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3.25.68 \(\int \frac {16384 x^5+e^{\frac {256+e^{16}+768 x+864 x^2+176 x^3-495 x^4-432 x^5-12 x^6+144 x^7+54 x^8-16 x^9-12 x^{10}+x^{12}+e^{12} (16+12 x-4 x^3)+e^8 (96+144 x+54 x^2-48 x^3-36 x^4+6 x^6)+e^4 (256+576 x+432 x^2-84 x^3-288 x^4-108 x^5+48 x^6+36 x^7-4 x^9)}{65536 x^4}} (-256-e^{16}-576 x-432 x^2-44 x^3-108 x^5-6 x^6+108 x^7+54 x^8-20 x^9-18 x^{10}+2 x^{12}+e^{12} (-16-9 x+x^3)+e^8 (-96-108 x-27 x^2+12 x^3+3 x^6)+e^4 (-256-432 x-216 x^2+21 x^3-27 x^5+24 x^6+27 x^7-5 x^9))}{16384 x^5} \, dx\)

Optimal. Leaf size=33 \[ e^{\frac {\left (4+\frac {e^4}{x}+\frac {4-x}{x}-x^2\right )^4}{65536}}+x \]

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Rubi [A]  time = 8.90, antiderivative size = 26, normalized size of antiderivative = 0.79, number of steps used = 4, number of rules used = 3, integrand size = 296, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.010, Rules used = {12, 14, 6706} \begin {gather*} e^{\frac {\left (-x^3+3 x+e^4+4\right )^4}{65536 x^4}}+x \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(16384*x^5 + E^((256 + E^16 + 768*x + 864*x^2 + 176*x^3 - 495*x^4 - 432*x^5 - 12*x^6 + 144*x^7 + 54*x^8 -
16*x^9 - 12*x^10 + x^12 + E^12*(16 + 12*x - 4*x^3) + E^8*(96 + 144*x + 54*x^2 - 48*x^3 - 36*x^4 + 6*x^6) + E^4
*(256 + 576*x + 432*x^2 - 84*x^3 - 288*x^4 - 108*x^5 + 48*x^6 + 36*x^7 - 4*x^9))/(65536*x^4))*(-256 - E^16 - 5
76*x - 432*x^2 - 44*x^3 - 108*x^5 - 6*x^6 + 108*x^7 + 54*x^8 - 20*x^9 - 18*x^10 + 2*x^12 + E^12*(-16 - 9*x + x
^3) + E^8*(-96 - 108*x - 27*x^2 + 12*x^3 + 3*x^6) + E^4*(-256 - 432*x - 216*x^2 + 21*x^3 - 27*x^5 + 24*x^6 + 2
7*x^7 - 5*x^9)))/(16384*x^5),x]

[Out]

E^((4 + E^4 + 3*x - x^3)^4/(65536*x^4)) + 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 14

Int[(u_)*((c_.)*(x_))^(m_.), x_Symbol] :> Int[ExpandIntegrand[(c*x)^m*u, x], x] /; FreeQ[{c, m}, x] && SumQ[u]
 &&  !LinearQ[u, x] &&  !MatchQ[u, (a_) + (b_.)*(v_) /; FreeQ[{a, b}, x] && InverseFunctionQ[v]]

