\(\int \frac {e^{16} (54+3 e^2-54 x-18 x^2-12 e x^2-18 x^3)+e^{16-\frac {x}{2}} (36+e^2 (6-3 x)-36 x-12 x^2-15 e x^2-12 x^3)+e^{16+\frac {x}{2}} (36-36 x-12 x^2-3 e x^2-12 x^3)+e^{16+x} (9-9 x-3 x^2-3 x^3)+e^{16-x} (9+e^2 (3-3 x)-9 x-3 x^2-6 e x^2-3 x^3)}{9+e^4+4 e^3 x+6 x^2+x^4+e^2 (6+6 x^2)+e (12 x+4 x^3)+e^{2 x} (9+6 x^2+x^4)+e^{3 x/2} (36+24 x^2+4 x^4+e (12 x+4 x^3))+e^x (54+36 x^2+6 x^4+e^2 (6+6 x^2)+e (36 x+12 x^3))+e^{x/2} (36+4 e^3 x+24 x^2+4 x^4+e^2 (12+12 x^2)+e (36 x+12 x^3))} \, dx\) [6964]

Optimal result

Integrand size = 338, antiderivative size = 31 \[ \int \frac {e^{16} \left (54+3 e^2-54 x-18 x^2-12 e x^2-18 x^3\right )+e^{16-\frac {x}{2}} \left (36+e^2 (6-3 x)-36 x-12 x^2-15 e x^2-12 x^3\right )+e^{16+\frac {x}{2}} \left (36-36 x-12 x^2-3 e x^2-12 x^3\right )+e^{16+x} \left (9-9 x-3 x^2-3 x^3\right )+e^{16-x} \left (9+e^2 (3-3 x)-9 x-3 x^2-6 e x^2-3 x^3\right )}{9+e^4+4 e^3 x+6 x^2+x^4+e^2 \left (6+6 x^2\right )+e \left (12 x+4 x^3\right )+e^{2 x} \left (9+6 x^2+x^4\right )+e^{3 x/2} \left (36+24 x^2+4 x^4+e \left (12 x+4 x^3\right )\right )+e^x \left (54+36 x^2+6 x^4+e^2 \left (6+6 x^2\right )+e \left (36 x+12 x^3\right )\right )+e^{x/2} \left (36+4 e^3 x+24 x^2+4 x^4+e^2 \left (12+12 x^2\right )+e \left (36 x+12 x^3\right )\right )} \, dx=\frac {3 e^{16-x} x}{3+\left (\frac {e}{1+e^{x/2}}+x\right )^2} \]

[Out]

3*exp(16-x)*x/(3+(x+exp(1)/(1+exp(1/2*x)))^2)

Rubi [F(-1)]

Timed out. \[ \int \frac {e^{16} \left (54+3 e^2-54 x-18 x^2-12 e x^2-18 x^3\right )+e^{16-\frac {x}{2}} \left (36+e^2 (6-3 x)-36 x-12 x^2-15 e x^2-12 x^3\right )+e^{16+\frac {x}{2}} \left (36-36 x-12 x^2-3 e x^2-12 x^3\right )+e^{16+x} \left (9-9 x-3 x^2-3 x^3\right )+e^{16-x} \left (9+e^2 (3-3 x)-9 x-3 x^2-6 e x^2-3 x^3\right )}{9+e^4+4 e^3 x+6 x^2+x^4+e^2 \left (6+6 x^2\right )+e \left (12 x+4 x^3\right )+e^{2 x} \left (9+6 x^2+x^4\right )+e^{3 x/2} \left (36+24 x^2+4 x^4+e \left (12 x+4 x^3\right )\right )+e^x \left (54+36 x^2+6 x^4+e^2 \left (6+6 x^2\right )+e \left (36 x+12 x^3\right )\right )+e^{x/2} \left (36+4 e^3 x+24 x^2+4 x^4+e^2 \left (12+12 x^2\right )+e \left (36 x+12 x^3\right )\right )} \, dx=\text {\$Aborted} \]

[In]

