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3.33.32 \(\int \frac {4 e^{\frac {4+4 e^3}{e^3}}+4 x^2+4 \log (4)}{e^{\frac {2 (4+4 e^3)}{e^3}}-2 x^3+x^4+(2 x-2 x^2) \log (4)+\log ^2(4)+e^{\frac {4+4 e^3}{e^3}} (2 x-2 x^2+2 \log (4))} \, dx\)

Optimal. Leaf size=27 \[ 2 \log \left (10+\frac {20 x}{e^{4+\frac {4}{e^3}}-x^2+\log (4)}\right ) \]

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Rubi [A]  time = 0.23, antiderivative size = 44, normalized size of antiderivative = 1.63, number of steps used = 4, number of rules used = 3, integrand size = 94, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.032, Rules used = {2074, 260, 628} \begin {gather*} 2 \log \left (-x^2+2 x+e^{4+\frac {4}{e^3}}+\log (4)\right )-2 \log \left (-x^2+e^{4+\frac {4}{e^3}}+\log (4)\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(4*E^((4 + 4*E^3)/E^3) + 4*x^2 + 4*Log[4])/(E^((2*(4 + 4*E^3))/E^3) - 2*x^3 + x^4 + (2*x - 2*x^2)*Log[4] +
 Log[4]^2 + E^((4 + 4*E^3)/E^3)*(2*x - 2*x^2 + 2*Log[4])),x]

[Out]

-2*Log[E^(4 + 4/E^3) - x^2 + Log[4]] + 2*Log[E^(4 + 4/E^3) + 2*x - x^2 + Log[4]]

Rule 260

Int[(x_)^(m_.)/((a_) + (b_.)*(x_)^(n_)), x_Symbol] :> Simp[Log[RemoveContent[a + b*x^n, x]]/(b*n), x] /; FreeQ
[{a, b, m, n}, x] && EqQ[m, n - 1]

Rule 628

Int[((d_) + (e_.)*(x_))/((a_.) + (b_.)*(x_) + (c_.)*(x_)^2), x_Symbol] :> Simp[(d*Log[RemoveContent[a + b*x +
c*x^2, x]])/b, x] /; FreeQ[{a, b, c, d, e}, x] && EqQ[2*c*d - b*e, 0]

Rule 2074

Int[(P_)^(p_)*(Q_)^(q_.), x_Symbol] :> With[{PP = Factor[P]}, Int[ExpandIntegrand[PP^p*Q^q, x], x] /;  !SumQ[N
onfreeFactors[PP, x]]] /; FreeQ[q, x] && PolyQ[P, x] && PolyQ[Q, x] && IntegerQ[p] && NeQ[P, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {4 x}{-e^{4+\frac {4}{e^3}}+x^2-\log (4)}+\frac {4 (-1+x)}{-e^{4+\frac {4}{e^3}}-2 x+x^2-\log (4)}\right ) \, dx\\ &=-\left (4 \int \frac {x}{-e^{4+\frac {4}{e^3}}+x^2-\log (4)} \, dx\right )+4 \int \frac {-1+x}{-e^{4+\frac {4}{e^3}}-2 x+x^2-\log (4)} \, dx\\ &=-2 \log \left (e^{4+\frac {4}{e^3}}-x^2+\log (4)\right )+2 \log \left (e^{4+\frac {4}{e^3}}+2 x-x^2+\log (4)\right )\\ \end {aligned} \end {gather*}

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Mathematica [C]  time = 0.15, size = 173, normalized size = 6.41 \begin {gather*} -4 \text {RootSum}\left [e^{8+\frac {8}{e^3}}+2 e^{4+\frac {4}{e^3}} \log (4)+\log ^2(4)+2 e^{4+\frac {4}{e^3}} \text {$\#$1}+\log (16) \text {$\#$1}-2 e^{4+\frac {4}{e^3}} \text {$\#$1}^2-2 \log (4) \text {$\#$1}^2-2 \text {$\#$1}^3+\text {$\#$1}^4\&,\frac {e^{4+\frac {4}{e^3}} \log (x-\text {$\#$1})+\log (4) \log (x-\text {$\#$1})+\log (x-\text {$\#$1}) \text {$\#$1}^2}{-2 e^{4+\frac {4}{e^3}}-\log (16)+4 e^{4+\frac {4}{e^3}} \text {$\#$1}+4 \log (4) \text {$\#$1}+6 \text {$\#$1}^2-4 \text {$\#$1}^3}\&\right ] \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(4*E^((4 + 4*E^3)/E^3) + 4*x^2 + 4*Log[4])/(E^((2*(4 + 4*E^3))/E^3) - 2*x^3 + x^4 + (2*x - 2*x^2)*Lo
g[4] + Log[4]^2 + E^((4 + 4*E^3)/E^3)*(2*x - 2*x^2 + 2*Log[4])),x]

