3.33.24 \(\int \frac {e^{\frac {2 (121 x^2+36 e^4 x^2+36 e^8 x^2+22 x^3+x^4+e^2 (-132 x^2-12 x^3)+e^4 (132 x^2-72 e^2 x^2+12 x^3))}{4-8 x+4 x^2+e^2 (-4+8 x-4 x^2)+e^4 (1-2 x+x^2)+e^8 (1-2 x+x^2)+e^4 (4-8 x+4 x^2+e^2 (-2+4 x-2 x^2))}} (-484 x-144 e^4 x-144 e^8 x-132 x^2+36 x^3+4 x^4+e^2 (528 x+72 x^2-24 x^3)+e^4 (-528 x+288 e^2 x-72 x^2+24 x^3))}{-4+12 x-12 x^2+4 x^3+e^2 (4-12 x+12 x^2-4 x^3)+e^4 (-1+3 x-3 x^2+x^3)+e^8 (-1+3 x-3 x^2+x^3)+e^4 (-4+12 x-12 x^2+4 x^3+e^2 (2-6 x+6 x^2-2 x^3))} \, dx\)

Optimal. Leaf size=29 \[ e^{2 \left (\frac {x}{-2+e^2-e^4}-\frac {6 x}{-1+x}\right )^2} \]

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Rubi [A]  time = 4.24, antiderivative size = 41, normalized size of antiderivative = 1.41, number of steps used = 6, number of rules used = 4, integrand size = 332, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.012, Rules used = {6, 6688, 12, 6706} \begin {gather*} \exp \left (\frac {2 x^2 \left (x+6 e^4-6 e^2+11\right )^2}{\left (2-e^2+e^4\right )^2 (1-x)^2}\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(E^((2*(121*x^2 + 36*E^4*x^2 + 36*E^8*x^2 + 22*x^3 + x^4 + E^2*(-132*x^2 - 12*x^3) + E^4*(132*x^2 - 72*E^2
*x^2 + 12*x^3)))/(4 - 8*x + 4*x^2 + E^2*(-4 + 8*x - 4*x^2) + E^4*(1 - 2*x + x^2) + E^8*(1 - 2*x + x^2) + E^4*(
4 - 8*x + 4*x^2 + E^2*(-2 + 4*x - 2*x^2))))*(-484*x - 144*E^4*x - 144*E^8*x - 132*x^2 + 36*x^3 + 4*x^4 + E^2*(
528*x + 72*x^2 - 24*x^3) + E^4*(-528*x + 288*E^2*x - 72*x^2 + 24*x^3)))/(-4 + 12*x - 12*x^2 + 4*x^3 + E^2*(4 -
12*x + 12*x^2 - 4*x^3) + E^4*(-1 + 3*x - 3*x^2 + x^3) + E^8*(-1 + 3*x - 3*x^2 + x^3) + E^4*(-4 + 12*x - 12*x^
2 + 4*x^3 + E^2*(2 - 6*x + 6*x^2 - 2*x^3))),x]

[Out]

E^((2*x^2*(11 - 6*E^2 + 6*E^4 + x)^2)/((2 - E^2 + E^4)^2*(1 - x)^2))

Rule 6

Int[(u_.)*((w_.) + (a_.)*(v_) + (b_.)*(v_))^(p_.), x_Symbol] :> Int[u*((a + b)*v + w)^p, x] /; FreeQ[{a, b}, x
] &&  !FreeQ[v, x]

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rule 6688

Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; SimplerIntegrandQ[v, u, x]]

