\(\int \frac {e^{\frac {x^2-2 e^{-48+4 e} x^3+e^{-96+8 e} (x+x^4)}{1-2 e^{-48+4 e} x+e^{-96+8 e} x^2}} (-2 x-2 x^3+e^{-48+4 e} (6 x^2+6 x^4)+e^{-96+8 e} (-x^2-6 x^3-6 x^5)+e^{-144+12 e} (-x^3+2 x^4+2 x^6))}{-16+48 e^{-48+4 e} x-48 e^{-96+8 e} x^2+16 e^{-144+12 e} x^3} \, dx\) [5201]

Optimal result

Integrand size = 172, antiderivative size = 30 \[ \int \frac {e^{\frac {x^2-2 e^{-48+4 e} x^3+e^{-96+8 e} \left (x+x^4\right )}{1-2 e^{-48+4 e} x+e^{-96+8 e} x^2}} \left (-2 x-2 x^3+e^{-48+4 e} \left (6 x^2+6 x^4\right )+e^{-96+8 e} \left (-x^2-6 x^3-6 x^5\right )+e^{-144+12 e} \left (-x^3+2 x^4+2 x^6\right )\right )}{-16+48 e^{-48+4 e} x-48 e^{-96+8 e} x^2+16 e^{-144+12 e} x^3} \, dx=\frac {1}{16} e^{x^2+\frac {x}{\left (-e^{4 (12-e)}+x\right )^2}} x^2 \]

[Out]

1/16*exp(x/(x-exp(48-4*exp(1)))^2+x^2)*x^2

Rubi [F]

\[ \int \frac {e^{\frac {x^2-2 e^{-48+4 e} x^3+e^{-96+8 e} \left (x+x^4\right )}{1-2 e^{-48+4 e} x+e^{-96+8 e} x^2}} \left (-2 x-2 x^3+e^{-48+4 e} \left (6 x^2+6 x^4\right )+e^{-96+8 e} \left (-x^2-6 x^3-6 x^5\right )+e^{-144+12 e} \left (-x^3+2 x^4+2 x^6\right )\right )}{-16+48 e^{-48+4 e} x-48 e^{-96+8 e} x^2+16 e^{-144+12 e} x^3} \, dx=\int \frac {\exp \left (\frac {x^2-2 e^{-48+4 e} x^3+e^{-96+8 e} \left (x+x^4\right )}{1-2 e^{-48+4 e} x+e^{-96+8 e} x^2}\right ) \left (-2 x-2 x^3+e^{-48+4 e} \left (6 x^2+6 x^4\right )+e^{-96+8 e} \left (-x^2-6 x^3-6 x^5\right )+e^{-144+12 e} \left (-x^3+2 x^4+2 x^6\right )\right )}{-16+48 e^{-48+4 e} x-48 e^{-96+8 e} x^2+16 e^{-144+12 e} x^3} \, dx \]

[In]

Int[(E^((x^2 - 2*E^(-48 + 4*E)*x^3 + E^(-96 + 8*E)*(x + x^4))/(1 - 2*E^(-48 + 4*E)*x + E^(-96 + 8*E)*x^2))*(-2
*x - 2*x^3 + E^(-48 + 4*E)*(6*x^2 + 6*x^4) + E^(-96 + 8*E)*(-x^2 - 6*x^3 - 6*x^5) + E^(-144 + 12*E)*(-x^3 + 2*
x^4 + 2*x^6)))/(-16 + 48*E^(-48 + 4*E)*x - 48*E^(-96 + 8*E)*x^2 + 16*E^(-144 + 12*E)*x^3),x]

[Out]

-1/16*Defer[Int][E^((x*(E^(8*E) + E^96*x - 2*E^(48 + 4*E)*x^2 + E^(8*E)*x^3))/(E^48 - E^(4*E)*x)^2), x] + Defe
r[Int][E^((x*(E^(8*E) + E^96*x - 2*E^(48 + 4*E)*x^2 + E^(8*E)*x^3))/(E^48 - E^(4*E)*x)^2)*x, x]/8 + Defer[Int]
[E^((x*(E^(8*E) + E^96*x - 2*E^(48 + 4*E)*x^2 + E^(8*E)*x^3))/(E^48 - E^(4*E)*x)^2)*x^3, x]/8 + Defer[Int][E^(
144 + (x*(E^(8*E) + E^96*x - 2*E^(48 + 4*E)*x^2 + E^(8*E)*x^3))/(E^48 - E^(4*E)*x)^2)/(E^48 - E^(4*E)*x)^3, x]
/8 - (5*Defer[Int][E^(96 + (x*(E^(8*E) + E^96*x - 2*E^(48 + 4*E)*x^2 + E^(8*E)*x^3))/(E^48 - E^(4*E)*x)^2)/(E^
48 - E^(4*E)*x)^2, x])/16 + Defer[Int][E^(48 + (x*(E^(8*E) + E^96*x - 2*E^(48 + 4*E)*x^2 + E^(8*E)*x^3))/(E^48
- E^(4*E)*x)^2)/(E^48 - E^(4*E)*x), x]/4