[Out]

-4*RootSum[E^(8 + 8/E^3) + 2*E^(4 + 4/E^3)*Log[4] + Log[4]^2 + 2*E^(4 + 4/E^3)*#1 + Log[16]*#1 - 2*E^(4 + 4/E^
3)*#1^2 - 2*Log[4]*#1^2 - 2*#1^3 + #1^4 & , (E^(4 + 4/E^3)*Log[x - #1] + Log[4]*Log[x - #1] + Log[x - #1]*#1^2
)/(-2*E^(4 + 4/E^3) - Log[16] + 4*E^(4 + 4/E^3)*#1 + 4*Log[4]*#1 + 6*#1^2 - 4*#1^3) & ]

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fricas [A]  time = 0.87, size = 48, normalized size = 1.78 \begin {gather*} 2 \, \log \left (x^{2} - 2 \, x - e^{\left (4 \, {\left (e^{3} + 1\right )} e^{\left (-3\right )}\right )} - 2 \, \log \relax (2)\right ) - 2 \, \log \left (x^{2} - e^{\left (4 \, {\left (e^{3} + 1\right )} e^{\left (-3\right )}\right )} - 2 \, \log \relax (2)\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4*exp((4*exp(3)+4)/exp(3))+8*log(2)+4*x^2)/(exp((4*exp(3)+4)/exp(3))^2+(4*log(2)-2*x^2+2*x)*exp((4*
exp(3)+4)/exp(3))+4*log(2)^2+2*(-2*x^2+2*x)*log(2)+x^4-2*x^3),x, algorithm="fricas")

[Out]

2*log(x^2 - 2*x - e^(4*(e^3 + 1)*e^(-3)) - 2*log(2)) - 2*log(x^2 - e^(4*(e^3 + 1)*e^(-3)) - 2*log(2))

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giac [A]  time = 0.37, size = 25, normalized size = 0.93 \begin {gather*} -2.00000000000000 \, \log \left (x + 8.24717230730000\right ) + 2.00000000000000 \, \log \left (x + 7.30757793020000\right ) - 2.00000000000000 \, \log \left (x - 8.24717230730000\right ) + 2.00000000000000 \, \log \left (x - 9.30757793020000\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4*exp((4*exp(3)+4)/exp(3))+8*log(2)+4*x^2)/(exp((4*exp(3)+4)/exp(3))^2+(4*log(2)-2*x^2+2*x)*exp((4*
exp(3)+4)/exp(3))+4*log(2)^2+2*(-2*x^2+2*x)*log(2)+x^4-2*x^3),x, algorithm="giac")

[Out]

-2.00000000000000*log(x + 8.24717230730000) + 2.00000000000000*log(x + 7.30757793020000) - 2.00000000000000*lo
g(x - 8.24717230730000) + 2.00000000000000*log(x - 9.30757793020000)

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maple [A]  time = 0.21, size = 45, normalized size = 1.67

