*x^4)*exp(5)^4*exp(exp(3))^3+((6 *x^6+108*x^5+486*x^4)*exp(5)^4+71*x^2*exp(5)^2)*exp(exp(3))^2+((-4*x^7-108 *x^6-972*x^5-2916*x^4)*exp(5)^4+(-140*x^3-1278*x^2)*exp(5)^2)*exp(exp(3))+ (x^8+36*x^7+486*x^6+2916*x^5+6561*x^4)*exp(5)^4+(69*x^4+1260*x^3+5751*x^2) *exp(5)^2+1332)/(x^4*exp(5)^4*exp(exp(3))^4+(-4*x^5-36*x^4)*exp(5)^4*exp(e xp(3))^3+((6*x^6+108*x^5+486*x^4)*exp(5)^4+72*x^2*exp(5)^2)*exp(exp(3))^2+ ((-4*x^7-108*x^6-972*x^5-2916*x^4)*exp(5)^4+(-144*x^3-1296*x^2)*exp(5)^2)* exp(exp(3))+(x^8+36*x^7+486*x^6+2916*x^5+6561*x^4)*exp(5)^4+(72*x^4+1296*x ^3+5832*x^2)*exp(5)^2+1296),x,method=_RETURNVERBOSE)
x+x/(x^2*exp(2*exp(3)+10)-2*x^3*exp(exp(3)+10)+x^4*exp(10)-18*x^2*exp(exp( 3)+10)+18*x^3*exp(10)+81*x^2*exp(10)+36)
Leaf count of result is larger than twice the leaf count of optimal. 97 vs. \(2 (25) = 50\).
Time = 0.26 (sec) , antiderivative size = 97, normalized size of antiderivative = 3.46 \[ \int \frac {1332+e^{20+4 e^3} x^4+e^{10} \left (5751 x^2+1260 x^3+69 x^4\right )+e^{20+3 e^3} \left (-36 x^4-4 x^5\right )+e^{20} \left (6561 x^4+2916 x^5+486 x^6+36 x^7+x^8\right )+e^{2 e^3} \left (71 e^{10} x^2+e^{20} \left (486 x^4+108 x^5+6 x^6\right )\right )+e^{e^3} \left (e^{10} \left (-1278 x^2-140 x^3\right )+e^{20} \left (-2916 x^4-972 x^5-108 x^6-4 x^7\right )\right )}{1296+e^{20+4 e^3} x^4+e^{10} \left (5832 x^2+1296 x^3+72 x^4\right )+e^{20+3 e^3} \left (-36 x^4-4 x^5\right )+e^{20} \left (6561 x^4+2916 x^5+486 x^6+36 x^7+x^8\right )+e^{2 e^3} \left (72 e^{10} x^2+e^{20} \left (486 x^4+108 x^5+6 x^6\right )\right )+e^{e^3} \left (e^{10} \left (-1296 x^2-144 x^3\right )+e^{20} \left (-2916 x^4-972 x^5-108 x^6-4 x^7\right )\right )} \, dx=\frac {x^{3} e^{\left (2 \, e^{3} + 10\right )} + {\left (x^{5} + 18 \, x^{4} + 81 \, x^{3}\right )} e^{10} - 2 \, {\left (x^{4} + 9 \, x^{3}\right )} e^{\left (e^{3} + 10\right )} + 37 \, x}{x^{2} e^{\left (2 \, e^{3} + 10\right )} + {\left (x^{4} + 18 \, x^{3} + 81 \, x^{2}\right )} e^{10} - 2 \, {\left (x^{3} + 9 \, x^{2}\right )} e^{\left (e^{3} + 10\right )} + 36} \]
integrate((x^4*exp(5)^4*exp(exp(3))^4+(-4*x^5-36*x^4)*exp(5)^4*exp(exp(3)) ^3+((6*x^6+108*x^5+486*x^4)*exp(5)^4+71*x^2*exp(5)^2)*exp(exp(3))^2+((-4*x ^7-108*x^6-972*x^5-2916*x^4)*exp(5)^4+(-140*x^3-1278*x^2)*exp(5)^2)*exp(ex p(3))+(x^8+36*x^7+486*x^6+2916*x^5+6561*x^4)*exp(5)^4+(69*x^4+1260*x^3+575 1*x^2)*exp(5)^2+1332)/(x^4*exp(5)^4*exp(exp(3))^4+(-4*x^5-36*x^4)*exp(5)^4 *exp(exp(3))^3+((6*x^6+108*x^5+486*x^4)*exp(5)^4+72*x^2*exp(5)^2)*exp(exp( 3))^2+((-4*x^7-108*x^6-972*x^5-2916*x^4)*exp(5)^4+(-144*x^3-1296*x^2)*exp( 5)^2)*exp(exp(3))+(x^8+36*x^7+486*x^6+2916*x^5+6561*x^4)*exp(5)^4+(72*x^4+ 1296*x^3+5832*x^2)*exp(5)^2+1296),x, algorithm=\
(x^3*e^(2*e^3 + 10) + (x^5 + 18*x^4 + 81*x^3)*e^10 - 2*(x^4 + 9*x^3)*e^(e^ 3 + 10) + 37*x)/(x^2*e^(2*e^3 + 10) + (x^4 + 18*x^3 + 81*x^2)*e^10 - 2*(x^ 3 + 9*x^2)*e^(e^3 + 10) + 36)
Leaf count of result is larger than twice the leaf count of optimal. 58 vs. \(2 (22) = 44\).