Rubi steps \begin{align*} \text {integral}& = \int \frac {\exp \left (\frac {x \left (e^{-96+8 e}+x-2 e^{-48+4 e} x^2+e^{-96+8 e} x^3\right )}{1-2 e^{-48+4 e} x+e^{-96+8 e} x^2}\right ) \left (2 x+2 x^3-e^{-48+4 e} \left (6 x^2+6 x^4\right )-e^{-96+8 e} \left (-x^2-6 x^3-6 x^5\right )-e^{-144+12 e} \left (-x^3+2 x^4+2 x^6\right )\right )}{16-48 e^{-48+4 e} x+48 e^{-96+8 e} x^2-16 e^{-12 (12-e)} x^3} \, dx \\ & = \int \frac {\exp \left (\frac {x \left (e^{8 e}+e^{96} x-2 e^{48+4 e} x^2+e^{8 e} x^3\right )}{\left (e^{48}-e^{4 e} x\right )^2}\right ) x \left (2 e^{144} \left (1+x^2\right )-6 e^{96+4 e} x \left (1+x^2\right )-e^{12 e} x^2 \left (-1+2 x+2 x^3\right )+e^{8 (6+e)} x \left (1+6 x+6 x^3\right )\right )}{16 \left (e^{48}-e^{4 e} x\right )^3} \, dx \\ & = \frac {1}{16} \int \frac {\exp \left (\frac {x \left (e^{8 e}+e^{96} x-2 e^{48+4 e} x^2+e^{8 e} x^3\right )}{\left (e^{48}-e^{4 e} x\right )^2}\right ) x \left (2 e^{144} \left (1+x^2\right )-6 e^{96+4 e} x \left (1+x^2\right )-e^{12 e} x^2 \left (-1+2 x+2 x^3\right )+e^{8 (6+e)} x \left (1+6 x+6 x^3\right )\right )}{\left (e^{48}-e^{4 e} x\right )^3} \, dx \\ & = \frac {1}{16} \int \left (-\exp \left (\frac {x \left (e^{8 e}+e^{96} x-2 e^{48+4 e} x^2+e^{8 e} x^3\right )}{\left (e^{48}-e^{4 e} x\right )^2}\right )+2 \exp \left (\frac {x \left (e^{8 e}+e^{96} x-2 e^{48+4 e} x^2+e^{8 e} x^3\right )}{\left (e^{48}-e^{4 e} x\right )^2}\right ) x+2 \exp \left (\frac {x \left (e^{8 e}+e^{96} x-2 e^{48+4 e} x^2+e^{8 e} x^3\right )}{\left (e^{48}-e^{4 e} x\right )^2}\right ) x^3+\frac {2 \exp \left (144+\frac {x \left (e^{8 e}+e^{96} x-2 e^{48+4 e} x^2+e^{8 e} x^3\right )}{\left (e^{48}-e^{4 e} x\right )^2}\right )}{\left (e^{48}-e^{4 e} x\right )^3}-\frac {5 \exp \left (96+\frac {x \left (e^{8 e}+e^{96} x-2 e^{48+4 e} x^2+e^{8 e} x^3\right )}{\left (e^{48}-e^{4 e} x\right )^2}\right )}{\left (e^{48}-e^{4 e} x\right )^2}+\frac {4 \exp \left (48+\frac {x \left (e^{8 e}+e^{96} x-2 e^{48+4 e} x^2+e^{8 e} x^3\right )}{\left (e^{48}-e^{4 e} x\right )^2}\right )}{e^{48}-e^{4 e} x}\right ) \, dx \\ & = -\left (\frac {1}{16} \int \exp \left (\frac {x \left (e^{8 e}+e^{96} x-2 e^{48+4 e} x^2+e^{8 e} x^3\right )}{\left (e^{48}-e^{4 e} x\right )^2}\right ) \, dx\right )+\frac {1}{8} \int \exp \left (\frac {x \left (e^{8 e}+e^{96} x-2 e^{48+4 e} x^2+e^{8 e} x^3\right )}{\left (e^{48}-e^{4 e} x\right )^2}\right ) x \, dx+\frac {1}{8} \int \exp \left (\frac {x \left (e^{8 e}+e^{96} x-2 e^{48+4 e} x^2+e^{8 e} x^3\right )}{\left (e^{48}-e^{4 e} x\right )^2}\right ) x^3 \, dx+\frac {1}{8} \int \frac {\exp \left (144+\frac {x \left (e^{8 e}+e^{96} x-2 e^{48+4 e} x^2+e^{8 e} x^3\right )}{\left (e^{48}-e^{4 e} x\right )^2}\right )}{\left (e^{48}-e^{4 e} x\right )^3} \, dx+\frac {1}{4} \int \frac {\exp \left (48+\frac {x \left (e^{8 e}+e^{96} x-2 e^{48+4 e} x^2+e^{8 e} x^3\right )}{\left (e^{48}-e^{4 e} x\right )^2}\right )}{e^{48}-e^{4 e} x} \, dx-\frac {5}{16} \int \frac {\exp \left (96+\frac {x \left (e^{8 e}+e^{96} x-2 e^{48+4 e} x^2+e^{8 e} x^3\right )}{\left (e^{48}-e^{4 e} x\right )^2}\right )}{\left (e^{48}-e^{4 e} x\right )^2} \, dx \\ \end{align*}