method result size
risch \(2 \ln \left ({\mathrm e}^{4 \,{\mathrm e}^{-3}+4}-x^{2}+2 \ln \relax (2)+2 x \right )-2 \ln \left ({\mathrm e}^{4 \,{\mathrm e}^{-3}+4}-x^{2}+2 \ln \relax (2)\right )\) \(45\)
norman \(-2 \ln \left (-x^{2}+{\mathrm e}^{\left (4 \,{\mathrm e}^{3}+4\right ) {\mathrm e}^{-3}}+2 \ln \relax (2)\right )+2 \ln \left (-x^{2}+{\mathrm e}^{\left (4 \,{\mathrm e}^{3}+4\right ) {\mathrm e}^{-3}}+2 \ln \relax (2)+2 x \right )\) \(55\)
default \(2 \left (\munderset {\textit {\_R} =\RootOf \left (\textit {\_Z}^{4}-2 \textit {\_Z}^{3}+\left (-4 \ln \relax (2)-2 \,{\mathrm e}^{4 \left ({\mathrm e}^{3}+1\right ) {\mathrm e}^{-3}}\right ) \textit {\_Z}^{2}+\left (4 \ln \relax (2)+2 \,{\mathrm e}^{4 \left ({\mathrm e}^{3}+1\right ) {\mathrm e}^{-3}}\right ) \textit {\_Z} +4 \ln \relax (2)^{2}+4 \ln \relax (2) {\mathrm e}^{4 \left ({\mathrm e}^{3}+1\right ) {\mathrm e}^{-3}}+{\mathrm e}^{8 \left ({\mathrm e}^{3}+1\right ) {\mathrm e}^{-3}}\right )}{\sum }\frac {\left (\textit {\_R}^{2}+2 \ln \relax (2)+{\mathrm e}^{4 \left ({\mathrm e}^{3}+1\right ) {\mathrm e}^{-3}}\right ) \ln \left (x -\textit {\_R} \right )}{2 \textit {\_R}^{3}-4 \textit {\_R} \ln \relax (2)-2 \,{\mathrm e}^{4 \left ({\mathrm e}^{3}+1\right ) {\mathrm e}^{-3}} \textit {\_R} -3 \textit {\_R}^{2}+2 \ln \relax (2)+{\mathrm e}^{4 \left ({\mathrm e}^{3}+1\right ) {\mathrm e}^{-3}}}\right )\) \(149\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((4*exp((4*exp(3)+4)/exp(3))+8*ln(2)+4*x^2)/(exp((4*exp(3)+4)/exp(3))^2+(4*ln(2)-2*x^2+2*x)*exp((4*exp(3)+4
)/exp(3))+4*ln(2)^2+2*(-2*x^2+2*x)*ln(2)+x^4-2*x^3),x,method=_RETURNVERBOSE)

[Out]

2*ln(exp(4*exp(-3)+4)-x^2+2*ln(2)+2*x)-2*ln(exp(4*exp(-3)+4)-x^2+2*ln(2))

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maxima [A]  time = 0.40, size = 48, normalized size = 1.78 \begin {gather*} 2 \, \log \left (x^{2} - 2 \, x - e^{\left (4 \, {\left (e^{3} + 1\right )} e^{\left (-3\right )}\right )} - 2 \, \log \relax (2)\right ) - 2 \, \log \left (x^{2} - e^{\left (4 \, {\left (e^{3} + 1\right )} e^{\left (-3\right )}\right )} - 2 \, \log \relax (2)\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4*exp((4*exp(3)+4)/exp(3))+8*log(2)+4*x^2)/(exp((4*exp(3)+4)/exp(3))^2+(4*log(2)-2*x^2+2*x)*exp((4*
exp(3)+4)/exp(3))+4*log(2)^2+2*(-2*x^2+2*x)*log(2)+x^4-2*x^3),x, algorithm="maxima")

[Out]

2*log(x^2 - 2*x - e^(4*(e^3 + 1)*e^(-3)) - 2*log(2)) - 2*log(x^2 - e^(4*(e^3 + 1)*e^(-3)) - 2*log(2))

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mupad [B]  time = 7.49, size = 11837, normalized size = 438.41 result too large to display

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((4*exp(exp(-3)*(4*exp(3) + 4)) + 8*log(2) + 4*x^2)/(exp(2*exp(-3)*(4*exp(3) + 4)) + 2*log(2)*(2*x - 2*x^2)
 + 4*log(2)^2 - 2*x^3 + x^4 + exp(exp(-3)*(4*exp(3) + 4))*(2*x + 4*log(2) - 2*x^2)),x)