Time = 3.53 (sec) , antiderivative size = 58, normalized size of antiderivative = 2.07 \[ \int \frac {1332+e^{20+4 e^3} x^4+e^{10} \left (5751 x^2+1260 x^3+69 x^4\right )+e^{20+3 e^3} \left (-36 x^4-4 x^5\right )+e^{20} \left (6561 x^4+2916 x^5+486 x^6+36 x^7+x^8\right )+e^{2 e^3} \left (71 e^{10} x^2+e^{20} \left (486 x^4+108 x^5+6 x^6\right )\right )+e^{e^3} \left (e^{10} \left (-1278 x^2-140 x^3\right )+e^{20} \left (-2916 x^4-972 x^5-108 x^6-4 x^7\right )\right )}{1296+e^{20+4 e^3} x^4+e^{10} \left (5832 x^2+1296 x^3+72 x^4\right )+e^{20+3 e^3} \left (-36 x^4-4 x^5\right )+e^{20} \left (6561 x^4+2916 x^5+486 x^6+36 x^7+x^8\right )+e^{2 e^3} \left (72 e^{10} x^2+e^{20} \left (486 x^4+108 x^5+6 x^6\right )\right )+e^{e^3} \left (e^{10} \left (-1296 x^2-144 x^3\right )+e^{20} \left (-2916 x^4-972 x^5-108 x^6-4 x^7\right )\right )} \, dx=x + \frac {x}{x^{4} e^{10} + x^{3} \left (- 2 e^{10} e^{e^{3}} + 18 e^{10}\right ) + x^{2} \left (- 18 e^{10} e^{e^{3}} + 81 e^{10} + e^{10} e^{2 e^{3}}\right ) + 36} \]
integrate((x**4*exp(5)**4*exp(exp(3))**4+(-4*x**5-36*x**4)*exp(5)**4*exp(e xp(3))**3+((6*x**6+108*x**5+486*x**4)*exp(5)**4+71*x**2*exp(5)**2)*exp(exp (3))**2+((-4*x**7-108*x**6-972*x**5-2916*x**4)*exp(5)**4+(-140*x**3-1278*x **2)*exp(5)**2)*exp(exp(3))+(x**8+36*x**7+486*x**6+2916*x**5+6561*x**4)*ex p(5)**4+(69*x**4+1260*x**3+5751*x**2)*exp(5)**2+1332)/(x**4*exp(5)**4*exp( exp(3))**4+(-4*x**5-36*x**4)*exp(5)**4*exp(exp(3))**3+((6*x**6+108*x**5+48 6*x**4)*exp(5)**4+72*x**2*exp(5)**2)*exp(exp(3))**2+((-4*x**7-108*x**6-972 *x**5-2916*x**4)*exp(5)**4+(-144*x**3-1296*x**2)*exp(5)**2)*exp(exp(3))+(x **8+36*x**7+486*x**6+2916*x**5+6561*x**4)*exp(5)**4+(72*x**4+1296*x**3+583 2*x**2)*exp(5)**2+1296),x)
x + x/(x**4*exp(10) + x**3*(-2*exp(10)*exp(exp(3)) + 18*exp(10)) + x**2*(- 18*exp(10)*exp(exp(3)) + 81*exp(10) + exp(10)*exp(2*exp(3))) + 36)
Leaf count of result is larger than twice the leaf count of optimal. 54 vs. \(2 (25) = 50\).