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} &=\frac {\int \frac {16384 x^5+\exp \left (\frac {256+e^{16}+768 x+864 x^2+176 x^3-495 x^4-432 x^5-12 x^6+144 x^7+54 x^8-16 x^9-12 x^{10}+x^{12}+e^{12} \left (16+12 x-4 x^3\right )+e^8 \left (96+144 x+54 x^2-48 x^3-36 x^4+6 x^6\right )+e^4 \left (256+576 x+432 x^2-84 x^3-288 x^4-108 x^5+48 x^6+36 x^7-4 x^9\right )}{65536 x^4}\right ) \left (-256-e^{16}-576 x-432 x^2-44 x^3-108 x^5-6 x^6+108 x^7+54 x^8-20 x^9-18 x^{10}+2 x^{12}+e^{12} \left (-16-9 x+x^3\right )+e^8 \left (-96-108 x-27 x^2+12 x^3+3 x^6\right )+e^4 \left (-256-432 x-216 x^2+21 x^3-27 x^5+24 x^6+27 x^7-5 x^9\right )\right )}{x^5} \, dx}{16384}\\ &=\frac {\int \left (16384+\frac {e^{\frac {\left (4+e^4+3 x-x^3\right )^4}{65536 x^4}} \left (-4-e^4-3 x+x^3\right )^3 \left (4+e^4+2 x^3\right )}{x^5}\right ) \, dx}{16384}\\ &=x+\frac {\int \frac {e^{\frac {\left (4+e^4+3 x-x^3\right )^4}{65536 x^4}} \left (-4-e^4-3 x+x^3\right )^3 \left (4+e^4+2 x^3\right )}{x^5} \, dx}{16384}\\ &=e^{\frac {\left (4+e^4+3 x-x^3\right )^4}{65536 x^4}}+x\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 2.11, size = 26, normalized size = 0.79 \begin {gather*} e^{\frac {\left (4+e^4+3 x-x^3\right )^4}{65536 x^4}}+x \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(16384*x^5 + E^((256 + E^16 + 768*x + 864*x^2 + 176*x^3 - 495*x^4 - 432*x^5 - 12*x^6 + 144*x^7 + 54*
x^8 - 16*x^9 - 12*x^10 + x^12 + E^12*(16 + 12*x - 4*x^3) + E^8*(96 + 144*x + 54*x^2 - 48*x^3 - 36*x^4 + 6*x^6)
 + E^4*(256 + 576*x + 432*x^2 - 84*x^3 - 288*x^4 - 108*x^5 + 48*x^6 + 36*x^7 - 4*x^9))/(65536*x^4))*(-256 - E^
16 - 576*x - 432*x^2 - 44*x^3 - 108*x^5 - 6*x^6 + 108*x^7 + 54*x^8 - 20*x^9 - 18*x^10 + 2*x^12 + E^12*(-16 - 9
*x + x^3) + E^8*(-96 - 108*x - 27*x^2 + 12*x^3 + 3*x^6) + E^4*(-256 - 432*x - 216*x^2 + 21*x^3 - 27*x^5 + 24*x
^6 + 27*x^7 - 5*x^9)))/(16384*x^5),x]

[Out]

E^((4 + E^4 + 3*x - x^3)^4/(65536*x^4)) + x

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fricas [B]  time = 0.71, size = 144, normalized size = 4.36 \begin {gather*} x + e^{\left (\frac {x^{12} - 12 \, x^{10} - 16 \, x^{9} + 54 \, x^{8} + 144 \, x^{7} - 12 \, x^{6} - 432 \, x^{5} - 495 \, x^{4} + 176 \, x^{3} + 864 \, x^{2} - 4 \, {\left (x^{3} - 3 \, x - 4\right )} e^{12} + 6 \, {\left (x^{6} - 6 \, x^{4} - 8 \, x^{3} + 9 \, x^{2} + 24 \, x + 16\right )} e^{8} - 4 \, {\left (x^{9} - 9 \, x^{7} - 12 \, x^{6} + 27 \, x^{5} + 72 \, x^{4} + 21 \, x^{3} - 108 \, x^{2} - 144 \, x - 64\right )} e^{4} + 768 \, x + e^{16} + 256}{65536 \, x^{4}}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/16384*((-exp(4)^4+(x^3-9*x-16)*exp(4)^3+(3*x^6+12*x^3-27*x^2-108*x-96)*exp(4)^2+(-5*x^9+27*x^7+24*
x^6-27*x^5+21*x^3-216*x^2-432*x-256)*exp(4)+2*x^12-18*x^10-20*x^9+54*x^8+108*x^7-6*x^6-108*x^5-44*x^3-432*x^2-
576*x-256)*exp(1/65536*(exp(4)^4+(-4*x^3+12*x+16)*exp(4)^3+(6*x^6-36*x^4-48*x^3+54*x^2+144*x+96)*exp(4)^2+(-4*
x^9+36*x^7+48*x^6-108*x^5-288*x^4-84*x^3+432*x^2+576*x+256)*exp(4)+x^12-12*x^10-16*x^9+54*x^8+144*x^7-12*x^6-4
32*x^5-495*x^4+176*x^3+864*x^2+768*x+256)/x^4)+16384*x^5)/x^5,x, algorithm="fricas")