Mathematica [A] (verified)

Time = 1.23 (sec) , antiderivative size = 54, normalized size of antiderivative = 1.80 \[ \int \frac {e^{\frac {x^2-2 e^{-48+4 e} x^3+e^{-96+8 e} \left (x+x^4\right )}{1-2 e^{-48+4 e} x+e^{-96+8 e} x^2}} \left (-2 x-2 x^3+e^{-48+4 e} \left (6 x^2+6 x^4\right )+e^{-96+8 e} \left (-x^2-6 x^3-6 x^5\right )+e^{-144+12 e} \left (-x^3+2 x^4+2 x^6\right )\right )}{-16+48 e^{-48+4 e} x-48 e^{-96+8 e} x^2+16 e^{-144+12 e} x^3} \, dx=\frac {1}{16} e^{\frac {x \left (e^{96} x-2 e^{48+4 e} x^2+e^{8 e} \left (1+x^3\right )\right )}{\left (e^{48}-e^{4 e} x\right )^2}} x^2 \]

[In]

Integrate[(E^((x^2 - 2*E^(-48 + 4*E)*x^3 + E^(-96 + 8*E)*(x + x^4))/(1 - 2*E^(-48 + 4*E)*x + E^(-96 + 8*E)*x^2
))*(-2*x - 2*x^3 + E^(-48 + 4*E)*(6*x^2 + 6*x^4) + E^(-96 + 8*E)*(-x^2 - 6*x^3 - 6*x^5) + E^(-144 + 12*E)*(-x^
3 + 2*x^4 + 2*x^6)))/(-16 + 48*E^(-48 + 4*E)*x - 48*E^(-96 + 8*E)*x^2 + 16*E^(-144 + 12*E)*x^3),x]

[Out]

(E^((x*(E^96*x - 2*E^(48 + 4*E)*x^2 + E^(8*E)*(1 + x^3)))/(E^48 - E^(4*E)*x)^2)*x^2)/16

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(65\) vs. \(2(25)=50\).

Time = 0.70 (sec) , antiderivative size = 66, normalized size of antiderivative = 2.20