Rule 6706

Int[(F_)^(v_)*(u_), x_Symbol] :> With[{q = DerivativeDivides[v, u, x]}, Simp[(q*F^v)/Log[F], x] /;  !FalseQ[q]
] /; FreeQ[F, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\exp \left (\frac {2 \left (121 x^2+36 e^4 x^2+36 e^8 x^2+22 x^3+x^4+e^2 \left (-132 x^2-12 x^3\right )+e^4 \left (132 x^2-72 e^2 x^2+12 x^3\right )\right )}{4-8 x+4 x^2+e^2 \left (-4+8 x-4 x^2\right )+e^4 \left (1-2 x+x^2\right )+e^8 \left (1-2 x+x^2\right )+e^4 \left (4-8 x+4 x^2+e^2 \left (-2+4 x-2 x^2\right )\right )}\right ) \left (-144 e^8 x+\left (-484-144 e^4\right ) x-132 x^2+36 x^3+4 x^4+e^2 \left (528 x+72 x^2-24 x^3\right )+e^4 \left (-528 x+288 e^2 x-72 x^2+24 x^3\right )\right )}{-4+12 x-12 x^2+4 x^3+e^2 \left (4-12 x+12 x^2-4 x^3\right )+e^4 \left (-1+3 x-3 x^2+x^3\right )+e^8 \left (-1+3 x-3 x^2+x^3\right )+e^4 \left (-4+12 x-12 x^2+4 x^3+e^2 \left (2-6 x+6 x^2-2 x^3\right )\right )} \, dx\\ &=\int \frac {\exp \left (\frac {2 \left (121 x^2+36 e^4 x^2+36 e^8 x^2+22 x^3+x^4+e^2 \left (-132 x^2-12 x^3\right )+e^4 \left (132 x^2-72 e^2 x^2+12 x^3\right )\right )}{4-8 x+4 x^2+e^2 \left (-4+8 x-4 x^2\right )+e^4 \left (1-2 x+x^2\right )+e^8 \left (1-2 x+x^2\right )+e^4 \left (4-8 x+4 x^2+e^2 \left (-2+4 x-2 x^2\right )\right )}\right ) \left (\left (-484-144 e^4-144 e^8\right ) x-132 x^2+36 x^3+4 x^4+e^2 \left (528 x+72 x^2-24 x^3\right )+e^4 \left (-528 x+288 e^2 x-72 x^2+24 x^3\right )\right )}{-4+12 x-12 x^2+4 x^3+e^2 \left (4-12 x+12 x^2-4 x^3\right )+e^4 \left (-1+3 x-3 x^2+x^3\right )+e^8 \left (-1+3 x-3 x^2+x^3\right )+e^4 \left (-4+12 x-12 x^2+4 x^3+e^2 \left (2-6 x+6 x^2-2 x^3\right )\right )} \, dx\\ &=\int \frac {\exp \left (\frac {2 \left (121 x^2+36 e^4 x^2+36 e^8 x^2+22 x^3+x^4+e^2 \left (-132 x^2-12 x^3\right )+e^4 \left (132 x^2-72 e^2 x^2+12 x^3\right )\right )}{4-8 x+4 x^2+e^2 \left (-4+8 x-4 x^2\right )+e^4 \left (1-2 x+x^2\right )+e^8 \left (1-2 x+x^2\right )+e^4 \left (4-8 x+4 x^2+e^2 \left (-2+4 x-2 x^2\right )\right )}\right ) \left (\left (-484-144 e^4-144 e^8\right ) x-132 x^2+36 x^3+4 x^4+e^2 \left (528 x+72 x^2-24 x^3\right )+e^4 \left (-528 x+288 e^2 x-72 x^2+24 x^3\right )\right )}{-4+12 x-12 x^2+4 x^3+e^2 \left (4-12 x+12 x^2-4 x^3\right )+\left (e^4+e^8\right ) \left (-1+3 x-3 x^2+x^3\right )+e^4 \left (-4+12 x-12 x^2+4 x^3+e^2 \left (2-6 x+6 x^2-2 x^3\right )\right )} \, dx\\ &=\int \frac {4 \exp \left (\frac {2 x^2 \left (11-6 e^2+6 e^4+x\right )^2}{\left (2-e^2+e^4\right )^2 (-1+x)^2}\right ) x \left (\left (11-6 e^2+6 e^4\right )^2+3 \left (11-6 e^2+6 e^4\right ) x-3 \left (3-2 e^2+2 e^4\right ) x^2-x^3\right )}{\left (2-e^2+e^4\right )^2 (1-x)^3} \, dx\\ &=\frac {4 \int \frac {\exp \left (\frac {2 x^2 \left (11-6 e^2+6 e^4+x\right )^2}{\left (2-e^2+e^4\right )^2 (-1+x)^2}\right ) x \left (\left (11-6 e^2+6 e^4\right )^2+3 \left (11-6 e^2+6 e^4\right ) x-3 \left (3-2 e^2+2 e^4\right ) x^2-x^3\right )}{(1-x)^3} \, dx}{\left (2-e^2+e^4\right )^2}\\ &=\exp \left (\frac {2 x^2 \left (11-6 e^2+6 e^4+x\right )^2}{\left (2-e^2+e^4\right )^2 (1-x)^2}\right )\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.15, size = 39, normalized size = 1.34 \begin {gather*} e^{\frac {2 x^2 \left (11-6 e^2+6 e^4+x\right )^2}{\left (2-e^2+e^4\right )^2 (-1+x)^2}} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^((2*(121*x^2 + 36*E^4*x^2 + 36*E^8*x^2 + 22*x^3 + x^4 + E^2*(-132*x^2 - 12*x^3) + E^4*(132*x^2 -
72*E^2*x^2 + 12*x^3)))/(4 - 8*x + 4*x^2 + E^2*(-4 + 8*x - 4*x^2) + E^4*(1 - 2*x + x^2) + E^8*(1 - 2*x + x^2) +
E^4*(4 - 8*x + 4*x^2 + E^2*(-2 + 4*x - 2*x^2))))*(-484*x - 144*E^4*x - 144*E^8*x - 132*x^2 + 36*x^3 + 4*x^4 +
E^2*(528*x + 72*x^2 - 24*x^3) + E^4*(-528*x + 288*E^2*x - 72*x^2 + 24*x^3)))/(-4 + 12*x - 12*x^2 + 4*x^3 + E^
2*(4 - 12*x + 12*x^2 - 4*x^3) + E^4*(-1 + 3*x - 3*x^2 + x^3) + E^8*(-1 + 3*x - 3*x^2 + x^3) + E^4*(-4 + 12*x -
12*x^2 + 4*x^3 + E^2*(2 - 6*x + 6*x^2 - 2*x^3))),x]

[Out]

E^((2*x^2*(11 - 6*E^2 + 6*E^4 + x)^2)/((2 - E^2 + E^4)^2*(-1 + x)^2))

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fricas [B]  time = 0.49, size = 116, normalized size = 4.00 \begin {gather*} e^{\left (\frac {2 \, {\left (x^{4} + 22 \, x^{3} + 36 \, x^{2} e^{8} - 72 \, x^{2} e^{6} + 121 \, x^{2} + 12 \, {\left (x^{3} + 14 \, x^{2}\right )} e^{4} - 12 \, {\left (x^{3} + 11 \, x^{2}\right )} e^{2}\right )}}{4 \, x^{2} + {\left (x^{2} - 2 \, x + 1\right )} e^{8} - 2 \, {\left (x^{2} - 2 \, x + 1\right )} e^{6} + 5 \, {\left (x^{2} - 2 \, x + 1\right )} e^{4} - 4 \, {\left (x^{2} - 2 \, x + 1\right )} e^{2} - 8 \, x + 4}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-144*x*exp(4)^2+(288*exp(2)*x+24*x^3-72*x^2-528*x)*exp(4)-144*x*exp(2)^2+(-24*x^3+72*x^2+528*x)*exp
(2)+4*x^4+36*x^3-132*x^2-484*x)*exp((36*x^2*exp(4)^2+(-72*x^2*exp(2)+12*x^3+132*x^2)*exp(4)+36*x^2*exp(2)^2+(-
12*x^3-132*x^2)*exp(2)+x^4+22*x^3+121*x^2)/((x^2-2*x+1)*exp(4)^2+((-2*x^2+4*x-2)*exp(2)+4*x^2-8*x+4)*exp(4)+(x
^2-2*x+1)*exp(2)^2+(-4*x^2+8*x-4)*exp(2)+4*x^2-8*x+4))^2/((x^3-3*x^2+3*x-1)*exp(4)^2+((-2*x^3+6*x^2-6*x+2)*exp
(2)+4*x^3-12*x^2+12*x-4)*exp(4)+(x^3-3*x^2+3*x-1)*exp(2)^2+(-4*x^3+12*x^2-12*x+4)*exp(2)+4*x^3-12*x^2+12*x-4),
x, algorithm="fricas")

[Out]

e^(2*(x^4 + 22*x^3 + 36*x^2*e^8 - 72*x^2*e^6 + 121*x^2 + 12*(x^3 + 14*x^2)*e^4 - 12*(x^3 + 11*x^2)*e^2)/(4*x^2
+ (x^2 - 2*x + 1)*e^8 - 2*(x^2 - 2*x + 1)*e^6 + 5*(x^2 - 2*x + 1)*e^4 - 4*(x^2 - 2*x + 1)*e^2 - 8*x + 4))