[Out]

x + e^(1/65536*(x^12 - 12*x^10 - 16*x^9 + 54*x^8 + 144*x^7 - 12*x^6 - 432*x^5 - 495*x^4 + 176*x^3 + 864*x^2 -
4*(x^3 - 3*x - 4)*e^12 + 6*(x^6 - 6*x^4 - 8*x^3 + 9*x^2 + 24*x + 16)*e^8 - 4*(x^9 - 9*x^7 - 12*x^6 + 27*x^5 +
72*x^4 + 21*x^3 - 108*x^2 - 144*x - 64)*e^4 + 768*x + e^16 + 256)/x^4)

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giac [B]  time = 5.00, size = 180, normalized size = 5.45 \begin {gather*} {\left (x e^{4} + e^{\left (\frac {x^{12} - 12 \, x^{10} - 4 \, x^{9} e^{4} - 16 \, x^{9} + 54 \, x^{8} + 36 \, x^{7} e^{4} + 144 \, x^{7} + 6 \, x^{6} e^{8} + 48 \, x^{6} e^{4} - 12 \, x^{6} - 108 \, x^{5} e^{4} - 432 \, x^{5} - 36 \, x^{4} e^{8} - 288 \, x^{4} e^{4} + 261649 \, x^{4} - 4 \, x^{3} e^{12} - 48 \, x^{3} e^{8} - 84 \, x^{3} e^{4} + 176 \, x^{3} + 54 \, x^{2} e^{8} + 432 \, x^{2} e^{4} + 864 \, x^{2} + 12 \, x e^{12} + 144 \, x e^{8} + 576 \, x e^{4} + 768 \, x + e^{16} + 16 \, e^{12} + 96 \, e^{8} + 256 \, e^{4} + 256}{65536 \, x^{4}}\right )}\right )} e^{\left (-4\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/16384*((-exp(4)^4+(x^3-9*x-16)*exp(4)^3+(3*x^6+12*x^3-27*x^2-108*x-96)*exp(4)^2+(-5*x^9+27*x^7+24*
x^6-27*x^5+21*x^3-216*x^2-432*x-256)*exp(4)+2*x^12-18*x^10-20*x^9+54*x^8+108*x^7-6*x^6-108*x^5-44*x^3-432*x^2-
576*x-256)*exp(1/65536*(exp(4)^4+(-4*x^3+12*x+16)*exp(4)^3+(6*x^6-36*x^4-48*x^3+54*x^2+144*x+96)*exp(4)^2+(-4*
x^9+36*x^7+48*x^6-108*x^5-288*x^4-84*x^3+432*x^2+576*x+256)*exp(4)+x^12-12*x^10-16*x^9+54*x^8+144*x^7-12*x^6-4
32*x^5-495*x^4+176*x^3+864*x^2+768*x+256)/x^4)+16384*x^5)/x^5,x, algorithm="giac")

[Out]

(x*e^4 + e^(1/65536*(x^12 - 12*x^10 - 4*x^9*e^4 - 16*x^9 + 54*x^8 + 36*x^7*e^4 + 144*x^7 + 6*x^6*e^8 + 48*x^6*
e^4 - 12*x^6 - 108*x^5*e^4 - 432*x^5 - 36*x^4*e^8 - 288*x^4*e^4 + 261649*x^4 - 4*x^3*e^12 - 48*x^3*e^8 - 84*x^
3*e^4 + 176*x^3 + 54*x^2*e^8 + 432*x^2*e^4 + 864*x^2 + 12*x*e^12 + 144*x*e^8 + 576*x*e^4 + 768*x + e^16 + 16*e
^12 + 96*e^8 + 256*e^4 + 256)/x^4))*e^(-4)