Time = 0.20 (sec) , antiderivative size = 54, normalized size of antiderivative = 1.93 \[ \int \frac {1332+e^{20+4 e^3} x^4+e^{10} \left (5751 x^2+1260 x^3+69 x^4\right )+e^{20+3 e^3} \left (-36 x^4-4 x^5\right )+e^{20} \left (6561 x^4+2916 x^5+486 x^6+36 x^7+x^8\right )+e^{2 e^3} \left (71 e^{10} x^2+e^{20} \left (486 x^4+108 x^5+6 x^6\right )\right )+e^{e^3} \left (e^{10} \left (-1278 x^2-140 x^3\right )+e^{20} \left (-2916 x^4-972 x^5-108 x^6-4 x^7\right )\right )}{1296+e^{20+4 e^3} x^4+e^{10} \left (5832 x^2+1296 x^3+72 x^4\right )+e^{20+3 e^3} \left (-36 x^4-4 x^5\right )+e^{20} \left (6561 x^4+2916 x^5+486 x^6+36 x^7+x^8\right )+e^{2 e^3} \left (72 e^{10} x^2+e^{20} \left (486 x^4+108 x^5+6 x^6\right )\right )+e^{e^3} \left (e^{10} \left (-1296 x^2-144 x^3\right )+e^{20} \left (-2916 x^4-972 x^5-108 x^6-4 x^7\right )\right )} \, dx=x + \frac {x}{x^{4} e^{10} + 2 \, x^{3} {\left (9 \, e^{10} - e^{\left (e^{3} + 10\right )}\right )} + x^{2} {\left (81 \, e^{10} + e^{\left (2 \, e^{3} + 10\right )} - 18 \, e^{\left (e^{3} + 10\right )}\right )} + 36} \]
integrate((x^4*exp(5)^4*exp(exp(3))^4+(-4*x^5-36*x^4)*exp(5)^4*exp(exp(3)) ^3+((6*x^6+108*x^5+486*x^4)*exp(5)^4+71*x^2*exp(5)^2)*exp(exp(3))^2+((-4*x ^7-108*x^6-972*x^5-2916*x^4)*exp(5)^4+(-140*x^3-1278*x^2)*exp(5)^2)*exp(ex p(3))+(x^8+36*x^7+486*x^6+2916*x^5+6561*x^4)*exp(5)^4+(69*x^4+1260*x^3+575 1*x^2)*exp(5)^2+1332)/(x^4*exp(5)^4*exp(exp(3))^4+(-4*x^5-36*x^4)*exp(5)^4 *exp(exp(3))^3+((6*x^6+108*x^5+486*x^4)*exp(5)^4+72*x^2*exp(5)^2)*exp(exp( 3))^2+((-4*x^7-108*x^6-972*x^5-2916*x^4)*exp(5)^4+(-144*x^3-1296*x^2)*exp( 5)^2)*exp(exp(3))+(x^8+36*x^7+486*x^6+2916*x^5+6561*x^4)*exp(5)^4+(72*x^4+ 1296*x^3+5832*x^2)*exp(5)^2+1296),x, algorithm=\
x + x/(x^4*e^10 + 2*x^3*(9*e^10 - e^(e^3 + 10)) + x^2*(81*e^10 + e^(2*e^3 + 10) - 18*e^(e^3 + 10)) + 36)
Timed out. \[ \int \frac {1332+e^{20+4 e^3} x^4+e^{10} \left (5751 x^2+1260 x^3+69 x^4\right )+e^{20+3 e^3} \left (-36 x^4-4 x^5\right )+e^{20} \left (6561 x^4+2916 x^5+486 x^6+36 x^7+x^8\right )+e^{2 e^3} \left (71 e^{10} x^2+e^{20} \left (486 x^4+108 x^5+6 x^6\right )\right )+e^{e^3} \left (e^{10} \left (-1278 x^2-140 x^3\right )+e^{20} \left (-2916 x^4-972 x^5-108 x^6-4 x^7\right )\right )}{1296+e^{20+4 e^3} x^4+e^{10} \left (5832 x^2+1296 x^3+72 x^4\right )+e^{20+3 e^3} \left (-36 x^4-4 x^5\right )+e^{20} \left (6561 x^4+2916 x^5+486 x^6+36 x^7+x^8\right )+e^{2 e^3} \left (72 e^{10} x^2+e^{20} \left (486 x^4+108 x^5+6 x^6\right )\right )+e^{e^3} \left (e^{10} \left (-1296 x^2-144 x^3\right )+e^{20} \left (-2916 x^4-972 x^5-108 x^6-4 x^7\right )\right )} \, dx=\text {Timed out} \]