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giac [B]  time = 1.45, size = 716, normalized size = 24.69 \begin {gather*} e^{\left (\frac {2 \, x^{4}}{x^{2} e^{8} - 2 \, x^{2} e^{6} + 5 \, x^{2} e^{4} - 4 \, x^{2} e^{2} + 4 \, x^{2} - 2 \, x e^{8} + 4 \, x e^{6} - 10 \, x e^{4} + 8 \, x e^{2} - 8 \, x + e^{8} - 2 \, e^{6} + 5 \, e^{4} - 4 \, e^{2} + 4} + \frac {24 \, x^{3} e^{4}}{x^{2} e^{8} - 2 \, x^{2} e^{6} + 5 \, x^{2} e^{4} - 4 \, x^{2} e^{2} + 4 \, x^{2} - 2 \, x e^{8} + 4 \, x e^{6} - 10 \, x e^{4} + 8 \, x e^{2} - 8 \, x + e^{8} - 2 \, e^{6} + 5 \, e^{4} - 4 \, e^{2} + 4} - \frac {24 \, x^{3} e^{2}}{x^{2} e^{8} - 2 \, x^{2} e^{6} + 5 \, x^{2} e^{4} - 4 \, x^{2} e^{2} + 4 \, x^{2} - 2 \, x e^{8} + 4 \, x e^{6} - 10 \, x e^{4} + 8 \, x e^{2} - 8 \, x + e^{8} - 2 \, e^{6} + 5 \, e^{4} - 4 \, e^{2} + 4} + \frac {44 \, x^{3}}{x^{2} e^{8} - 2 \, x^{2} e^{6} + 5 \, x^{2} e^{4} - 4 \, x^{2} e^{2} + 4 \, x^{2} - 2 \, x e^{8} + 4 \, x e^{6} - 10 \, x e^{4} + 8 \, x e^{2} - 8 \, x + e^{8} - 2 \, e^{6} + 5 \, e^{4} - 4 \, e^{2} + 4} + \frac {72 \, x^{2} e^{8}}{x^{2} e^{8} - 2 \, x^{2} e^{6} + 5 \, x^{2} e^{4} - 4 \, x^{2} e^{2} + 4 \, x^{2} - 2 \, x e^{8} + 4 \, x e^{6} - 10 \, x e^{4} + 8 \, x e^{2} - 8 \, x + e^{8} - 2 \, e^{6} + 5 \, e^{4} - 4 \, e^{2} + 4} - \frac {144 \, x^{2} e^{6}}{x^{2} e^{8} - 2 \, x^{2} e^{6} + 5 \, x^{2} e^{4} - 4 \, x^{2} e^{2} + 4 \, x^{2} - 2 \, x e^{8} + 4 \, x e^{6} - 10 \, x e^{4} + 8 \, x e^{2} - 8 \, x + e^{8} - 2 \, e^{6} + 5 \, e^{4} - 4 \, e^{2} + 4} + \frac {336 \, x^{2} e^{4}}{x^{2} e^{8} - 2 \, x^{2} e^{6} + 5 \, x^{2} e^{4} - 4 \, x^{2} e^{2} + 4 \, x^{2} - 2 \, x e^{8} + 4 \, x e^{6} - 10 \, x e^{4} + 8 \, x e^{2} - 8 \, x + e^{8} - 2 \, e^{6} + 5 \, e^{4} - 4 \, e^{2} + 4} - \frac {264 \, x^{2} e^{2}}{x^{2} e^{8} - 2 \, x^{2} e^{6} + 5 \, x^{2} e^{4} - 4 \, x^{2} e^{2} + 4 \, x^{2} - 2 \, x e^{8} + 4 \, x e^{6} - 10 \, x e^{4} + 8 \, x e^{2} - 8 \, x + e^{8} - 2 \, e^{6} + 5 \, e^{4} - 4 \, e^{2} + 4} + \frac {242 \, x^{2}}{x^{2} e^{8} - 2 \, x^{2} e^{6} + 5 \, x^{2} e^{4} - 4 \, x^{2} e^{2} + 4 \, x^{2} - 2 \, x e^{8} + 4 \, x e^{6} - 10 \, x e^{4} + 8 \, x e^{2} - 8 \, x + e^{8} - 2 \, e^{6} + 5 \, e^{4} - 4 \, e^{2} + 4}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-144*x*exp(4)^2+(288*exp(2)*x+24*x^3-72*x^2-528*x)*exp(4)-144*x*exp(2)^2+(-24*x^3+72*x^2+528*x)*exp
(2)+4*x^4+36*x^3-132*x^2-484*x)*exp((36*x^2*exp(4)^2+(-72*x^2*exp(2)+12*x^3+132*x^2)*exp(4)+36*x^2*exp(2)^2+(-
12*x^3-132*x^2)*exp(2)+x^4+22*x^3+121*x^2)/((x^2-2*x+1)*exp(4)^2+((-2*x^2+4*x-2)*exp(2)+4*x^2-8*x+4)*exp(4)+(x
^2-2*x+1)*exp(2)^2+(-4*x^2+8*x-4)*exp(2)+4*x^2-8*x+4))^2/((x^3-3*x^2+3*x-1)*exp(4)^2+((-2*x^3+6*x^2-6*x+2)*exp
(2)+4*x^3-12*x^2+12*x-4)*exp(4)+(x^3-3*x^2+3*x-1)*exp(2)^2+(-4*x^3+12*x^2-12*x+4)*exp(2)+4*x^3-12*x^2+12*x-4),
x, algorithm="giac")