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maple [F]  time = 180.00, size = 0, normalized size = 0.00 \[\int \frac {\left (-{\mathrm e}^{16}+\left (x^{3}-9 x -16\right ) {\mathrm e}^{12}+\left (3 x^{6}+12 x^{3}-27 x^{2}-108 x -96\right ) {\mathrm e}^{8}+\left (-5 x^{9}+27 x^{7}+24 x^{6}-27 x^{5}+21 x^{3}-216 x^{2}-432 x -256\right ) {\mathrm e}^{4}+2 x^{12}-18 x^{10}-20 x^{9}+54 x^{8}+108 x^{7}-6 x^{6}-108 x^{5}-44 x^{3}-432 x^{2}-576 x -256\right ) {\mathrm e}^{\frac {{\mathrm e}^{16}+\left (-4 x^{3}+12 x +16\right ) {\mathrm e}^{12}+\left (6 x^{6}-36 x^{4}-48 x^{3}+54 x^{2}+144 x +96\right ) {\mathrm e}^{8}+\left (-4 x^{9}+36 x^{7}+48 x^{6}-108 x^{5}-288 x^{4}-84 x^{3}+432 x^{2}+576 x +256\right ) {\mathrm e}^{4}+x^{12}-12 x^{10}-16 x^{9}+54 x^{8}+144 x^{7}-12 x^{6}-432 x^{5}-495 x^{4}+176 x^{3}+864 x^{2}+768 x +256}{65536 x^{4}}}+16384 x^{5}}{16384 x^{5}}\, dx\]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/16384*((-exp(4)^4+(x^3-9*x-16)*exp(4)^3+(3*x^6+12*x^3-27*x^2-108*x-96)*exp(4)^2+(-5*x^9+27*x^7+24*x^6-27
*x^5+21*x^3-216*x^2-432*x-256)*exp(4)+2*x^12-18*x^10-20*x^9+54*x^8+108*x^7-6*x^6-108*x^5-44*x^3-432*x^2-576*x-
256)*exp(1/65536*(exp(4)^4+(-4*x^3+12*x+16)*exp(4)^3+(6*x^6-36*x^4-48*x^3+54*x^2+144*x+96)*exp(4)^2+(-4*x^9+36
*x^7+48*x^6-108*x^5-288*x^4-84*x^3+432*x^2+576*x+256)*exp(4)+x^12-12*x^10-16*x^9+54*x^8+144*x^7-12*x^6-432*x^5
-495*x^4+176*x^3+864*x^2+768*x+256)/x^4)+16384*x^5)/x^5,x)

[Out]

int(1/16384*((-exp(4)^4+(x^3-9*x-16)*exp(4)^3+(3*x^6+12*x^3-27*x^2-108*x-96)*exp(4)^2+(-5*x^9+27*x^7+24*x^6-27
*x^5+21*x^3-216*x^2-432*x-256)*exp(4)+2*x^12-18*x^10-20*x^9+54*x^8+108*x^7-6*x^6-108*x^5-44*x^3-432*x^2-576*x-
256)*exp(1/65536*(exp(4)^4+(-4*x^3+12*x+16)*exp(4)^3+(6*x^6-36*x^4-48*x^3+54*x^2+144*x+96)*exp(4)^2+(-4*x^9+36
*x^7+48*x^6-108*x^5-288*x^4-84*x^3+432*x^2+576*x+256)*exp(4)+x^12-12*x^10-16*x^9+54*x^8+144*x^7-12*x^6-432*x^5
-495*x^4+176*x^3+864*x^2+768*x+256)/x^4)+16384*x^5)/x^5,x)