[Out]

symsum(log(- 256*exp(8*exp(-3) + 8) - 16*log(16)*log(256) - 256*exp(4*exp(-3) + 4)*log(2) - 64*exp(4*exp(-3) +
 4)*log(16) - 64*exp(4*exp(-3) + 4)*log(256) - x*(64*log(16) + 32*log(256) + 256*exp(4*exp(-3) + 4)) - 256*log
(2)^2 - 4*log(256)^2 - root(4096*z^4*exp(4*exp(-3)*(exp(3) + 1))*log(2)^3*log(16)^2 + 1536*z^4*exp(8*exp(-3)*(
exp(3) + 1))*log(2)^2*log(16)^2 - 768*z^4*exp(4*exp(-3)*(exp(3) + 1))*log(2)^2*log(16)^2 - 512*z^4*exp(4*exp(-
3)*(exp(3) + 1))*log(2)^2*log(16)^3 + 16384*z^4*exp(8*exp(-3)*(exp(3) + 1))*log(2)^3*log(16) + 10240*z^4*exp(1
2*exp(-3)*(exp(3) + 1))*log(2)^2*log(16) + 8192*z^4*exp(4*exp(-3)*(exp(3) + 1))*log(2)^4*log(16) + 6144*z^4*ex
p(4*exp(-3)*(exp(3) + 1))*log(2)^3*log(16) + 3072*z^4*exp(8*exp(-3)*(exp(3) + 1))*log(2)^2*log(16) - 1920*z^4*
exp(4*exp(-3)*(exp(3) + 1))*log(2)^2*log(16) - 768*z^4*exp(8*exp(-3)*(exp(3) + 1))*log(2)*log(16)^2 - 512*z^4*
exp(12*exp(-3)*(exp(3) + 1))*log(2)*log(16)^2 - 512*z^4*exp(8*exp(-3)*(exp(3) + 1))*log(2)*log(16)^3 - 480*z^4
*exp(4*exp(-3)*(exp(3) + 1))*log(2)*log(16)^2 - 128*z^4*exp(4*exp(-3)*(exp(3) + 1))*log(2)*log(16)^3 - 64*z^4*
exp(4*exp(-3)*(exp(3) + 1))*log(2)*log(16)^4 + 2048*z^4*exp(16*exp(-3)*(exp(3) + 1))*log(2)*log(16) - 1920*z^4
*exp(8*exp(-3)*(exp(3) + 1))*log(2)*log(16) - 53248*z^4*exp(8*exp(-3)*(exp(3) + 1))*log(2)^4 - 49152*z^4*exp(4
*exp(-3)*(exp(3) + 1))*log(2)^5 - 24576*z^4*exp(12*exp(-3)*(exp(3) + 1))*log(2)^3 + 13824*z^4*exp(4*exp(-3)*(e
xp(3) + 1))*log(2)^3 + 12288*z^4*exp(8*exp(-3)*(exp(3) + 1))*log(2)^3 + 8448*z^4*exp(8*exp(-3)*(exp(3) + 1))*l
og(2)^2 + 8192*z^4*exp(12*exp(-3)*(exp(3) + 1))*log(2)^2 + 6144*z^4*exp(4*exp(-3)*(exp(3) + 1))*log(2)^4 - 409
6*z^4*exp(16*exp(-3)*(exp(3) + 1))*log(2)^2 - 512*z^4*exp(12*exp(-3)*(exp(3) + 1))*log(16)^2 - 432*z^4*exp(8*e
xp(-3)*(exp(3) + 1))*log(16)^2 - 256*z^4*exp(16*exp(-3)*(exp(3) + 1))*log(16)^2 - 192*z^4*exp(8*exp(-3)*(exp(3
) + 1))*log(16)^3 - 192*z^4*exp(4*exp(-3)*(exp(3) + 1))*log(16)^2 - 128*z^4*exp(12*exp(-3)*(exp(3) + 1))*log(1
6)^3 - 104*z^4*exp(4*exp(-3)*(exp(3) + 1))*log(16)^3 - 40*z^4*exp(4*exp(-3)*(exp(3) + 1))*log(16)^4 - 16*z^4*e
xp(8*exp(-3)*(exp(3) + 1))*log(16)^4 + 2048*z^4*log(2)^4*log(16)^2 - 480*z^4*log(2)^2*log(16)^2 - 128*z^4*log(
2)^2*log(16)^3 - 64*z^4*log(2)^2*log(16)^4 + 2048*z^4*exp(16*exp(-3)*(exp(3) + 1))*log(2) + 1536*z^4*exp(12*ex