[Out]

e^(2*x^4/(x^2*e^8 - 2*x^2*e^6 + 5*x^2*e^4 - 4*x^2*e^2 + 4*x^2 - 2*x*e^8 + 4*x*e^6 - 10*x*e^4 + 8*x*e^2 - 8*x +
e^8 - 2*e^6 + 5*e^4 - 4*e^2 + 4) + 24*x^3*e^4/(x^2*e^8 - 2*x^2*e^6 + 5*x^2*e^4 - 4*x^2*e^2 + 4*x^2 - 2*x*e^8
+ 4*x*e^6 - 10*x*e^4 + 8*x*e^2 - 8*x + e^8 - 2*e^6 + 5*e^4 - 4*e^2 + 4) - 24*x^3*e^2/(x^2*e^8 - 2*x^2*e^6 + 5*
x^2*e^4 - 4*x^2*e^2 + 4*x^2 - 2*x*e^8 + 4*x*e^6 - 10*x*e^4 + 8*x*e^2 - 8*x + e^8 - 2*e^6 + 5*e^4 - 4*e^2 + 4)
+ 44*x^3/(x^2*e^8 - 2*x^2*e^6 + 5*x^2*e^4 - 4*x^2*e^2 + 4*x^2 - 2*x*e^8 + 4*x*e^6 - 10*x*e^4 + 8*x*e^2 - 8*x +
e^8 - 2*e^6 + 5*e^4 - 4*e^2 + 4) + 72*x^2*e^8/(x^2*e^8 - 2*x^2*e^6 + 5*x^2*e^4 - 4*x^2*e^2 + 4*x^2 - 2*x*e^8
+ 4*x*e^6 - 10*x*e^4 + 8*x*e^2 - 8*x + e^8 - 2*e^6 + 5*e^4 - 4*e^2 + 4) - 144*x^2*e^6/(x^2*e^8 - 2*x^2*e^6 + 5
*x^2*e^4 - 4*x^2*e^2 + 4*x^2 - 2*x*e^8 + 4*x*e^6 - 10*x*e^4 + 8*x*e^2 - 8*x + e^8 - 2*e^6 + 5*e^4 - 4*e^2 + 4)
+ 336*x^2*e^4/(x^2*e^8 - 2*x^2*e^6 + 5*x^2*e^4 - 4*x^2*e^2 + 4*x^2 - 2*x*e^8 + 4*x*e^6 - 10*x*e^4 + 8*x*e^2 -
8*x + e^8 - 2*e^6 + 5*e^4 - 4*e^2 + 4) - 264*x^2*e^2/(x^2*e^8 - 2*x^2*e^6 + 5*x^2*e^4 - 4*x^2*e^2 + 4*x^2 - 2
*x*e^8 + 4*x*e^6 - 10*x*e^4 + 8*x*e^2 - 8*x + e^8 - 2*e^6 + 5*e^4 - 4*e^2 + 4) + 242*x^2/(x^2*e^8 - 2*x^2*e^6
+ 5*x^2*e^4 - 4*x^2*e^2 + 4*x^2 - 2*x*e^8 + 4*x*e^6 - 10*x*e^4 + 8*x*e^2 - 8*x + e^8 - 2*e^6 + 5*e^4 - 4*e^2 +
4))

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maple [B]  time = 50.00, size = 68, normalized size = 2.34

method	result	size
risch	\({\mathrm e}^{\frac {2 x^{2} \left (72 \,{\mathrm e}^{6}+12 \,{\mathrm e}^{2} x -12 x \,{\mathrm e}^{4}-x^{2}+132 \,{\mathrm e}^{2}-168 \,{\mathrm e}^{4}-36 \,{\mathrm e}^{8}-22 x -121\right )}{\left (x -1\right )^{2} \left (4 \,{\mathrm e}^{2}-5 \,{\mathrm e}^{4}+2 \,{\mathrm e}^{6}-{\mathrm e}^{8}-4\right )}}\)	\(68\)
gosper	\({\mathrm e}^{\frac {2 x^{2} \left (168 \,{\mathrm e}^{4}-72 \,{\mathrm e}^{6}-12 \,{\mathrm e}^{2} x +36 \,{\mathrm e}^{8}+12 x \,{\mathrm e}^{4}+x^{2}-132 \,{\mathrm e}^{2}+22 x +121\right )}{5 x^{2} {\mathrm e}^{4}-2 x^{2} {\mathrm e}^{6}+x^{2} {\mathrm e}^{8}-10 x \,{\mathrm e}^{4}+4 x \,{\mathrm e}^{6}-4 x^{2} {\mathrm e}^{2}-2 x \,{\mathrm e}^{8}+5 \,{\mathrm e}^{4}-2 \,{\mathrm e}^{6}+8 \,{\mathrm e}^{2} x +{\mathrm e}^{8}+4 x^{2}-4 \,{\mathrm e}^{2}-8 x +4}}\)	\(156\)
norman	\(\frac {\left ({\mathrm e}^{2}-2-{\mathrm e}^{4}\right ) {\mathrm e}^{\frac {72 x^{2} {\mathrm e}^{8}+2 \left (-72 x^{2} {\mathrm e}^{2}+12 x^{3}+132 x^{2}\right ) {\mathrm e}^{4}+72 x^{2} {\mathrm e}^{4}+2 \left (-12 x^{3}-132 x^{2}\right ) {\mathrm e}^{2}+2 x^{4}+44 x^{3}+242 x^{2}}{\left (x^{2}-2 x +1\right ) {\mathrm e}^{8}+\left (\left (-2 x^{2}+4 x -2\right ) {\mathrm e}^{2}+4 x^{2}-8 x +4\right ) {\mathrm e}^{4}+\left (x^{2}-2 x +1\right ) {\mathrm e}^{4}+\left (-4 x^{2}+8 x -4\right ) {\mathrm e}^{2}+4 x^{2}-8 x +4}}+\left (-2 \,{\mathrm e}^{2}+2 \,{\mathrm e}^{4}+4\right ) x \,{\mathrm e}^{\frac {72 x^{2} {\mathrm e}^{8}+2 \left (-72 x^{2} {\mathrm e}^{2}+12 x^{3}+132 x^{2}\right ) {\mathrm e}^{4}+72 x^{2} {\mathrm e}^{4}+2 \left (-12 x^{3}-132 x^{2}\right ) {\mathrm e}^{2}+2 x^{4}+44 x^{3}+242 x^{2}}{\left (x^{2}-2 x +1\right ) {\mathrm e}^{8}+\left (\left (-2 x^{2}+4 x -2\right ) {\mathrm e}^{2}+4 x^{2}-8 x +4\right ) {\mathrm e}^{4}+\left (x^{2}-2 x +1\right ) {\mathrm e}^{4}+\left (-4 x^{2}+8 x -4\right ) {\mathrm e}^{2}+4 x^{2}-8 x +4}}+\left ({\mathrm e}^{2}-2-{\mathrm e}^{4}\right ) x^{2} {\mathrm e}^{\frac {72 x^{2} {\mathrm e}^{8}+2 \left (-72 x^{2} {\mathrm e}^{2}+12 x^{3}+132 x^{2}\right ) {\mathrm e}^{4}+72 x^{2} {\mathrm e}^{4}+2 \left (-12 x^{3}-132 x^{2}\right ) {\mathrm e}^{2}+2 x^{4}+44 x^{3}+242 x^{2}}{\left (x^{2}-2 x +1\right ) {\mathrm e}^{8}+\left (\left (-2 x^{2}+4 x -2\right ) {\mathrm e}^{2}+4 x^{2}-8 x +4\right ) {\mathrm e}^{4}+\left (x^{2}-2 x +1\right ) {\mathrm e}^{4}+\left (-4 x^{2}+8 x -4\right ) {\mathrm e}^{2}+4 x^{2}-8 x +4}}}{\left (x -1\right )^{2} \left ({\mathrm e}^{2}-2-{\mathrm e}^{4}\right )}\)	\(495\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((-144*x*exp(4)^2+(288*exp(2)*x+24*x^3-72*x^2-528*x)*exp(4)-144*x*exp(2)^2+(-24*x^3+72*x^2+528*x)*exp(2)+4*
x^4+36*x^3-132*x^2-484*x)*exp((36*x^2*exp(4)^2+(-72*x^2*exp(2)+12*x^3+132*x^2)*exp(4)+36*x^2*exp(2)^2+(-12*x^3
-132*x^2)*exp(2)+x^4+22*x^3+121*x^2)/((x^2-2*x+1)*exp(4)^2+((-2*x^2+4*x-2)*exp(2)+4*x^2-8*x+4)*exp(4)+(x^2-2*x
+1)*exp(2)^2+(-4*x^2+8*x-4)*exp(2)+4*x^2-8*x+4))^2/((x^3-3*x^2+3*x-1)*exp(4)^2+((-2*x^3+6*x^2-6*x+2)*exp(2)+4*
x^3-12*x^2+12*x-4)*exp(4)+(x^3-3*x^2+3*x-1)*exp(2)^2+(-4*x^3+12*x^2-12*x+4)*exp(2)+4*x^3-12*x^2+12*x-4),x,meth
od=_RETURNVERBOSE)