Int[(E^16*(54 + 3*E^2 - 54*x - 18*x^2 - 12*E*x^2 - 18*x^3) + E^(16 - x/2)*(36 + E^2*(6 - 3*x) - 36*x - 12*x^2
- 15*E*x^2 - 12*x^3) + E^(16 + x/2)*(36 - 36*x - 12*x^2 - 3*E*x^2 - 12*x^3) + E^(16 + x)*(9 - 9*x - 3*x^2 - 3*
x^3) + E^(16 - x)*(9 + E^2*(3 - 3*x) - 9*x - 3*x^2 - 6*E*x^2 - 3*x^3))/(9 + E^4 + 4*E^3*x + 6*x^2 + x^4 + E^2*
(6 + 6*x^2) + E*(12*x + 4*x^3) + E^(2*x)*(9 + 6*x^2 + x^4) + E^((3*x)/2)*(36 + 24*x^2 + 4*x^4 + E*(12*x + 4*x^
3)) + E^x*(54 + 36*x^2 + 6*x^4 + E^2*(6 + 6*x^2) + E*(36*x + 12*x^3)) + E^(x/2)*(36 + 4*E^3*x + 24*x^2 + 4*x^4
+ E^2*(12 + 12*x^2) + E*(36*x + 12*x^3))),x]

[Out]

$Aborted

Rubi steps Aborted

Mathematica [B] (verified)

Leaf count is larger than twice the leaf count of optimal. \(70\) vs. \(2(31)=62\).

Time = 8.11 (sec) , antiderivative size = 70, normalized size of antiderivative = 2.26 \[ \int \frac {e^{16} \left (54+3 e^2-54 x-18 x^2-12 e x^2-18 x^3\right )+e^{16-\frac {x}{2}} \left (36+e^2 (6-3 x)-36 x-12 x^2-15 e x^2-12 x^3\right )+e^{16+\frac {x}{2}} \left (36-36 x-12 x^2-3 e x^2-12 x^3\right )+e^{16+x} \left (9-9 x-3 x^2-3 x^3\right )+e^{16-x} \left (9+e^2 (3-3 x)-9 x-3 x^2-6 e x^2-3 x^3\right )}{9+e^4+4 e^3 x+6 x^2+x^4+e^2 \left (6+6 x^2\right )+e \left (12 x+4 x^3\right )+e^{2 x} \left (9+6 x^2+x^4\right )+e^{3 x/2} \left (36+24 x^2+4 x^4+e \left (12 x+4 x^3\right )\right )+e^x \left (54+36 x^2+6 x^4+e^2 \left (6+6 x^2\right )+e \left (36 x+12 x^3\right )\right )+e^{x/2} \left (36+4 e^3 x+24 x^2+4 x^4+e^2 \left (12+12 x^2\right )+e \left (36 x+12 x^3\right )\right )} \, dx=\frac {3 e^{16-x} \left (1+e^{x/2}\right )^2 x}{3+e^2+2 e x+2 e^{1+\frac {x}{2}} x+x^2+2 e^{x/2} \left (3+x^2\right )+e^x \left (3+x^2\right )} \]

[In]

Integrate[(E^16*(54 + 3*E^2 - 54*x - 18*x^2 - 12*E*x^2 - 18*x^3) + E^(16 - x/2)*(36 + E^2*(6 - 3*x) - 36*x - 1
2*x^2 - 15*E*x^2 - 12*x^3) + E^(16 + x/2)*(36 - 36*x - 12*x^2 - 3*E*x^2 - 12*x^3) + E^(16 + x)*(9 - 9*x - 3*x^
2 - 3*x^3) + E^(16 - x)*(9 + E^2*(3 - 3*x) - 9*x - 3*x^2 - 6*E*x^2 - 3*x^3))/(9 + E^4 + 4*E^3*x + 6*x^2 + x^4
+ E^2*(6 + 6*x^2) + E*(12*x + 4*x^3) + E^(2*x)*(9 + 6*x^2 + x^4) + E^((3*x)/2)*(36 + 24*x^2 + 4*x^4 + E*(12*x
+ 4*x^3)) + E^x*(54 + 36*x^2 + 6*x^4 + E^2*(6 + 6*x^2) + E*(36*x + 12*x^3)) + E^(x/2)*(36 + 4*E^3*x + 24*x^2 +
4*x^4 + E^2*(12 + 12*x^2) + E*(36*x + 12*x^3))),x]

[Out]

(3*E^(16 - x)*(1 + E^(x/2))^2*x)/(3 + E^2 + 2*E*x + 2*E^(1 + x/2)*x + x^2 + 2*E^(x/2)*(3 + x^2) + E^x*(3 + x^2
))

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(97\) vs. \(2(28)=56\).