method	result	size
risch	\(\frac {x^{2} {\mathrm e}^{\frac {x \left ({\mathrm e}^{8 \,{\mathrm e}-96} x^{3}-2 x^{2} {\mathrm e}^{4 \,{\mathrm e}-48}+{\mathrm e}^{8 \,{\mathrm e}-96}+x \right )}{x^{2} {\mathrm e}^{8 \,{\mathrm e}-96}-2 x \,{\mathrm e}^{4 \,{\mathrm e}-48}+1}}}{16}\)	\(66\)
parallelrisch	\(\frac {x^{2} {\mathrm e}^{\frac {\left (x^{4}+x \right ) {\mathrm e}^{8 \,{\mathrm e}-96}-2 x^{3} {\mathrm e}^{4 \,{\mathrm e}-48}+x^{2}}{x^{2} {\mathrm e}^{8 \,{\mathrm e}-96}-2 x \,{\mathrm e}^{4 \,{\mathrm e}-48}+1}}}{16}\)	\(66\)
gosper	\(\frac {x^{2} {\mathrm e}^{\frac {x \left ({\mathrm e}^{8 \,{\mathrm e}-96} x^{3}-2 x^{2} {\mathrm e}^{4 \,{\mathrm e}-48}+{\mathrm e}^{8 \,{\mathrm e}-96}+x \right )}{x^{2} {\mathrm e}^{8 \,{\mathrm e}-96}-2 x \,{\mathrm e}^{4 \,{\mathrm e}-48}+1}}}{16}\)	\(72\)
norman	\(\frac {\frac {x^{2} {\mathrm e}^{\frac {\left (x^{4}+x \right ) {\mathrm e}^{8 \,{\mathrm e}-96}-2 x^{3} {\mathrm e}^{4 \,{\mathrm e}-48}+x^{2}}{x^{2} {\mathrm e}^{8 \,{\mathrm e}-96}-2 x \,{\mathrm e}^{4 \,{\mathrm e}-48}+1}}}{16}-\frac {x^{3} {\mathrm e}^{4 \,{\mathrm e}} {\mathrm e}^{-48} {\mathrm e}^{\frac {\left (x^{4}+x \right ) {\mathrm e}^{8 \,{\mathrm e}-96}-2 x^{3} {\mathrm e}^{4 \,{\mathrm e}-48}+x^{2}}{x^{2} {\mathrm e}^{8 \,{\mathrm e}-96}-2 x \,{\mathrm e}^{4 \,{\mathrm e}-48}+1}}}{8}+\frac {{\mathrm e}^{8 \,{\mathrm e}} {\mathrm e}^{-96} x^{4} {\mathrm e}^{\frac {\left (x^{4}+x \right ) {\mathrm e}^{8 \,{\mathrm e}-96}-2 x^{3} {\mathrm e}^{4 \,{\mathrm e}-48}+x^{2}}{x^{2} {\mathrm e}^{8 \,{\mathrm e}-96}-2 x \,{\mathrm e}^{4 \,{\mathrm e}-48}+1}}}{16}}{\left (x \,{\mathrm e}^{4 \,{\mathrm e}-48}-1\right )^{2}}\)	\(227\)

[In]

int(((2*x^6+2*x^4-x^3)*exp(4*exp(1)-48)^3+(-6*x^5-6*x^3-x^2)*exp(4*exp(1)-48)^2+(6*x^4+6*x^2)*exp(4*exp(1)-48)
-2*x^3-2*x)*exp(((x^4+x)*exp(4*exp(1)-48)^2-2*x^3*exp(4*exp(1)-48)+x^2)/(x^2*exp(4*exp(1)-48)^2-2*x*exp(4*exp(
1)-48)+1))/(16*x^3*exp(4*exp(1)-48)^3-48*x^2*exp(4*exp(1)-48)^2+48*x*exp(4*exp(1)-48)-16),x,method=_RETURNVERB
OSE)

[Out]

1/16*x^2*exp(x*(exp(8*exp(1)-96)*x^3-2*x^2*exp(4*exp(1)-48)+exp(8*exp(1)-96)+x)/(x^2*exp(8*exp(1)-96)-2*x*exp(
4*exp(1)-48)+1))

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 65 vs. \(2 (25) = 50\).

Time = 0.26 (sec) , antiderivative size = 65, normalized size of antiderivative = 2.17 \[ \int \frac {e^{\frac {x^2-2 e^{-48+4 e} x^3+e^{-96+8 e} \left (x+x^4\right )}{1-2 e^{-48+4 e} x+e^{-96+8 e} x^2}} \left (-2 x-2 x^3+e^{-48+4 e} \left (6 x^2+6 x^4\right )+e^{-96+8 e} \left (-x^2-6 x^3-6 x^5\right )+e^{-144+12 e} \left (-x^3+2 x^4+2 x^6\right )\right )}{-16+48 e^{-48+4 e} x-48 e^{-96+8 e} x^2+16 e^{-144+12 e} x^3} \, dx=\frac {1}{16} \, x^{2} e^{\left (-\frac {2 \, x^{3} e^{\left (4 \, e - 48\right )} - x^{2} - {\left (x^{4} + x\right )} e^{\left (8 \, e - 96\right )}}{x^{2} e^{\left (8 \, e - 96\right )} - 2 \, x e^{\left (4 \, e - 48\right )} + 1}\right )} \]