[Out]

exp(2*x^2*(72*exp(6)+12*exp(2)*x-12*x*exp(4)-x^2+132*exp(2)-168*exp(4)-36*exp(8)-22*x-121)/(x-1)^2/(4*exp(2)-5
*exp(4)+2*exp(6)-exp(8)-4))

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maxima [B]  time = 6.38, size = 711, normalized size = 24.52 \begin {gather*} e^{\left (\frac {2 \, x^{2}}{e^{8} - 2 \, e^{6} + 5 \, e^{4} - 4 \, e^{2} + 4} + \frac {24 \, x e^{4}}{e^{8} - 2 \, e^{6} + 5 \, e^{4} - 4 \, e^{2} + 4} - \frac {24 \, x e^{2}}{e^{8} - 2 \, e^{6} + 5 \, e^{4} - 4 \, e^{2} + 4} + \frac {48 \, x}{e^{8} - 2 \, e^{6} + 5 \, e^{4} - 4 \, e^{2} + 4} + \frac {72 \, e^{8}}{x^{2} {\left (e^{8} - 2 \, e^{6} + 5 \, e^{4} - 4 \, e^{2} + 4\right )} - 2 \, x {\left (e^{8} - 2 \, e^{6} + 5 \, e^{4} - 4 \, e^{2} + 4\right )} + e^{8} - 2 \, e^{6} + 5 \, e^{4} - 4 \, e^{2} + 4} + \frac {144 \, e^{8}}{x {\left (e^{8} - 2 \, e^{6} + 5 \, e^{4} - 4 \, e^{2} + 4\right )} - e^{8} + 2 \, e^{6} - 5 \, e^{4} + 4 \, e^{2} - 4} + \frac {72 \, e^{8}}{e^{8} - 2 \, e^{6} + 5 \, e^{4} - 4 \, e^{2} + 4} - \frac {144 \, e^{6}}{x^{2} {\left (e^{8} - 2 \, e^{6} + 5 \, e^{4} - 4 \, e^{2} + 4\right )} - 2 \, x {\left (e^{8} - 2 \, e^{6} + 5 \, e^{4} - 4 \, e^{2} + 4\right )} + e^{8} - 2 \, e^{6} + 5 \, e^{4} - 4 \, e^{2} + 4} - \frac {288 \, e^{6}}{x {\left (e^{8} - 2 \, e^{6} + 5 \, e^{4} - 4 \, e^{2} + 4\right )} - e^{8} + 2 \, e^{6} - 5 \, e^{4} + 4 \, e^{2} - 4} - \frac {144 \, e^{6}}{e^{8} - 2 \, e^{6} + 5 \, e^{4} - 4 \, e^{2} + 4} + \frac {360 \, e^{4}}{x^{2} {\left (e^{8} - 2 \, e^{6} + 5 \, e^{4} - 4 \, e^{2} + 4\right )} - 2 \, x {\left (e^{8} - 2 \, e^{6} + 5 \, e^{4} - 4 \, e^{2} + 4\right )} + e^{8} - 2 \, e^{6} + 5 \, e^{4} - 4 \, e^{2} + 4} + \frac {744 \, e^{4}}{x {\left (e^{8} - 2 \, e^{6} + 5 \, e^{4} - 4 \, e^{2} + 4\right )} - e^{8} + 2 \, e^{6} - 5 \, e^{4} + 4 \, e^{2} - 4} + \frac {384 \, e^{4}}{e^{8} - 2 \, e^{6} + 5 \, e^{4} - 4 \, e^{2} + 4} - \frac {288 \, e^{2}}{x^{2} {\left (e^{8} - 2 \, e^{6} + 5 \, e^{4} - 4 \, e^{2} + 4\right )} - 2 \, x {\left (e^{8} - 2 \, e^{6} + 5 \, e^{4} - 4 \, e^{2} + 4\right )} + e^{8} - 2 \, e^{6} + 5 \, e^{4} - 4 \, e^{2} + 4} - \frac {600 \, e^{2}}{x {\left (e^{8} - 2 \, e^{6} + 5 \, e^{4} - 4 \, e^{2} + 4\right )} - e^{8} + 2 \, e^{6} - 5 \, e^{4} + 4 \, e^{2} - 4} - \frac {312 \, e^{2}}{e^{8} - 2 \, e^{6} + 5 \, e^{4} - 4 \, e^{2} + 4} + \frac {288}{x^{2} {\left (e^{8} - 2 \, e^{6} + 5 \, e^{4} - 4 \, e^{2} + 4\right )} - 2 \, x {\left (e^{8} - 2 \, e^{6} + 5 \, e^{4} - 4 \, e^{2} + 4\right )} + e^{8} - 2 \, e^{6} + 5 \, e^{4} - 4 \, e^{2} + 4} + \frac {624}{x {\left (e^{8} - 2 \, e^{6} + 5 \, e^{4} - 4 \, e^{2} + 4\right )} - e^{8} + 2 \, e^{6} - 5 \, e^{4} + 4 \, e^{2} - 4} + \frac {336}{e^{8} - 2 \, e^{6} + 5 \, e^{4} - 4 \, e^{2} + 4}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-144*x*exp(4)^2+(288*exp(2)*x+24*x^3-72*x^2-528*x)*exp(4)-144*x*exp(2)^2+(-24*x^3+72*x^2+528*x)*exp
(2)+4*x^4+36*x^3-132*x^2-484*x)*exp((36*x^2*exp(4)^2+(-72*x^2*exp(2)+12*x^3+132*x^2)*exp(4)+36*x^2*exp(2)^2+(-
12*x^3-132*x^2)*exp(2)+x^4+22*x^3+121*x^2)/((x^2-2*x+1)*exp(4)^2+((-2*x^2+4*x-2)*exp(2)+4*x^2-8*x+4)*exp(4)+(x
^2-2*x+1)*exp(2)^2+(-4*x^2+8*x-4)*exp(2)+4*x^2-8*x+4))^2/((x^3-3*x^2+3*x-1)*exp(4)^2+((-2*x^3+6*x^2-6*x+2)*exp
(2)+4*x^3-12*x^2+12*x-4)*exp(4)+(x^3-3*x^2+3*x-1)*exp(2)^2+(-4*x^3+12*x^2-12*x+4)*exp(2)+4*x^3-12*x^2+12*x-4),
x, algorithm="maxima")