Time = 2.95 (sec) , antiderivative size = 98, normalized size of antiderivative = 3.16

method	result	size
parallelrisch	\(\frac {3 \,{\mathrm e}^{16-x} x \,{\mathrm e}^{x}+6 \,{\mathrm e}^{16-x} x \,{\mathrm e}^{\frac {x}{2}}+3 \,{\mathrm e}^{16-x} x}{{\mathrm e}^{x} x^{2}+2 \,{\mathrm e} \,{\mathrm e}^{\frac {x}{2}} x +2 x^{2} {\mathrm e}^{\frac {x}{2}}+{\mathrm e}^{2}+2 x \,{\mathrm e}+3 \,{\mathrm e}^{x}+x^{2}+6 \,{\mathrm e}^{\frac {x}{2}}+3}\)	\(98\)
risch	\(\frac {6 x \left (x +{\mathrm e}\right ) {\mathrm e}^{17-\frac {x}{2}}}{\left ({\mathrm e}^{2}+2 x \,{\mathrm e}+x^{2}+3\right )^{2}}+\frac {3 x \,{\mathrm e}^{16-x}}{{\mathrm e}^{2}+2 x \,{\mathrm e}+x^{2}+3}+\frac {3 \,{\mathrm e}^{17} x \left (-2 x^{2} {\mathrm e}^{1+\frac {x}{2}}-2 \,{\mathrm e}^{\frac {x}{2}} x^{3}+{\mathrm e}^{3}-3 x^{2} {\mathrm e}-2 x^{3}-6 \,{\mathrm e}^{1+\frac {x}{2}}-6 x \,{\mathrm e}^{\frac {x}{2}}-9 \,{\mathrm e}-6 x \right )}{\left ({\mathrm e}^{2}+2 x \,{\mathrm e}+x^{2}+3\right )^{2} \left ({\mathrm e}^{x} x^{2}+2 x \,{\mathrm e}^{1+\frac {x}{2}}+2 x^{2} {\mathrm e}^{\frac {x}{2}}+{\mathrm e}^{2}+2 x \,{\mathrm e}+3 \,{\mathrm e}^{x}+x^{2}+6 \,{\mathrm e}^{\frac {x}{2}}+3\right )}\)	\(176\)

[In]

int(((-3*x^3-3*x^2-9*x+9)*exp(16-x)*exp(1/2*x)^4+(-3*x^2*exp(1)-12*x^3-12*x^2-36*x+36)*exp(16-x)*exp(1/2*x)^3+
(3*exp(1)^2-12*x^2*exp(1)-18*x^3-18*x^2-54*x+54)*exp(16-x)*exp(1/2*x)^2+((-3*x+6)*exp(1)^2-15*x^2*exp(1)-12*x^
3-12*x^2-36*x+36)*exp(16-x)*exp(1/2*x)+((-3*x+3)*exp(1)^2-6*x^2*exp(1)-3*x^3-3*x^2-9*x+9)*exp(16-x))/((x^4+6*x
^2+9)*exp(1/2*x)^4+((4*x^3+12*x)*exp(1)+4*x^4+24*x^2+36)*exp(1/2*x)^3+((6*x^2+6)*exp(1)^2+(12*x^3+36*x)*exp(1)
+6*x^4+36*x^2+54)*exp(1/2*x)^2+(4*x*exp(1)^3+(12*x^2+12)*exp(1)^2+(12*x^3+36*x)*exp(1)+4*x^4+24*x^2+36)*exp(1/
2*x)+exp(1)^4+4*x*exp(1)^3+(6*x^2+6)*exp(1)^2+(4*x^3+12*x)*exp(1)+x^4+6*x^2+9),x,method=_RETURNVERBOSE)

[Out]

(3*exp(16-x)*x*exp(1/2*x)^2+6*exp(16-x)*x*exp(1/2*x)+3*exp(16-x)*x)/(x^2*exp(1/2*x)^2+2*exp(1)*exp(1/2*x)*x+2*
x^2*exp(1/2*x)+exp(1)^2+2*x*exp(1)+3*exp(1/2*x)^2+x^2+6*exp(1/2*x)+3)

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 79 vs. \(2 (28) = 56\).