p(-3)*(exp(3) + 1))*log(2) - 896*z^4*exp(12*exp(-3)*(exp(3) + 1))*log(16) - 512*z^4*exp(16*exp(-3)*(exp(3) + 1
))*log(16) - 384*z^4*exp(8*exp(-3)*(exp(3) + 1))*log(16) + 3072*z^4*log(2)^4*log(16) - 256*z^4*exp(16*exp(-3)*
(exp(3) + 1)) - 256*z^4*exp(12*exp(-3)*(exp(3) + 1)) - 16384*z^4*log(2)^6 + 6912*z^4*log(2)^4 - 32*z^4*log(16)
^3 - 13*z^4*log(16)^4 - 4*z^4*log(16)^5 + 512*z^2*exp(4*exp(-3)*(exp(3) + 1))*log(2)^2*log(16)*log(256) + 256*
z^2*exp(4*exp(-3)*(exp(3) + 1))*log(2)*log(16)^2*log(256) - 64*z^2*exp(4*exp(-3)*(exp(3) + 1))*log(2)*log(16)*
log(256)^2 + 512*z^2*exp(8*exp(-3)*(exp(3) + 1))*log(2)*log(16)*log(256) + 128*z^2*exp(4*exp(-3)*(exp(3) + 1))
*log(2)*log(16)*log(256) + 128*z^2*log(2)^2*log(16)*log(256) + 2560*z^2*exp(4*exp(-3)*(exp(3) + 1))*log(2)^2*l
og(16)^2 - 128*z^2*exp(4*exp(-3)*(exp(3) + 1))*log(2)^2*log(256)^2 + 24*z^2*exp(4*exp(-3)*(exp(3) + 1))*log(16
)^2*log(256)^2 - 8192*z^2*exp(4*exp(-3)*(exp(3) + 1))*log(2)^3*log(256) - 8192*z^2*exp(4*exp(-3)*(exp(3) + 1))
*log(2)^3*log(16) - 6144*z^2*exp(8*exp(-3)*(exp(3) + 1))*log(2)^2*log(256) + 6144*z^2*exp(4*exp(-3)*(exp(3) +
1))*log(2)^2*log(16) + 2560*z^2*exp(8*exp(-3)*(exp(3) + 1))*log(2)*log(16)^2 + 1408*z^2*exp(4*exp(-3)*(exp(3)
+ 1))*log(2)*log(16)^2 - 512*z^2*exp(4*exp(-3)*(exp(3) + 1))*log(2)^2*log(256) + 256*z^2*exp(8*exp(-3)*(exp(3)
 + 1))*log(16)^2*log(256) + 256*z^2*exp(4*exp(-3)*(exp(3) + 1))*log(16)^2*log(256) - 128*z^2*exp(8*exp(-3)*(ex
p(3) + 1))*log(2)*log(256)^2 - 96*z^2*exp(4*exp(-3)*(exp(3) + 1))*log(2)*log(256)^2 + 56*z^2*exp(4*exp(-3)*(ex
p(3) + 1))*log(16)*log(256)^2 + 32*z^2*exp(8*exp(-3)*(exp(3) + 1))*log(16)*log(256)^2 + 32*z^2*exp(4*exp(-3)*(
exp(3) + 1))*log(16)^3*log(256) + 256*z^2*exp(4*exp(-3)*(exp(3) + 1))*log(2)*log(16)^3 + 256*z^2*log(2)^2*log(
16)^2*log(256) - 64*z^2*log(2)^2*log(16)*log(256)^2 + 6144*z^2*exp(8*exp(-3)*(exp(3) + 1))*log(2)*log(16) + 40
96*z^2*exp(12*exp(-3)*(exp(3) + 1))*log(2)*log(16) - 2048*z^2*exp(12*exp(-3)*(exp(3) + 1))*log(2)*log(256) + 7
68*z^2*exp(8*exp(-3)*(exp(3) + 1))*log(16)*log(256) + 512*z^2*exp(12*exp(-3)*(exp(3) + 1))*log(16)*log(256) -
512*z^2*exp(8*exp(-3)*(exp(3) + 1))*log(2)*log(256) + 320*z^2*exp(4*exp(-3)*(exp(3) + 1))*log(16)*log(256) - 4
9152*z^2*exp(8*exp(-3)*(exp(3) + 1))*log(2)^3 - 36864*z^2*exp(4*exp(-3)*(exp(3) + 1))*log(2)^3 - 32768*z^2*exp