[Out]

e^(2*x^2/(e^8 - 2*e^6 + 5*e^4 - 4*e^2 + 4) + 24*x*e^4/(e^8 - 2*e^6 + 5*e^4 - 4*e^2 + 4) - 24*x*e^2/(e^8 - 2*e^
6 + 5*e^4 - 4*e^2 + 4) + 48*x/(e^8 - 2*e^6 + 5*e^4 - 4*e^2 + 4) + 72*e^8/(x^2*(e^8 - 2*e^6 + 5*e^4 - 4*e^2 + 4
) - 2*x*(e^8 - 2*e^6 + 5*e^4 - 4*e^2 + 4) + e^8 - 2*e^6 + 5*e^4 - 4*e^2 + 4) + 144*e^8/(x*(e^8 - 2*e^6 + 5*e^4
- 4*e^2 + 4) - e^8 + 2*e^6 - 5*e^4 + 4*e^2 - 4) + 72*e^8/(e^8 - 2*e^6 + 5*e^4 - 4*e^2 + 4) - 144*e^6/(x^2*(e^
8 - 2*e^6 + 5*e^4 - 4*e^2 + 4) - 2*x*(e^8 - 2*e^6 + 5*e^4 - 4*e^2 + 4) + e^8 - 2*e^6 + 5*e^4 - 4*e^2 + 4) - 28
8*e^6/(x*(e^8 - 2*e^6 + 5*e^4 - 4*e^2 + 4) - e^8 + 2*e^6 - 5*e^4 + 4*e^2 - 4) - 144*e^6/(e^8 - 2*e^6 + 5*e^4 -
4*e^2 + 4) + 360*e^4/(x^2*(e^8 - 2*e^6 + 5*e^4 - 4*e^2 + 4) - 2*x*(e^8 - 2*e^6 + 5*e^4 - 4*e^2 + 4) + e^8 - 2
*e^6 + 5*e^4 - 4*e^2 + 4) + 744*e^4/(x*(e^8 - 2*e^6 + 5*e^4 - 4*e^2 + 4) - e^8 + 2*e^6 - 5*e^4 + 4*e^2 - 4) +
384*e^4/(e^8 - 2*e^6 + 5*e^4 - 4*e^2 + 4) - 288*e^2/(x^2*(e^8 - 2*e^6 + 5*e^4 - 4*e^2 + 4) - 2*x*(e^8 - 2*e^6
+ 5*e^4 - 4*e^2 + 4) + e^8 - 2*e^6 + 5*e^4 - 4*e^2 + 4) - 600*e^2/(x*(e^8 - 2*e^6 + 5*e^4 - 4*e^2 + 4) - e^8 +
2*e^6 - 5*e^4 + 4*e^2 - 4) - 312*e^2/(e^8 - 2*e^6 + 5*e^4 - 4*e^2 + 4) + 288/(x^2*(e^8 - 2*e^6 + 5*e^4 - 4*e^
2 + 4) - 2*x*(e^8 - 2*e^6 + 5*e^4 - 4*e^2 + 4) + e^8 - 2*e^6 + 5*e^4 - 4*e^2 + 4) + 624/(x*(e^8 - 2*e^6 + 5*e^
4 - 4*e^2 + 4) - e^8 + 2*e^6 - 5*e^4 + 4*e^2 - 4) + 336/(e^8 - 2*e^6 + 5*e^4 - 4*e^2 + 4))