Time = 0.33 (sec) , antiderivative size = 79, normalized size of antiderivative = 2.55 \[ \int \frac {e^{16} \left (54+3 e^2-54 x-18 x^2-12 e x^2-18 x^3\right )+e^{16-\frac {x}{2}} \left (36+e^2 (6-3 x)-36 x-12 x^2-15 e x^2-12 x^3\right )+e^{16+\frac {x}{2}} \left (36-36 x-12 x^2-3 e x^2-12 x^3\right )+e^{16+x} \left (9-9 x-3 x^2-3 x^3\right )+e^{16-x} \left (9+e^2 (3-3 x)-9 x-3 x^2-6 e x^2-3 x^3\right )}{9+e^4+4 e^3 x+6 x^2+x^4+e^2 \left (6+6 x^2\right )+e \left (12 x+4 x^3\right )+e^{2 x} \left (9+6 x^2+x^4\right )+e^{3 x/2} \left (36+24 x^2+4 x^4+e \left (12 x+4 x^3\right )\right )+e^x \left (54+36 x^2+6 x^4+e^2 \left (6+6 x^2\right )+e \left (36 x+12 x^3\right )\right )+e^{x/2} \left (36+4 e^3 x+24 x^2+4 x^4+e^2 \left (12+12 x^2\right )+e \left (36 x+12 x^3\right )\right )} \, dx=\frac {3 \, {\left (x e^{80} + x e^{\left (x + 80\right )} + 2 \, x e^{\left (\frac {1}{2} \, x + 80\right )}\right )}}{{\left (x^{2} + 3\right )} e^{\left (2 \, x + 64\right )} + 2 \, {\left (x e^{17} + {\left (x^{2} + 3\right )} e^{16}\right )} e^{\left (\frac {3}{2} \, x + 48\right )} + {\left (2 \, x e^{33} + {\left (x^{2} + 3\right )} e^{32} + e^{34}\right )} e^{\left (x + 32\right )}} \]

[In]

integrate(((-3*x^3-3*x^2-9*x+9)*exp(16-x)*exp(1/2*x)^4+(-3*x^2*exp(1)-12*x^3-12*x^2-36*x+36)*exp(16-x)*exp(1/2
*x)^3+(3*exp(1)^2-12*x^2*exp(1)-18*x^3-18*x^2-54*x+54)*exp(16-x)*exp(1/2*x)^2+((-3*x+6)*exp(1)^2-15*x^2*exp(1)
-12*x^3-12*x^2-36*x+36)*exp(16-x)*exp(1/2*x)+((-3*x+3)*exp(1)^2-6*x^2*exp(1)-3*x^3-3*x^2-9*x+9)*exp(16-x))/((x
^4+6*x^2+9)*exp(1/2*x)^4+((4*x^3+12*x)*exp(1)+4*x^4+24*x^2+36)*exp(1/2*x)^3+((6*x^2+6)*exp(1)^2+(12*x^3+36*x)*
exp(1)+6*x^4+36*x^2+54)*exp(1/2*x)^2+(4*x*exp(1)^3+(12*x^2+12)*exp(1)^2+(12*x^3+36*x)*exp(1)+4*x^4+24*x^2+36)*
exp(1/2*x)+exp(1)^4+4*x*exp(1)^3+(6*x^2+6)*exp(1)^2+(4*x^3+12*x)*exp(1)+x^4+6*x^2+9),x, algorithm="fricas")

[Out]

3*(x*e^80 + x*e^(x + 80) + 2*x*e^(1/2*x + 80))/((x^2 + 3)*e^(2*x + 64) + 2*(x*e^17 + (x^2 + 3)*e^16)*e^(3/2*x
+ 48) + (2*x*e^33 + (x^2 + 3)*e^32 + e^34)*e^(x + 32))

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 600 vs. \(2 (22) = 44\).

