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

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

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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} $$\begin{array}{c}\exp \left(\frac{2x^2{(x+6e^4-6e^2+11)}^2}{{(2-e^2+e^4)}^2(1-x{)}^2}\right)\end{array}$$

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

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

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

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 $$\begin{array}{c}{e}^{\left(\frac{2(x^4+22x^3+36x^2{e}^8-72x^2{e}^6+121x^2+12(x^3+14x^2)e^4-12(x^3+11x^2)e^2)}{4x^2+(x^2-2x+1)e^8-2(x^2-2x+1)e^6+5(x^2-2x+1)e^4-4(x^2-2x+1)e^2-8x+4}\right)}\end{array}$$

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 $$\begin{array}{c}{e}^{(\frac{2x^4}{x^2{e}^8-2x^2{e}^6+5x^2{e}^4-4x^2{e}^2+4x^2-2x{e}^8+4x{e}^6-10x{e}^4+8x{e}^2-8x+e^8-2e^6+5e^4-4e^2+4}+\frac{24x^3{e}^4}{x^2{e}^8-2x^2{e}^6+5x^2{e}^4-4x^2{e}^2+4x^2-2x{e}^8+4x{e}^6-10x{e}^4+8x{e}^2-8x+e^8-2e^6+5e^4-4e^2+4}-\frac{24x^3{e}^2}{x^2{e}^8-2x^2{e}^6+5x^2{e}^4-4x^2{e}^2+4x^2-2x{e}^8+4x{e}^6-10x{e}^4+8x{e}^2-8x+e^8-2e^6+5e^4-4e^2+4}+\frac{44x^3}{x^2{e}^8-2x^2{e}^6+5x^2{e}^4-4x^2{e}^2+4x^2-2x{e}^8+4x{e}^6-10x{e}^4+8x{e}^2-8x+e^8-2e^6+5e^4-4e^2+4}+\frac{72x^2{e}^8}{x^2{e}^8-2x^2{e}^6+5x^2{e}^4-4x^2{e}^2+4x^2-2x{e}^8+4x{e}^6-10x{e}^4+8x{e}^2-8x+e^8-2e^6+5e^4-4e^2+4}-\frac{144x^2{e}^6}{x^2{e}^8-2x^2{e}^6+5x^2{e}^4-4x^2{e}^2+4x^2-2x{e}^8+4x{e}^6-10x{e}^4+8x{e}^2-8x+e^8-2e^6+5e^4-4e^2+4}+\frac{336x^2{e}^4}{x^2{e}^8-2x^2{e}^6+5x^2{e}^4-4x^2{e}^2+4x^2-2x{e}^8+4x{e}^6-10x{e}^4+8x{e}^2-8x+e^8-2e^6+5e^4-4e^2+4}-\frac{264x^2{e}^2}{x^2{e}^8-2x^2{e}^6+5x^2{e}^4-4x^2{e}^2+4x^2-2x{e}^8+4x{e}^6-10x{e}^4+8x{e}^2-8x+e^8-2e^6+5e^4-4e^2+4}+\frac{242x^2}{x^2{e}^8-2x^2{e}^6+5x^2{e}^4-4x^2{e}^2+4x^2-2x{e}^8+4x{e}^6-10x{e}^4+8x{e}^2-8x+e^8-2e^6+5e^4-4e^2+4})}\end{array}$$

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

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 $$\begin{array}{c}{e}^{(\frac{2x^2}{e^8-2e^6+5e^4-4e^2+4}+\frac{24x{e}^4}{e^8-2e^6+5e^4-4e^2+4}-\frac{24x{e}^2}{e^8-2e^6+5e^4-4e^2+4}+\frac{48x}{e^8-2e^6+5e^4-4e^2+4}+\frac{72e^8}{x^2(e^8-2e^6+5e^4-4e^2+4)-2x(e^8-2e^6+5e^4-4e^2+4)+e^8-2e^6+5e^4-4e^2+4}+\frac{144e^8}{x(e^8-2e^6+5e^4-4e^2+4)-e^8+2e^6-5e^4+4e^2-4}+\frac{72e^8}{e^8-2e^6+5e^4-4e^2+4}-\frac{144e^6}{x^2(e^8-2e^6+5e^4-4e^2+4)-2x(e^8-2e^6+5e^4-4e^2+4)+e^8-2e^6+5e^4-4e^2+4}-\frac{288e^6}{x(e^8-2e^6+5e^4-4e^2+4)-e^8+2e^6-5e^4+4e^2-4}-\frac{144e^6}{e^8-2e^6+5e^4-4e^2+4}+\frac{360e^4}{x^2(e^8-2e^6+5e^4-4e^2+4)-2x(e^8-2e^6+5e^4-4e^2+4)+e^8-2e^6+5e^4-4e^2+4}+\frac{744e^4}{x(e^8-2e^6+5e^4-4e^2+4)-e^8+2e^6-5e^4+4e^2-4}+\frac{384e^4}{e^8-2e^6+5e^4-4e^2+4}-\frac{288e^2}{x^2(e^8-2e^6+5e^4-4e^2+4)-2x(e^8-2e^6+5e^4-4e^2+4)+e^8-2e^6+5e^4-4e^2+4}-\frac{600e^2}{x(e^8-2e^6+5e^4-4e^2+4)-e^8+2e^6-5e^4+4e^2-4}-\frac{312e^2}{e^8-2e^6+5e^4-4e^2+4}+\frac{288}{x^2(e^8-2e^6+5e^4-4e^2+4)-2x(e^8-2e^6+5e^4-4e^2+4)+e^8-2e^6+5e^4-4e^2+4}+\frac{624}{x(e^8-2e^6+5e^4-4e^2+4)-e^8+2e^6-5e^4+4e^2-4}+\frac{336}{e^8-2e^6+5e^4-4e^2+4})}\end{array}$$