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mupad [B]  time = 3.13, size = 724, normalized size = 24.97 \begin {gather*} {\mathrm {e}}^{\frac {2\,x^4}{5\,{\mathrm {e}}^4-4\,{\mathrm {e}}^2-8\,x-2\,{\mathrm {e}}^6+{\mathrm {e}}^8+8\,x\,{\mathrm {e}}^2-10\,x\,{\mathrm {e}}^4+4\,x\,{\mathrm {e}}^6-2\,x\,{\mathrm {e}}^8-4\,x^2\,{\mathrm {e}}^2+5\,x^2\,{\mathrm {e}}^4-2\,x^2\,{\mathrm {e}}^6+x^2\,{\mathrm {e}}^8+4\,x^2+4}}\,{\mathrm {e}}^{\frac {44\,x^3}{5\,{\mathrm {e}}^4-4\,{\mathrm {e}}^2-8\,x-2\,{\mathrm {e}}^6+{\mathrm {e}}^8+8\,x\,{\mathrm {e}}^2-10\,x\,{\mathrm {e}}^4+4\,x\,{\mathrm {e}}^6-2\,x\,{\mathrm {e}}^8-4\,x^2\,{\mathrm {e}}^2+5\,x^2\,{\mathrm {e}}^4-2\,x^2\,{\mathrm {e}}^6+x^2\,{\mathrm {e}}^8+4\,x^2+4}}\,{\mathrm {e}}^{\frac {242\,x^2}{5\,{\mathrm {e}}^4-4\,{\mathrm {e}}^2-8\,x-2\,{\mathrm {e}}^6+{\mathrm {e}}^8+8\,x\,{\mathrm {e}}^2-10\,x\,{\mathrm {e}}^4+4\,x\,{\mathrm {e}}^6-2\,x\,{\mathrm {e}}^8-4\,x^2\,{\mathrm {e}}^2+5\,x^2\,{\mathrm {e}}^4-2\,x^2\,{\mathrm {e}}^6+x^2\,{\mathrm {e}}^8+4\,x^2+4}}\,{\mathrm {e}}^{-\frac {24\,x^3\,{\mathrm {e}}^2}{5\,{\mathrm {e}}^4-4\,{\mathrm {e}}^2-8\,x-2\,{\mathrm {e}}^6+{\mathrm {e}}^8+8\,x\,{\mathrm {e}}^2-10\,x\,{\mathrm {e}}^4+4\,x\,{\mathrm {e}}^6-2\,x\,{\mathrm {e}}^8-4\,x^2\,{\mathrm {e}}^2+5\,x^2\,{\mathrm {e}}^4-2\,x^2\,{\mathrm {e}}^6+x^2\,{\mathrm {e}}^8+4\,x^2+4}}\,{\mathrm {e}}^{\frac {24\,x^3\,{\mathrm {e}}^4}{5\,{\mathrm {e}}^4-4\,{\mathrm {e}}^2-8\,x-2\,{\mathrm {e}}^6+{\mathrm {e}}^8+8\,x\,{\mathrm {e}}^2-10\,x\,{\mathrm {e}}^4+4\,x\,{\mathrm {e}}^6-2\,x\,{\mathrm {e}}^8-4\,x^2\,{\mathrm {e}}^2+5\,x^2\,{\mathrm {e}}^4-2\,x^2\,{\mathrm {e}}^6+x^2\,{\mathrm {e}}^8+4\,x^2+4}}\,{\mathrm {e}}^{\frac {72\,x^2\,{\mathrm {e}}^8}{5\,{\mathrm {e}}^4-4\,{\mathrm {e}}^2-8\,x-2\,{\mathrm {e}}^6+{\mathrm {e}}^8+8\,x\,{\mathrm {e}}^2-10\,x\,{\mathrm {e}}^4+4\,x\,{\mathrm {e}}^6-2\,x\,{\mathrm {e}}^8-4\,x^2\,{\mathrm {e}}^2+5\,x^2\,{\mathrm {e}}^4-2\,x^2\,{\mathrm {e}}^6+x^2\,{\mathrm {e}}^8+4\,x^2+4}}\,{\mathrm {e}}^{-\frac {144\,x^2\,{\mathrm {e}}^6}{5\,{\mathrm {e}}^4-4\,{\mathrm {e}}^2-8\,x-2\,{\mathrm {e}}^6+{\mathrm {e}}^8+8\,x\,{\mathrm {e}}^2-10\,x\,{\mathrm {e}}^4+4\,x\,{\mathrm {e}}^6-2\,x\,{\mathrm {e}}^8-4\,x^2\,{\mathrm {e}}^2+5\,x^2\,{\mathrm {e}}^4-2\,x^2\,{\mathrm {e}}^6+x^2\,{\mathrm {e}}^8+4\,x^2+4}}\,{\mathrm {e}}^{-\frac {264\,x^2\,{\mathrm {e}}^2}{5\,{\mathrm {e}}^4-4\,{\mathrm {e}}^2-8\,x-2\,{\mathrm {e}}^6+{\mathrm {e}}^8+8\,x\,{\mathrm {e}}^2-10\,x\,{\mathrm {e}}^4+4\,x\,{\mathrm {e}}^6-2\,x\,{\mathrm {e}}^8-4\,x^2\,{\mathrm {e}}^2+5\,x^2\,{\mathrm {e}}^4-2\,x^2\,{\mathrm {e}}^6+x^2\,{\mathrm {e}}^8+4\,x^2+4}}\,{\mathrm {e}}^{\frac {336\,x^2\,{\mathrm {e}}^4}{5\,{\mathrm {e}}^4-4\,{\mathrm {e}}^2-8\,x-2\,{\mathrm {e}}^6+{\mathrm {e}}^8+8\,x\,{\mathrm {e}}^2-10\,x\,{\mathrm {e}}^4+4\,x\,{\mathrm {e}}^6-2\,x\,{\mathrm {e}}^8-4\,x^2\,{\mathrm {e}}^2+5\,x^2\,{\mathrm {e}}^4-2\,x^2\,{\mathrm {e}}^6+x^2\,{\mathrm {e}}^8+4\,x^2+4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp((2*(exp(4)*(132*x^2 - 72*x^2*exp(2) + 12*x^3) - exp(2)*(132*x^2 + 12*x^3) + 36*x^2*exp(4) + 36*x^2*e
xp(8) + 121*x^2 + 22*x^3 + x^4))/(exp(4)*(x^2 - 2*x + 1) - exp(2)*(4*x^2 - 8*x + 4) - exp(4)*(8*x + exp(2)*(2*
x^2 - 4*x + 2) - 4*x^2 - 4) - 8*x + exp(8)*(x^2 - 2*x + 1) + 4*x^2 + 4))*(484*x + 144*x*exp(4) + 144*x*exp(8)
- exp(2)*(528*x + 72*x^2 - 24*x^3) + exp(4)*(528*x - 288*x*exp(2) + 72*x^2 - 24*x^3) + 132*x^2 - 36*x^3 - 4*x^
4))/(12*x + exp(4)*(3*x - 3*x^2 + x^3 - 1) + exp(8)*(3*x - 3*x^2 + x^3 - 1) - exp(2)*(12*x - 12*x^2 + 4*x^3 -
4) - exp(4)*(exp(2)*(6*x - 6*x^2 + 2*x^3 - 2) - 12*x + 12*x^2 - 4*x^3 + 4) - 12*x^2 + 4*x^3 - 4),x)