Time = 1.28 (sec) , antiderivative size = 600, normalized size of antiderivative = 19.35 \[ \int \frac {e^{16} \left (54+3 e^2-54 x-18 x^2-12 e x^2-18 x^3\right )+e^{16-\frac {x}{2}} \left (36+e^2 (6-3 x)-36 x-12 x^2-15 e x^2-12 x^3\right )+e^{16+\frac {x}{2}} \left (36-36 x-12 x^2-3 e x^2-12 x^3\right )+e^{16+x} \left (9-9 x-3 x^2-3 x^3\right )+e^{16-x} \left (9+e^2 (3-3 x)-9 x-3 x^2-6 e x^2-3 x^3\right )}{9+e^4+4 e^3 x+6 x^2+x^4+e^2 \left (6+6 x^2\right )+e \left (12 x+4 x^3\right )+e^{2 x} \left (9+6 x^2+x^4\right )+e^{3 x/2} \left (36+24 x^2+4 x^4+e \left (12 x+4 x^3\right )\right )+e^x \left (54+36 x^2+6 x^4+e^2 \left (6+6 x^2\right )+e \left (36 x+12 x^3\right )\right )+e^{x/2} \left (36+4 e^3 x+24 x^2+4 x^4+e^2 \left (12+12 x^2\right )+e \left (36 x+12 x^3\right )\right )} \, dx=\frac {\left (6 x^{4} e^{17} + 18 x^{3} e^{18} + 18 x^{2} e^{17} + 18 x^{2} e^{19} + 18 x e^{18} + 6 x e^{20}\right ) e^{- \frac {x}{2}} + \left (3 x^{5} e^{16} + 12 x^{4} e^{17} + 18 x^{3} e^{16} + 18 x^{3} e^{18} + 36 x^{2} e^{17} + 12 x^{2} e^{19} + 27 x e^{16} + 18 x e^{18} + 3 x e^{20}\right ) e^{- x}}{x^{6} + 6 e x^{5} + 9 x^{4} + 15 x^{4} e^{2} + 36 e x^{3} + 20 x^{3} e^{3} + 27 x^{2} + 54 x^{2} e^{2} + 15 x^{2} e^{4} + 54 e x + 36 x e^{3} + 6 x e^{5} + 27 + 27 e^{2} + e^{6} + 9 e^{4}} + \frac {- 6 x^{4} e^{17} - 9 x^{3} e^{18} - 18 x^{2} e^{17} - 27 x e^{18} + 3 x e^{20} + \left (- 6 x^{4} e^{17} - 6 x^{3} e^{18} - 18 x^{2} e^{17} - 18 x e^{18}\right ) e^{\frac {x}{2}}}{x^{6} + 6 e x^{5} + 9 x^{4} + 15 x^{4} e^{2} + 36 e x^{3} + 20 x^{3} e^{3} + 27 x^{2} + 54 x^{2} e^{2} + 15 x^{2} e^{4} + 54 e x + 36 x e^{3} + 6 x e^{5} + \left (x^{6} + 4 e x^{5} + 9 x^{4} + 6 x^{4} e^{2} + 24 e x^{3} + 4 x^{3} e^{3} + 27 x^{2} + x^{2} e^{4} + 24 x^{2} e^{2} + 36 e x + 12 x e^{3} + 27 + 18 e^{2} + 3 e^{4}\right ) e^{x} + \left (2 x^{6} + 10 e x^{5} + 18 x^{4} + 20 x^{4} e^{2} + 60 e x^{3} + 20 x^{3} e^{3} + 54 x^{2} + 72 x^{2} e^{2} + 10 x^{2} e^{4} + 90 e x + 2 x e^{5} + 36 x e^{3} + 54 + 36 e^{2} + 6 e^{4}\right ) e^{\frac {x}{2}} + 27 + 27 e^{2} + e^{6} + 9 e^{4}} \]