[In]

integrate(((2*x^6+2*x^4-x^3)*exp(4*exp(1)-48)^3+(-6*x^5-6*x^3-x^2)*exp(4*exp(1)-48)^2+(6*x^4+6*x^2)*exp(4*exp(
1)-48)-2*x^3-2*x)*exp(((x^4+x)*exp(4*exp(1)-48)^2-2*x^3*exp(4*exp(1)-48)+x^2)/(x^2*exp(4*exp(1)-48)^2-2*x*exp(
4*exp(1)-48)+1))/(16*x^3*exp(4*exp(1)-48)^3-48*x^2*exp(4*exp(1)-48)^2+48*x*exp(4*exp(1)-48)-16),x, algorithm="
fricas")

[Out]

1/16*x^2*e^(-(2*x^3*e^(4*e - 48) - x^2 - (x^4 + x)*e^(8*e - 96))/(x^2*e^(8*e - 96) - 2*x*e^(4*e - 48) + 1))

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 61 vs. \(2 (22) = 44\).

Time = 0.44 (sec) , antiderivative size = 61, normalized size of antiderivative = 2.03 \[ \int \frac {e^{\frac {x^2-2 e^{-48+4 e} x^3+e^{-96+8 e} \left (x+x^4\right )}{1-2 e^{-48+4 e} x+e^{-96+8 e} x^2}} \left (-2 x-2 x^3+e^{-48+4 e} \left (6 x^2+6 x^4\right )+e^{-96+8 e} \left (-x^2-6 x^3-6 x^5\right )+e^{-144+12 e} \left (-x^3+2 x^4+2 x^6\right )\right )}{-16+48 e^{-48+4 e} x-48 e^{-96+8 e} x^2+16 e^{-144+12 e} x^3} \, dx=\frac {x^{2} e^{\frac {- \frac {2 x^{3}}{e^{48 - 4 e}} + x^{2} + \frac {x^{4} + x}{e^{96 - 8 e}}}{\frac {x^{2}}{e^{96 - 8 e}} - \frac {2 x}{e^{48 - 4 e}} + 1}}}{16} \]

[In]

integrate(((2*x**6+2*x**4-x**3)*exp(4*exp(1)-48)**3+(-6*x**5-6*x**3-x**2)*exp(4*exp(1)-48)**2+(6*x**4+6*x**2)*
exp(4*exp(1)-48)-2*x**3-2*x)*exp(((x**4+x)*exp(4*exp(1)-48)**2-2*x**3*exp(4*exp(1)-48)+x**2)/(x**2*exp(4*exp(1
)-48)**2-2*x*exp(4*exp(1)-48)+1))/(16*x**3*exp(4*exp(1)-48)**3-48*x**2*exp(4*exp(1)-48)**2+48*x*exp(4*exp(1)-4
8)-16),x)

[Out]

x**2*exp((-2*x**3*exp(-48 + 4*E) + x**2 + (x**4 + x)*exp(-96 + 8*E))/(x**2*exp(-96 + 8*E) - 2*x*exp(-48 + 4*E)
+ 1))/16

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 62 vs. \(2 (25) = 50\).

Time = 0.53 (sec) , antiderivative size = 62, normalized size of antiderivative = 2.07 \[ \int \frac {e^{\frac {x^2-2 e^{-48+4 e} x^3+e^{-96+8 e} \left (x+x^4\right )}{1-2 e^{-48+4 e} x+e^{-96+8 e} x^2}} \left (-2 x-2 x^3+e^{-48+4 e} \left (6 x^2+6 x^4\right )+e^{-96+8 e} \left (-x^2-6 x^3-6 x^5\right )+e^{-144+12 e} \left (-x^3+2 x^4+2 x^6\right )\right )}{-16+48 e^{-48+4 e} x-48 e^{-96+8 e} x^2+16 e^{-144+12 e} x^3} \, dx=\frac {1}{16} \, x^{2} e^{\left (x^{2} + \frac {e^{\left (4 \, e\right )}}{x e^{\left (4 \, e\right )} - e^{48}} + \frac {e^{\left (4 \, e + 48\right )}}{x^{2} e^{\left (8 \, e\right )} - 2 \, x e^{\left (4 \, e + 48\right )} + e^{96}}\right )} \]