(12*exp(-3)*(exp(3) + 1))*log(2)^2 - 24576*z^2*exp(4*exp(-3)*(exp(3) + 1))*log(2)^4 - 22528*z^2*exp(8*exp(-3)*
(exp(3) + 1))*log(2)^2 + 1536*z^2*exp(8*exp(-3)*(exp(3) + 1))*log(16)^2 + 1024*z^2*exp(12*exp(-3)*(exp(3) + 1)
)*log(16)^2 + 704*z^2*exp(4*exp(-3)*(exp(3) + 1))*log(16)^2 + 48*z^2*exp(4*exp(-3)*(exp(3) + 1))*log(256)^2 +
32*z^2*exp(8*exp(-3)*(exp(3) + 1))*log(256)^2 + 224*z^2*exp(4*exp(-3)*(exp(3) + 1))*log(16)^3 + 128*z^2*exp(8*
exp(-3)*(exp(3) + 1))*log(16)^3 + 1408*z^2*log(2)^2*log(16)^2 - 96*z^2*log(2)^2*log(256)^2 + 14*z^2*log(16)^2*
log(256)^2 + 4*z^2*log(16)^3*log(256)^2 + 256*z^2*log(2)^2*log(16)^3 - 8192*z^2*exp(16*exp(-3)*(exp(3) + 1))*l
og(2) + 4096*z^2*exp(12*exp(-3)*(exp(3) + 1))*log(16) - 4096*z^2*exp(12*exp(-3)*(exp(3) + 1))*log(2) + 2048*z^
2*exp(16*exp(-3)*(exp(3) + 1))*log(16) + 2048*z^2*exp(8*exp(-3)*(exp(3) + 1))*log(16) + 512*z^2*exp(12*exp(-3)
*(exp(3) + 1))*log(256) + 512*z^2*exp(8*exp(-3)*(exp(3) + 1))*log(256) - 4096*z^2*log(2)^4*log(256) - 4096*z^2
*log(2)^4*log(16) + 32*z^2*log(16)^2*log(256) + 24*z^2*log(16)^3*log(256) + 24*z^2*log(16)*log(256)^2 + 2048*z
^2*exp(16*exp(-3)*(exp(3) + 1)) + 2048*z^2*exp(12*exp(-3)*(exp(3) + 1)) - 18432*z^2*log(2)^4 + 96*z^2*log(16)^
3 + 16*z^2*log(16)^4 + 4096*z*exp(8*exp(-3)*(exp(3) + 1))*log(2)*log(16) + 2048*z*exp(8*exp(-3)*(exp(3) + 1))*
log(2)*log(256) - 512*z*exp(8*exp(-3)*(exp(3) + 1))*log(16)*log(256) - 256*z*exp(4*exp(-3)*(exp(3) + 1))*log(1
6)*log(256) + 4096*z*exp(4*exp(-3)*(exp(3) + 1))*log(2)^2*log(16) + 2048*z*exp(4*exp(-3)*(exp(3) + 1))*log(2)^
2*log(256) + 1024*z*exp(4*exp(-3)*(exp(3) + 1))*log(2)*log(16)^2 + 256*z*exp(4*exp(-3)*(exp(3) + 1))*log(2)*lo
g(256)^2 - 128*z*exp(4*exp(-3)*(exp(3) + 1))*log(16)^2*log(256) - 64*z*exp(4*exp(-3)*(exp(3) + 1))*log(16)*log
(256)^2 - 32768*z*exp(4*exp(-3)*(exp(3) + 1))*log(2)^3 - 16384*z*exp(8*exp(-3)*(exp(3) + 1))*log(2)^2 + 64*z*e
xp(4*exp(-3)*(exp(3) + 1))*log(256)^2 + 256*z*exp(4*exp(-3)*(exp(3) + 1))*log(16)^2 + 1024*z*log(2)^2*log(16)^
2 + 256*z*log(2)^2*log(256)^2 - 16*z*log(16)^2*log(256)^2 - 32*z*log(16)^2*log(256) - 16*z*log(16)*log(256)^2
- 16384*z*log(2)^4 + 8*z*log(256)^3 + 64*z*log(16)^3 - 512*exp(4*exp(-3)*(exp(3) + 1))*log(2)*log(16)*log(256)
 - 2048*exp(4*exp(-3)*(exp(3) + 1))*log(2)^2*log(256) - 2048*exp(4*exp(-3)*(exp(3) + 1))*log(2)^2*log(16) - 16