[In]

integrate(((-3*x**3-3*x**2-9*x+9)*exp(16-x)*exp(1/2*x)**4+(-3*x**2*exp(1)-12*x**3-12*x**2-36*x+36)*exp(16-x)*e
xp(1/2*x)**3+(3*exp(1)**2-12*x**2*exp(1)-18*x**3-18*x**2-54*x+54)*exp(16-x)*exp(1/2*x)**2+((-3*x+6)*exp(1)**2-
15*x**2*exp(1)-12*x**3-12*x**2-36*x+36)*exp(16-x)*exp(1/2*x)+((-3*x+3)*exp(1)**2-6*x**2*exp(1)-3*x**3-3*x**2-9
*x+9)*exp(16-x))/((x**4+6*x**2+9)*exp(1/2*x)**4+((4*x**3+12*x)*exp(1)+4*x**4+24*x**2+36)*exp(1/2*x)**3+((6*x**
2+6)*exp(1)**2+(12*x**3+36*x)*exp(1)+6*x**4+36*x**2+54)*exp(1/2*x)**2+(4*x*exp(1)**3+(12*x**2+12)*exp(1)**2+(1
2*x**3+36*x)*exp(1)+4*x**4+24*x**2+36)*exp(1/2*x)+exp(1)**4+4*x*exp(1)**3+(6*x**2+6)*exp(1)**2+(4*x**3+12*x)*e
xp(1)+x**4+6*x**2+9),x)

[Out]

((6*x**4*exp(17) + 18*x**3*exp(18) + 18*x**2*exp(17) + 18*x**2*exp(19) + 18*x*exp(18) + 6*x*exp(20))*exp(-x/2)
+ (3*x**5*exp(16) + 12*x**4*exp(17) + 18*x**3*exp(16) + 18*x**3*exp(18) + 36*x**2*exp(17) + 12*x**2*exp(19) +
27*x*exp(16) + 18*x*exp(18) + 3*x*exp(20))*exp(-x))/(x**6 + 6*E*x**5 + 9*x**4 + 15*x**4*exp(2) + 36*E*x**3 +
20*x**3*exp(3) + 27*x**2 + 54*x**2*exp(2) + 15*x**2*exp(4) + 54*E*x + 36*x*exp(3) + 6*x*exp(5) + 27 + 27*exp(2
) + exp(6) + 9*exp(4)) + (-6*x**4*exp(17) - 9*x**3*exp(18) - 18*x**2*exp(17) - 27*x*exp(18) + 3*x*exp(20) + (-
6*x**4*exp(17) - 6*x**3*exp(18) - 18*x**2*exp(17) - 18*x*exp(18))*exp(x/2))/(x**6 + 6*E*x**5 + 9*x**4 + 15*x**
4*exp(2) + 36*E*x**3 + 20*x**3*exp(3) + 27*x**2 + 54*x**2*exp(2) + 15*x**2*exp(4) + 54*E*x + 36*x*exp(3) + 6*x
*exp(5) + (x**6 + 4*E*x**5 + 9*x**4 + 6*x**4*exp(2) + 24*E*x**3 + 4*x**3*exp(3) + 27*x**2 + x**2*exp(4) + 24*x
**2*exp(2) + 36*E*x + 12*x*exp(3) + 27 + 18*exp(2) + 3*exp(4))*exp(x) + (2*x**6 + 10*E*x**5 + 18*x**4 + 20*x**
4*exp(2) + 60*E*x**3 + 20*x**3*exp(3) + 54*x**2 + 72*x**2*exp(2) + 10*x**2*exp(4) + 90*E*x + 2*x*exp(5) + 36*x
*exp(3) + 54 + 36*exp(2) + 6*exp(4))*exp(x/2) + 27 + 27*exp(2) + exp(6) + 9*exp(4))

Maxima [F(-2)]