[In]

integrate(((2*x^6+2*x^4-x^3)*exp(4*exp(1)-48)^3+(-6*x^5-6*x^3-x^2)*exp(4*exp(1)-48)^2+(6*x^4+6*x^2)*exp(4*exp(
1)-48)-2*x^3-2*x)*exp(((x^4+x)*exp(4*exp(1)-48)^2-2*x^3*exp(4*exp(1)-48)+x^2)/(x^2*exp(4*exp(1)-48)^2-2*x*exp(
4*exp(1)-48)+1))/(16*x^3*exp(4*exp(1)-48)^3-48*x^2*exp(4*exp(1)-48)^2+48*x*exp(4*exp(1)-48)-16),x, algorithm="
maxima")

[Out]

1/16*x^2*e^(x^2 + e^(4*e)/(x*e^(4*e) - e^48) + e^(4*e + 48)/(x^2*e^(8*e) - 2*x*e^(4*e + 48) + e^96))

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 68 vs. \(2 (25) = 50\).

Time = 0.88 (sec) , antiderivative size = 68, normalized size of antiderivative = 2.27 \[ \int \frac {e^{\frac {x^2-2 e^{-48+4 e} x^3+e^{-96+8 e} \left (x+x^4\right )}{1-2 e^{-48+4 e} x+e^{-96+8 e} x^2}} \left (-2 x-2 x^3+e^{-48+4 e} \left (6 x^2+6 x^4\right )+e^{-96+8 e} \left (-x^2-6 x^3-6 x^5\right )+e^{-144+12 e} \left (-x^3+2 x^4+2 x^6\right )\right )}{-16+48 e^{-48+4 e} x-48 e^{-96+8 e} x^2+16 e^{-144+12 e} x^3} \, dx=\frac {1}{16} \, x^{2} e^{\left (\frac {x^{4} e^{\left (8 \, e - 96\right )} - 2 \, x^{3} e^{\left (4 \, e - 48\right )} + x^{2} + x e^{\left (8 \, e - 96\right )}}{x^{2} e^{\left (8 \, e - 96\right )} - 2 \, x e^{\left (4 \, e - 48\right )} + 1}\right )} \]

[In]

integrate(((2*x^6+2*x^4-x^3)*exp(4*exp(1)-48)^3+(-6*x^5-6*x^3-x^2)*exp(4*exp(1)-48)^2+(6*x^4+6*x^2)*exp(4*exp(
1)-48)-2*x^3-2*x)*exp(((x^4+x)*exp(4*exp(1)-48)^2-2*x^3*exp(4*exp(1)-48)+x^2)/(x^2*exp(4*exp(1)-48)^2-2*x*exp(
4*exp(1)-48)+1))/(16*x^3*exp(4*exp(1)-48)^3-48*x^2*exp(4*exp(1)-48)^2+48*x*exp(4*exp(1)-48)-16),x, algorithm="
giac")

[Out]

1/16*x^2*e^((x^4*e^(8*e - 96) - 2*x^3*e^(4*e - 48) + x^2 + x*e^(8*e - 96))/(x^2*e^(8*e - 96) - 2*x*e^(4*e - 48
) + 1))

Mupad [F(-1)]

Timed out. \[ \int \frac {e^{\frac {x^2-2 e^{-48+4 e} x^3+e^{-96+8 e} \left (x+x^4\right )}{1-2 e^{-48+4 e} x+e^{-96+8 e} x^2}} \left (-2 x-2 x^3+e^{-48+4 e} \left (6 x^2+6 x^4\right )+e^{-96+8 e} \left (-x^2-6 x^3-6 x^5\right )+e^{-144+12 e} \left (-x^3+2 x^4+2 x^6\right )\right )}{-16+48 e^{-48+4 e} x-48 e^{-96+8 e} x^2+16 e^{-144+12 e} x^3} \, dx=\text {Hanged} \]

[In]

int(-(exp((exp(8*exp(1) - 96)*(x + x^4) - 2*x^3*exp(4*exp(1) - 48) + x^2)/(x^2*exp(8*exp(1) - 96) - 2*x*exp(4*
exp(1) - 48) + 1))*(2*x + exp(8*exp(1) - 96)*(x^2 + 6*x^3 + 6*x^5) - exp(4*exp(1) - 48)*(6*x^2 + 6*x^4) + 2*x^
3 - exp(12*exp(1) - 144)*(2*x^4 - x^3 + 2*x^6)))/(48*x*exp(4*exp(1) - 48) - 48*x^2*exp(8*exp(1) - 96) + 16*x^3
*exp(12*exp(1) - 144) - 16),x)

[Out]

\text{Hanged}