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maxima [B]  time = 2.45, size = 183, normalized size = 5.55 \begin {gather*} x + e^{\left (\frac {1}{65536} \, x^{8} - \frac {3}{16384} \, x^{6} - \frac {1}{16384} \, x^{5} e^{4} - \frac {1}{4096} \, x^{5} + \frac {27}{32768} \, x^{4} + \frac {9}{16384} \, x^{3} e^{4} + \frac {9}{4096} \, x^{3} + \frac {3}{32768} \, x^{2} e^{8} + \frac {3}{4096} \, x^{2} e^{4} - \frac {3}{16384} \, x^{2} - \frac {27}{16384} \, x e^{4} - \frac {27}{4096} \, x - \frac {e^{12}}{16384 \, x} - \frac {3 \, e^{8}}{4096 \, x} - \frac {21 \, e^{4}}{16384 \, x} + \frac {11}{4096 \, x} + \frac {27 \, e^{8}}{32768 \, x^{2}} + \frac {27 \, e^{4}}{4096 \, x^{2}} + \frac {27}{2048 \, x^{2}} + \frac {3 \, e^{12}}{16384 \, x^{3}} + \frac {9 \, e^{8}}{4096 \, x^{3}} + \frac {9 \, e^{4}}{1024 \, x^{3}} + \frac {3}{256 \, x^{3}} + \frac {e^{16}}{65536 \, x^{4}} + \frac {e^{12}}{4096 \, x^{4}} + \frac {3 \, e^{8}}{2048 \, x^{4}} + \frac {e^{4}}{256 \, x^{4}} + \frac {1}{256 \, x^{4}} - \frac {9}{16384} \, e^{8} - \frac {9}{2048} \, e^{4} - \frac {495}{65536}\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/16384*((-exp(4)^4+(x^3-9*x-16)*exp(4)^3+(3*x^6+12*x^3-27*x^2-108*x-96)*exp(4)^2+(-5*x^9+27*x^7+24*
x^6-27*x^5+21*x^3-216*x^2-432*x-256)*exp(4)+2*x^12-18*x^10-20*x^9+54*x^8+108*x^7-6*x^6-108*x^5-44*x^3-432*x^2-
576*x-256)*exp(1/65536*(exp(4)^4+(-4*x^3+12*x+16)*exp(4)^3+(6*x^6-36*x^4-48*x^3+54*x^2+144*x+96)*exp(4)^2+(-4*
x^9+36*x^7+48*x^6-108*x^5-288*x^4-84*x^3+432*x^2+576*x+256)*exp(4)+x^12-12*x^10-16*x^9+54*x^8+144*x^7-12*x^6-4
32*x^5-495*x^4+176*x^3+864*x^2+768*x+256)/x^4)+16384*x^5)/x^5,x, algorithm="maxima")

[Out]

x + e^(1/65536*x^8 - 3/16384*x^6 - 1/16384*x^5*e^4 - 1/4096*x^5 + 27/32768*x^4 + 9/16384*x^3*e^4 + 9/4096*x^3
+ 3/32768*x^2*e^8 + 3/4096*x^2*e^4 - 3/16384*x^2 - 27/16384*x*e^4 - 27/4096*x - 1/16384*e^12/x - 3/4096*e^8/x
- 21/16384*e^4/x + 11/4096/x + 27/32768*e^8/x^2 + 27/4096*e^4/x^2 + 27/2048/x^2 + 3/16384*e^12/x^3 + 9/4096*e^
8/x^3 + 9/1024*e^4/x^3 + 3/256/x^3 + 1/65536*e^16/x^4 + 1/4096*e^12/x^4 + 3/2048*e^8/x^4 + 1/256*e^4/x^4 + 1/2
56/x^4 - 9/16384*e^8 - 9/2048*e^4 - 495/65536)