Exception generated. \[ \int \frac {e^{16} \left (54+3 e^2-54 x-18 x^2-12 e x^2-18 x^3\right )+e^{16-\frac {x}{2}} \left (36+e^2 (6-3 x)-36 x-12 x^2-15 e x^2-12 x^3\right )+e^{16+\frac {x}{2}} \left (36-36 x-12 x^2-3 e x^2-12 x^3\right )+e^{16+x} \left (9-9 x-3 x^2-3 x^3\right )+e^{16-x} \left (9+e^2 (3-3 x)-9 x-3 x^2-6 e x^2-3 x^3\right )}{9+e^4+4 e^3 x+6 x^2+x^4+e^2 \left (6+6 x^2\right )+e \left (12 x+4 x^3\right )+e^{2 x} \left (9+6 x^2+x^4\right )+e^{3 x/2} \left (36+24 x^2+4 x^4+e \left (12 x+4 x^3\right )\right )+e^x \left (54+36 x^2+6 x^4+e^2 \left (6+6 x^2\right )+e \left (36 x+12 x^3\right )\right )+e^{x/2} \left (36+4 e^3 x+24 x^2+4 x^4+e^2 \left (12+12 x^2\right )+e \left (36 x+12 x^3\right )\right )} \, dx=\text {Exception raised: RuntimeError} \]

[In]

integrate(((-3*x^3-3*x^2-9*x+9)*exp(16-x)*exp(1/2*x)^4+(-3*x^2*exp(1)-12*x^3-12*x^2-36*x+36)*exp(16-x)*exp(1/2
*x)^3+(3*exp(1)^2-12*x^2*exp(1)-18*x^3-18*x^2-54*x+54)*exp(16-x)*exp(1/2*x)^2+((-3*x+6)*exp(1)^2-15*x^2*exp(1)
-12*x^3-12*x^2-36*x+36)*exp(16-x)*exp(1/2*x)+((-3*x+3)*exp(1)^2-6*x^2*exp(1)-3*x^3-3*x^2-9*x+9)*exp(16-x))/((x
^4+6*x^2+9)*exp(1/2*x)^4+((4*x^3+12*x)*exp(1)+4*x^4+24*x^2+36)*exp(1/2*x)^3+((6*x^2+6)*exp(1)^2+(12*x^3+36*x)*
exp(1)+6*x^4+36*x^2+54)*exp(1/2*x)^2+(4*x*exp(1)^3+(12*x^2+12)*exp(1)^2+(12*x^3+36*x)*exp(1)+4*x^4+24*x^2+36)*
exp(1/2*x)+exp(1)^4+4*x*exp(1)^3+(6*x^2+6)*exp(1)^2+(4*x^3+12*x)*exp(1)+x^4+6*x^2+9),x, algorithm="maxima")

[Out]

Exception raised: RuntimeError >> ECL says: THROW: The catch RAT-ERR is undefined.

Giac [F(-1)]

Timed out. \[ \int \frac {e^{16} \left (54+3 e^2-54 x-18 x^2-12 e x^2-18 x^3\right )+e^{16-\frac {x}{2}} \left (36+e^2 (6-3 x)-36 x-12 x^2-15 e x^2-12 x^3\right )+e^{16+\frac {x}{2}} \left (36-36 x-12 x^2-3 e x^2-12 x^3\right )+e^{16+x} \left (9-9 x-3 x^2-3 x^3\right )+e^{16-x} \left (9+e^2 (3-3 x)-9 x-3 x^2-6 e x^2-3 x^3\right )}{9+e^4+4 e^3 x+6 x^2+x^4+e^2 \left (6+6 x^2\right )+e \left (12 x+4 x^3\right )+e^{2 x} \left (9+6 x^2+x^4\right )+e^{3 x/2} \left (36+24 x^2+4 x^4+e \left (12 x+4 x^3\right )\right )+e^x \left (54+36 x^2+6 x^4+e^2 \left (6+6 x^2\right )+e \left (36 x+12 x^3\right )\right )+e^{x/2} \left (36+4 e^3 x+24 x^2+4 x^4+e^2 \left (12+12 x^2\right )+e \left (36 x+12 x^3\right )\right )} \, dx=\text {Timed out} \]