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{array}{c}{\mathrm{e}}^{\frac{2x^4}{5{\mathrm{e}}^4-4{\mathrm{e}}^2-8x-2{\mathrm{e}}^6+{\mathrm{e}}^8+8x{\mathrm{e}}^2-10x{\mathrm{e}}^4+4x{\mathrm{e}}^6-2x{\mathrm{e}}^8-4x^2{\mathrm{e}}^2+5x^2{\mathrm{e}}^4-2x^2{\mathrm{e}}^6+x^2{\mathrm{e}}^8+4x^2+4}}{\mathrm{e}}^{\frac{44x^3}{5{\mathrm{e}}^4-4{\mathrm{e}}^2-8x-2{\mathrm{e}}^6+{\mathrm{e}}^8+8x{\mathrm{e}}^2-10x{\mathrm{e}}^4+4x{\mathrm{e}}^6-2x{\mathrm{e}}^8-4x^2{\mathrm{e}}^2+5x^2{\mathrm{e}}^4-2x^2{\mathrm{e}}^6+x^2{\mathrm{e}}^8+4x^2+4}}{\mathrm{e}}^{\frac{242x^2}{5{\mathrm{e}}^4-4{\mathrm{e}}^2-8x-2{\mathrm{e}}^6+{\mathrm{e}}^8+8x{\mathrm{e}}^2-10x{\mathrm{e}}^4+4x{\mathrm{e}}^6-2x{\mathrm{e}}^8-4x^2{\mathrm{e}}^2+5x^2{\mathrm{e}}^4-2x^2{\mathrm{e}}^6+x^2{\mathrm{e}}^8+4x^2+4}}{\mathrm{e}}^{-\frac{24x^3{\mathrm{e}}^2}{5{\mathrm{e}}^4-4{\mathrm{e}}^2-8x-2{\mathrm{e}}^6+{\mathrm{e}}^8+8x{\mathrm{e}}^2-10x{\mathrm{e}}^4+4x{\mathrm{e}}^6-2x{\mathrm{e}}^8-4x^2{\mathrm{e}}^2+5x^2{\mathrm{e}}^4-2x^2{\mathrm{e}}^6+x^2{\mathrm{e}}^8+4x^2+4}}{\mathrm{e}}^{\frac{24x^3{\mathrm{e}}^4}{5{\mathrm{e}}^4-4{\mathrm{e}}^2-8x-2{\mathrm{e}}^6+{\mathrm{e}}^8+8x{\mathrm{e}}^2-10x{\mathrm{e}}^4+4x{\mathrm{e}}^6-2x{\mathrm{e}}^8-4x^2{\mathrm{e}}^2+5x^2{\mathrm{e}}^4-2x^2{\mathrm{e}}^6+x^2{\mathrm{e}}^8+4x^2+4}}{\mathrm{e}}^{\frac{72x^2{\mathrm{e}}^8}{5{\mathrm{e}}^4-4{\mathrm{e}}^2-8x-2{\mathrm{e}}^6+{\mathrm{e}}^8+8x{\mathrm{e}}^2-10x{\mathrm{e}}^4+4x{\mathrm{e}}^6-2x{\mathrm{e}}^8-4x^2{\mathrm{e}}^2+5x^2{\mathrm{e}}^4-2x^2{\mathrm{e}}^6+x^2{\mathrm{e}}^8+4x^2+4}}{\mathrm{e}}^{-\frac{144x^2{\mathrm{e}}^6}{5{\mathrm{e}}^4-4{\mathrm{e}}^2-8x-2{\mathrm{e}}^6+{\mathrm{e}}^8+8x{\mathrm{e}}^2-10x{\mathrm{e}}^4+4x{\mathrm{e}}^6-2x{\mathrm{e}}^8-4x^2{\mathrm{e}}^2+5x^2{\mathrm{e}}^4-2x^2{\mathrm{e}}^6+x^2{\mathrm{e}}^8+4x^2+4}}{\mathrm{e}}^{-\frac{264x^2{\mathrm{e}}^2}{5{\mathrm{e}}^4-4{\mathrm{e}}^2-8x-2{\mathrm{e}}^6+{\mathrm{e}}^8+8x{\mathrm{e}}^2-10x{\mathrm{e}}^4+4x{\mathrm{e}}^6-2x{\mathrm{e}}^8-4x^2{\mathrm{e}}^2+5x^2{\mathrm{e}}^4-2x^2{\mathrm{e}}^6+x^2{\mathrm{e}}^8+4x^2+4}}{\mathrm{e}}^{\frac{336x^2{\mathrm{e}}^4}{5{\mathrm{e}}^4-4{\mathrm{e}}^2-8x-2{\mathrm{e}}^6+{\mathrm{e}}^8+8x{\mathrm{e}}^2-10x{\mathrm{e}}^4+4x{\mathrm{e}}^6-2x{\mathrm{e}}^8-4x^2{\mathrm{e}}^2+5x^2{\mathrm{e}}^4-2x^2{\mathrm{e}}^6+x^2{\mathrm{e}}^8+4x^2+4}}\end{array}$$

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 $$\begin{array}{c}{e}^{\frac{2(x^4+22x^3+121x^2+36x^2{e}^4+36x^2{e}^8+(-12x^3-132x^2)e^2+(12x^3-72x^2{e}^2+132x^2)e^4)}{4x^2-8x+(-4x^2+8x-4)e^2+(x^2-2x+1)e^4+(x^2-2x+1)e^8+(4x^2-8x+(-2x^2+4x-2)e^2+4)e^4+4}}\end{array}$$

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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