integrate((x^4*exp(5)^4*exp(exp(3))^4+(-4*x^5-36*x^4)*exp(5)^4*exp(exp(3)) ^3+((6*x^6+108*x^5+486*x^4)*exp(5)^4+71*x^2*exp(5)^2)*exp(exp(3))^2+((-4*x ^7-108*x^6-972*x^5-2916*x^4)*exp(5)^4+(-140*x^3-1278*x^2)*exp(5)^2)*exp(ex p(3))+(x^8+36*x^7+486*x^6+2916*x^5+6561*x^4)*exp(5)^4+(69*x^4+1260*x^3+575 1*x^2)*exp(5)^2+1332)/(x^4*exp(5)^4*exp(exp(3))^4+(-4*x^5-36*x^4)*exp(5)^4 *exp(exp(3))^3+((6*x^6+108*x^5+486*x^4)*exp(5)^4+72*x^2*exp(5)^2)*exp(exp( 3))^2+((-4*x^7-108*x^6-972*x^5-2916*x^4)*exp(5)^4+(-144*x^3-1296*x^2)*exp( 5)^2)*exp(exp(3))+(x^8+36*x^7+486*x^6+2916*x^5+6561*x^4)*exp(5)^4+(72*x^4+ 1296*x^3+5832*x^2)*exp(5)^2+1296),x, algorithm=\
Timed out. \[ \int \frac {1332+e^{20+4 e^3} x^4+e^{10} \left (5751 x^2+1260 x^3+69 x^4\right )+e^{20+3 e^3} \left (-36 x^4-4 x^5\right )+e^{20} \left (6561 x^4+2916 x^5+486 x^6+36 x^7+x^8\right )+e^{2 e^3} \left (71 e^{10} x^2+e^{20} \left (486 x^4+108 x^5+6 x^6\right )\right )+e^{e^3} \left (e^{10} \left (-1278 x^2-140 x^3\right )+e^{20} \left (-2916 x^4-972 x^5-108 x^6-4 x^7\right )\right )}{1296+e^{20+4 e^3} x^4+e^{10} \left (5832 x^2+1296 x^3+72 x^4\right )+e^{20+3 e^3} \left (-36 x^4-4 x^5\right )+e^{20} \left (6561 x^4+2916 x^5+486 x^6+36 x^7+x^8\right )+e^{2 e^3} \left (72 e^{10} x^2+e^{20} \left (486 x^4+108 x^5+6 x^6\right )\right )+e^{e^3} \left (e^{10} \left (-1296 x^2-144 x^3\right )+e^{20} \left (-2916 x^4-972 x^5-108 x^6-4 x^7\right )\right )} \, dx=\text {Hanged} \]
int((exp(2*exp(3))*(71*x^2*exp(10) + exp(20)*(486*x^4 + 108*x^5 + 6*x^6)) - exp(exp(3))*(exp(10)*(1278*x^2 + 140*x^3) + exp(20)*(2916*x^4 + 972*x^5 + 108*x^6 + 4*x^7)) + exp(10)*(5751*x^2 + 1260*x^3 + 69*x^4) + exp(20)*(65 61*x^4 + 2916*x^5 + 486*x^6 + 36*x^7 + x^8) - exp(3*exp(3))*exp(20)*(36*x^ 4 + 4*x^5) + x^4*exp(4*exp(3))*exp(20) + 1332)/(exp(2*exp(3))*(72*x^2*exp( 10) + exp(20)*(486*x^4 + 108*x^5 + 6*x^6)) - exp(exp(3))*(exp(10)*(1296*x^ 2 + 144*x^3) + exp(20)*(2916*x^4 + 972*x^5 + 108*x^6 + 4*x^7)) + exp(10)*( 5832*x^2 + 1296*x^3 + 72*x^4) + exp(20)*(6561*x^4 + 2916*x^5 + 486*x^6 + 3 6*x^7 + x^8) - exp(3*exp(3))*exp(20)*(36*x^4 + 4*x^5) + x^4*exp(4*exp(3))* exp(20) + 1296),x)