[Out]

exp((2*x^4)/(5*exp(4) - 4*exp(2) - 8*x - 2*exp(6) + exp(8) + 8*x*exp(2) - 10*x*exp(4) + 4*x*exp(6) - 2*x*exp(8
) - 4*x^2*exp(2) + 5*x^2*exp(4) - 2*x^2*exp(6) + x^2*exp(8) + 4*x^2 + 4))*exp((44*x^3)/(5*exp(4) - 4*exp(2) -
8*x - 2*exp(6) + exp(8) + 8*x*exp(2) - 10*x*exp(4) + 4*x*exp(6) - 2*x*exp(8) - 4*x^2*exp(2) + 5*x^2*exp(4) - 2
*x^2*exp(6) + x^2*exp(8) + 4*x^2 + 4))*exp((242*x^2)/(5*exp(4) - 4*exp(2) - 8*x - 2*exp(6) + exp(8) + 8*x*exp(
2) - 10*x*exp(4) + 4*x*exp(6) - 2*x*exp(8) - 4*x^2*exp(2) + 5*x^2*exp(4) - 2*x^2*exp(6) + x^2*exp(8) + 4*x^2 +
4))*exp(-(24*x^3*exp(2))/(5*exp(4) - 4*exp(2) - 8*x - 2*exp(6) + exp(8) + 8*x*exp(2) - 10*x*exp(4) + 4*x*exp(
6) - 2*x*exp(8) - 4*x^2*exp(2) + 5*x^2*exp(4) - 2*x^2*exp(6) + x^2*exp(8) + 4*x^2 + 4))*exp((24*x^3*exp(4))/(5
*exp(4) - 4*exp(2) - 8*x - 2*exp(6) + exp(8) + 8*x*exp(2) - 10*x*exp(4) + 4*x*exp(6) - 2*x*exp(8) - 4*x^2*exp(
2) + 5*x^2*exp(4) - 2*x^2*exp(6) + x^2*exp(8) + 4*x^2 + 4))*exp((72*x^2*exp(8))/(5*exp(4) - 4*exp(2) - 8*x - 2
*exp(6) + exp(8) + 8*x*exp(2) - 10*x*exp(4) + 4*x*exp(6) - 2*x*exp(8) - 4*x^2*exp(2) + 5*x^2*exp(4) - 2*x^2*ex
p(6) + x^2*exp(8) + 4*x^2 + 4))*exp(-(144*x^2*exp(6))/(5*exp(4) - 4*exp(2) - 8*x - 2*exp(6) + exp(8) + 8*x*exp
(2) - 10*x*exp(4) + 4*x*exp(6) - 2*x*exp(8) - 4*x^2*exp(2) + 5*x^2*exp(4) - 2*x^2*exp(6) + x^2*exp(8) + 4*x^2
+ 4))*exp(-(264*x^2*exp(2))/(5*exp(4) - 4*exp(2) - 8*x - 2*exp(6) + exp(8) + 8*x*exp(2) - 10*x*exp(4) + 4*x*ex
p(6) - 2*x*exp(8) - 4*x^2*exp(2) + 5*x^2*exp(4) - 2*x^2*exp(6) + x^2*exp(8) + 4*x^2 + 4))*exp((336*x^2*exp(4))
/(5*exp(4) - 4*exp(2) - 8*x - 2*exp(6) + exp(8) + 8*x*exp(2) - 10*x*exp(4) + 4*x*exp(6) - 2*x*exp(8) - 4*x^2*e
xp(2) + 5*x^2*exp(4) - 2*x^2*exp(6) + x^2*exp(8) + 4*x^2 + 4))

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sympy [B]  time = 3.60, size = 148, normalized size = 5.10 \begin {gather*} e^{\frac {2 \left (x^{4} + 22 x^{3} + 121 x^{2} + 36 x^{2} e^{4} + 36 x^{2} e^{8} + \left (- 12 x^{3} - 132 x^{2}\right ) e^{2} + \left (12 x^{3} - 72 x^{2} e^{2} + 132 x^{2}\right ) e^{4}\right )}{4 x^{2} - 8 x + \left (- 4 x^{2} + 8 x - 4\right ) e^{2} + \left (x^{2} - 2 x + 1\right ) e^{4} + \left (x^{2} - 2 x + 1\right ) e^{8} + \left (4 x^{2} - 8 x + \left (- 2 x^{2} + 4 x - 2\right ) e^{2} + 4\right ) e^{4} + 4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((-144*x*exp(4)**2+(288*exp(2)*x+24*x**3-72*x**2-528*x)*exp(4)-144*x*exp(2)**2+(-24*x**3+72*x**2+528*
x)*exp(2)+4*x**4+36*x**3-132*x**2-484*x)*exp((36*x**2*exp(4)**2+(-72*x**2*exp(2)+12*x**3+132*x**2)*exp(4)+36*x
**2*exp(2)**2+(-12*x**3-132*x**2)*exp(2)+x**4+22*x**3+121*x**2)/((x**2-2*x+1)*exp(4)**2+((-2*x**2+4*x-2)*exp(2
)+4*x**2-8*x+4)*exp(4)+(x**2-2*x+1)*exp(2)**2+(-4*x**2+8*x-4)*exp(2)+4*x**2-8*x+4))**2/((x**3-3*x**2+3*x-1)*ex
p(4)**2+((-2*x**3+6*x**2-6*x+2)*exp(2)+4*x**3-12*x**2+12*x-4)*exp(4)+(x**3-3*x**2+3*x-1)*exp(2)**2+(-4*x**3+12
*x**2-12*x+4)*exp(2)+4*x**3-12*x**2+12*x-4),x)

[Out]

exp(2*(x**4 + 22*x**3 + 121*x**2 + 36*x**2*exp(4) + 36*x**2*exp(8) + (-12*x**3 - 132*x**2)*exp(2) + (12*x**3 -
72*x**2*exp(2) + 132*x**2)*exp(4))/(4*x**2 - 8*x + (-4*x**2 + 8*x - 4)*exp(2) + (x**2 - 2*x + 1)*exp(4) + (x*
*2 - 2*x + 1)*exp(8) + (4*x**2 - 8*x + (-2*x**2 + 4*x - 2)*exp(2) + 4)*exp(4) + 4))

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