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mupad [B]  time = 2.46, size = 230, normalized size = 6.97 \begin {gather*} x+\frac {{\left ({\mathrm {e}}^{\frac {{\mathrm {e}}^4}{x^2}}\right )}^{27/4096}\,{\left ({\mathrm {e}}^{x^2\,{\mathrm {e}}^4}\right )}^{3/4096}\,{\left ({\mathrm {e}}^{\frac {{\mathrm {e}}^4}{x^3}}\right )}^{9/1024}\,{\left ({\mathrm {e}}^{x^3\,{\mathrm {e}}^4}\right )}^{9/16384}\,{\left ({\mathrm {e}}^{\frac {{\mathrm {e}}^4}{x^4}}\right )}^{1/256}\,{\left ({\mathrm {e}}^{\frac {{\mathrm {e}}^8}{x^2}}\right )}^{27/32768}\,{\left ({\mathrm {e}}^{x^2\,{\mathrm {e}}^8}\right )}^{3/32768}\,{\left ({\mathrm {e}}^{\frac {{\mathrm {e}}^8}{x^3}}\right )}^{9/4096}\,{\left ({\mathrm {e}}^{\frac {{\mathrm {e}}^8}{x^4}}\right )}^{3/2048}\,{\left ({\mathrm {e}}^{\frac {{\mathrm {e}}^{12}}{x^3}}\right )}^{3/16384}\,{\left ({\mathrm {e}}^{\frac {{\mathrm {e}}^{12}}{x^4}}\right )}^{1/4096}\,{\left ({\mathrm {e}}^{\frac {{\mathrm {e}}^{16}}{x^4}}\right )}^{1/65536}\,{\left ({\mathrm {e}}^{1/x}\right )}^{11/4096}\,{\left ({\mathrm {e}}^{\frac {1}{x^2}}\right )}^{27/2048}\,{\left ({\mathrm {e}}^{\frac {1}{x^3}}\right )}^{3/256}\,{\left ({\mathrm {e}}^{x^3}\right )}^{9/4096}\,{\left ({\mathrm {e}}^{\frac {1}{x^4}}\right )}^{1/256}\,{\left ({\mathrm {e}}^{x^4}\right )}^{27/32768}\,{\left ({\mathrm {e}}^{x^8}\right )}^{1/65536}\,{\mathrm {e}}^{-\frac {495}{65536}}}{{\left ({\mathrm {e}}^{\frac {{\mathrm {e}}^4}{x}}\right )}^{21/16384}\,{\left ({\mathrm {e}}^{\frac {{\mathrm {e}}^8}{x}}\right )}^{3/4096}\,{\left ({\mathrm {e}}^{x^5\,{\mathrm {e}}^4}\right )}^{1/16384}\,{\left ({\mathrm {e}}^{\frac {{\mathrm {e}}^{12}}{x}}\right )}^{1/16384}\,{\left ({\mathrm {e}}^{x^2}\right )}^{3/16384}\,{\left ({\mathrm {e}}^{x^5}\right )}^{1/4096}\,{\left ({\mathrm {e}}^{x^6}\right )}^{3/16384}\,{\left ({\mathrm {e}}^{x\,{\mathrm {e}}^4}\right )}^{27/16384}\,{\left ({\mathrm {e}}^{{\mathrm {e}}^4}\right )}^{9/2048}\,{\left ({\mathrm {e}}^{{\mathrm {e}}^8}\right )}^{9/16384}\,{\left ({\mathrm {e}}^x\right )}^{27/4096}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-((exp(((3*x)/256 + exp(16)/65536 + (exp(12)*(12*x - 4*x^3 + 16))/65536 + (exp(4)*(576*x + 432*x^2 - 84*x^
3 - 288*x^4 - 108*x^5 + 48*x^6 + 36*x^7 - 4*x^9 + 256))/65536 + (exp(8)*(144*x + 54*x^2 - 48*x^3 - 36*x^4 + 6*
x^6 + 96))/65536 + (27*x^2)/2048 + (11*x^3)/4096 - (495*x^4)/65536 - (27*x^5)/4096 - (3*x^6)/16384 + (9*x^7)/4
096 + (27*x^8)/32768 - x^9/4096 - (3*x^10)/16384 + x^12/65536 + 1/256)/x^4)*(576*x + exp(16) + exp(12)*(9*x -
x^3 + 16) + exp(4)*(432*x + 216*x^2 - 21*x^3 + 27*x^5 - 24*x^6 - 27*x^7 + 5*x^9 + 256) + exp(8)*(108*x + 27*x^
2 - 12*x^3 - 3*x^6 + 96) + 432*x^2 + 44*x^3 + 108*x^5 + 6*x^6 - 108*x^7 - 54*x^8 + 20*x^9 + 18*x^10 - 2*x^12 +
 256))/16384 - x^5)/x^5,x)