[In]

integrate(((-3*x^3-3*x^2-9*x+9)*exp(16-x)*exp(1/2*x)^4+(-3*x^2*exp(1)-12*x^3-12*x^2-36*x+36)*exp(16-x)*exp(1/2
*x)^3+(3*exp(1)^2-12*x^2*exp(1)-18*x^3-18*x^2-54*x+54)*exp(16-x)*exp(1/2*x)^2+((-3*x+6)*exp(1)^2-15*x^2*exp(1)
-12*x^3-12*x^2-36*x+36)*exp(16-x)*exp(1/2*x)+((-3*x+3)*exp(1)^2-6*x^2*exp(1)-3*x^3-3*x^2-9*x+9)*exp(16-x))/((x
^4+6*x^2+9)*exp(1/2*x)^4+((4*x^3+12*x)*exp(1)+4*x^4+24*x^2+36)*exp(1/2*x)^3+((6*x^2+6)*exp(1)^2+(12*x^3+36*x)*
exp(1)+6*x^4+36*x^2+54)*exp(1/2*x)^2+(4*x*exp(1)^3+(12*x^2+12)*exp(1)^2+(12*x^3+36*x)*exp(1)+4*x^4+24*x^2+36)*
exp(1/2*x)+exp(1)^4+4*x*exp(1)^3+(6*x^2+6)*exp(1)^2+(4*x^3+12*x)*exp(1)+x^4+6*x^2+9),x, algorithm="giac")

[Out]

Timed out

Mupad [F(-1)]

Timed out. \[ \int \frac {e^{16} \left (54+3 e^2-54 x-18 x^2-12 e x^2-18 x^3\right )+e^{16-\frac {x}{2}} \left (36+e^2 (6-3 x)-36 x-12 x^2-15 e x^2-12 x^3\right )+e^{16+\frac {x}{2}} \left (36-36 x-12 x^2-3 e x^2-12 x^3\right )+e^{16+x} \left (9-9 x-3 x^2-3 x^3\right )+e^{16-x} \left (9+e^2 (3-3 x)-9 x-3 x^2-6 e x^2-3 x^3\right )}{9+e^4+4 e^3 x+6 x^2+x^4+e^2 \left (6+6 x^2\right )+e \left (12 x+4 x^3\right )+e^{2 x} \left (9+6 x^2+x^4\right )+e^{3 x/2} \left (36+24 x^2+4 x^4+e \left (12 x+4 x^3\right )\right )+e^x \left (54+36 x^2+6 x^4+e^2 \left (6+6 x^2\right )+e \left (36 x+12 x^3\right )\right )+e^{x/2} \left (36+4 e^3 x+24 x^2+4 x^4+e^2 \left (12+12 x^2\right )+e \left (36 x+12 x^3\right )\right )} \, dx=\text {Hanged} \]

[In]

int(-(exp(16 - x)*(9*x + 6*x^2*exp(1) + 3*x^2 + 3*x^3 + exp(2)*(3*x - 3) - 9) + exp(x/2)*exp(16 - x)*(36*x + 1
5*x^2*exp(1) + 12*x^2 + 12*x^3 + exp(2)*(3*x - 6) - 36) + exp((3*x)/2)*exp(16 - x)*(36*x + 3*x^2*exp(1) + 12*x
^2 + 12*x^3 - 36) + exp(2*x)*exp(16 - x)*(9*x + 3*x^2 + 3*x^3 - 9) + exp(16 - x)*exp(x)*(54*x - 3*exp(2) + 12*
x^2*exp(1) + 18*x^2 + 18*x^3 - 54))/(exp(4) + exp(2*x)*(6*x^2 + x^4 + 9) + exp(1)*(12*x + 4*x^3) + exp(x/2)*(e
xp(1)*(36*x + 12*x^3) + 4*x*exp(3) + exp(2)*(12*x^2 + 12) + 24*x^2 + 4*x^4 + 36) + 4*x*exp(3) + exp(2)*(6*x^2
+ 6) + exp(x)*(exp(1)*(36*x + 12*x^3) + exp(2)*(6*x^2 + 6) + 36*x^2 + 6*x^4 + 54) + exp((3*x)/2)*(exp(1)*(12*x
+ 4*x^3) + 24*x^2 + 4*x^4 + 36) + 6*x^2 + x^4 + 9),x)

[Out]

\text{Hanged}