[Out]

x + (exp(exp(4)/x^2)^(27/4096)*exp(x^2*exp(4))^(3/4096)*exp(exp(4)/x^3)^(9/1024)*exp(x^3*exp(4))^(9/16384)*exp
(exp(4)/x^4)^(1/256)*exp(exp(8)/x^2)^(27/32768)*exp(x^2*exp(8))^(3/32768)*exp(exp(8)/x^3)^(9/4096)*exp(exp(8)/
x^4)^(3/2048)*exp(exp(12)/x^3)^(3/16384)*exp(exp(12)/x^4)^(1/4096)*exp(exp(16)/x^4)^(1/65536)*exp(1/x)^(11/409
6)*exp(1/x^2)^(27/2048)*exp(1/x^3)^(3/256)*exp(x^3)^(9/4096)*exp(1/x^4)^(1/256)*exp(x^4)^(27/32768)*exp(x^8)^(
1/65536)*exp(-495/65536))/(exp(exp(4)/x)^(21/16384)*exp(exp(8)/x)^(3/4096)*exp(x^5*exp(4))^(1/16384)*exp(exp(1
2)/x)^(1/16384)*exp(x^2)^(3/16384)*exp(x^5)^(1/4096)*exp(x^6)^(3/16384)*exp(x*exp(4))^(27/16384)*exp(exp(4))^(
9/2048)*exp(exp(8))^(9/16384)*exp(x)^(27/4096))

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sympy [B]  time = 2.98, size = 175, normalized size = 5.30 \begin {gather*} x + e^{\frac {\frac {x^{12}}{65536} - \frac {3 x^{10}}{16384} - \frac {x^{9}}{4096} + \frac {27 x^{8}}{32768} + \frac {9 x^{7}}{4096} - \frac {3 x^{6}}{16384} - \frac {27 x^{5}}{4096} - \frac {495 x^{4}}{65536} + \frac {11 x^{3}}{4096} + \frac {27 x^{2}}{2048} + \frac {3 x}{256} + \frac {\left (- 4 x^{3} + 12 x + 16\right ) e^{12}}{65536} + \frac {\left (6 x^{6} - 36 x^{4} - 48 x^{3} + 54 x^{2} + 144 x + 96\right ) e^{8}}{65536} + \frac {\left (- 4 x^{9} + 36 x^{7} + 48 x^{6} - 108 x^{5} - 288 x^{4} - 84 x^{3} + 432 x^{2} + 576 x + 256\right ) e^{4}}{65536} + \frac {1}{256} + \frac {e^{16}}{65536}}{x^{4}}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/16384*((-exp(4)**4+(x**3-9*x-16)*exp(4)**3+(3*x**6+12*x**3-27*x**2-108*x-96)*exp(4)**2+(-5*x**9+27
*x**7+24*x**6-27*x**5+21*x**3-216*x**2-432*x-256)*exp(4)+2*x**12-18*x**10-20*x**9+54*x**8+108*x**7-6*x**6-108*
x**5-44*x**3-432*x**2-576*x-256)*exp(1/65536*(exp(4)**4+(-4*x**3+12*x+16)*exp(4)**3+(6*x**6-36*x**4-48*x**3+54
*x**2+144*x+96)*exp(4)**2+(-4*x**9+36*x**7+48*x**6-108*x**5-288*x**4-84*x**3+432*x**2+576*x+256)*exp(4)+x**12-
12*x**10-16*x**9+54*x**8+144*x**7-12*x**6-432*x**5-495*x**4+176*x**3+864*x**2+768*x+256)/x**4)+16384*x**5)/x**
5,x)

[Out]

x + exp((x**12/65536 - 3*x**10/16384 - x**9/4096 + 27*x**8/32768 + 9*x**7/4096 - 3*x**6/16384 - 27*x**5/4096 -
 495*x**4/65536 + 11*x**3/4096 + 27*x**2/2048 + 3*x/256 + (-4*x**3 + 12*x + 16)*exp(12)/65536 + (6*x**6 - 36*x
**4 - 48*x**3 + 54*x**2 + 144*x + 96)*exp(8)/65536 + (-4*x**9 + 36*x**7 + 48*x**6 - 108*x**5 - 288*x**4 - 84*x
**3 + 432*x**2 + 576*x + 256)*exp(4)/65536 + 1/256 + exp(16)/65536)/x**4)

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