0*exp(4*exp(-3)*(exp(3) + 1))*log(16)*log(256)^2 - 128*exp(4*exp(-3)*(exp(3) + 1))*log(16)^2*log(256) - 128*ex
p(4*exp(-3)*(exp(3) + 1))*log(2)*log(256)^2 - 2048*exp(8*exp(-3)*(exp(3) + 1))*log(2)*log(256) - 2048*exp(8*ex
p(-3)*(exp(3) + 1))*log(2)*log(16) - 1024*exp(8*exp(-3)*(exp(3) + 1))*log(16)*log(256) - 768*exp(4*exp(-3)*(ex
p(3) + 1))*log(16)*log(256) - 512*log(2)^2*log(16)*log(256) - 128*log(2)^2*log(256)^2 - 16*log(16)^2*log(256)^
2 - 8192*exp(12*exp(-3)*(exp(3) + 1))*log(2) - 2048*exp(12*exp(-3)*(exp(3) + 1))*log(256) - 2048*exp(8*exp(-3)
*(exp(3) + 1))*log(256) - 2048*exp(12*exp(-3)*(exp(3) + 1))*log(16) - 2048*exp(8*exp(-3)*(exp(3) + 1))*log(16)
 - 64*log(16)^2*log(256) - 64*log(16)*log(256)^2 - 8*log(16)*log(256)^3 - 12288*exp(8*exp(-3)*(exp(3) + 1))*lo
g(2)^2 - 8192*exp(4*exp(-3)*(exp(3) + 1))*log(2)^3 - 384*exp(8*exp(-3)*(exp(3) + 1))*log(256)^2 - 320*exp(4*ex
p(-3)*(exp(3) + 1))*log(256)^2 - 32*exp(4*exp(-3)*(exp(3) + 1))*log(256)^3 - 256*exp(8*exp(-3)*(exp(3) + 1))*l
og(16)^2 - 256*exp(4*exp(-3)*(exp(3) + 1))*log(16)^2 - log(256)^4 - 4096*exp(16*exp(-3)*(exp(3) + 1)) - 4096*e
xp(12*exp(-3)*(exp(3) + 1)) - 4096*log(2)^4 - 16*log(256)^3, z, k)*(128*exp(8*exp(-3) + 8) - root(4096*z^4*exp
(4*exp(-3)*(exp(3) + 1))*log(2)^3*log(16)^2 + 1536*z^4*exp(8*exp(-3)*(exp(3) + 1))*log(2)^2*log(16)^2 - 768*z^
4*exp(4*exp(-3)*(exp(3) + 1))*log(2)^2*log(16)^2 - 512*z^4*exp(4*exp(-3)*(exp(3) + 1))*log(2)^2*log(16)^3 + 16
384*z^4*exp(8*exp(-3)*(exp(3) + 1))*log(2)^3*log(16) + 10240*z^4*exp(12*exp(-3)*(exp(3) + 1))*log(2)^2*log(16)
 + 8192*z^4*exp(4*exp(-3)*(exp(3) + 1))*log(2)^4*log(16) + 6144*z^4*exp(4*exp(-3)*(exp(3) + 1))*log(2)^3*log(1
6) + 3072*z^4*exp(8*exp(-3)*(exp(3) + 1))*log(2)^2*log(16) - 1920*z^4*exp(4*exp(-3)*(exp(3) + 1))*log(2)^2*log
(16) - 768*z^4*exp(8*exp(-3)*(exp(3) + 1))*log(2)*log(16)^2 - 512*z^4*exp(12*exp(-3)*(exp(3) + 1))*log(2)*log(
16)^2 - 512*z^4*exp(8*exp(-3)*(exp(3) + 1))*log(2)*log(16)^3 - 480*z^4*exp(4*exp(-3)*(exp(3) + 1))*log(2)*log(
16)^2 - 128*z^4*exp(4*exp(-3)*(exp(3) + 1))*log(2)*log(16)^3 - 64*z^4*exp(4*exp(-3)*(exp(3) + 1))*log(2)*log(1
6)^4 + 2048*z^4*exp(16*exp(-3)*(exp(3) + 1))*log(2)*log(16) - 1920*z^4*exp(8*exp(-3)*(exp(3) + 1))*log(2)*log(
16) - 53248*z^4*exp(8*exp(-3)*(exp(3) + 1))*log(2)^4 - 49152*z^4*exp(4*exp(-3)*(exp(3) + 1))*log(2)^5 - 24576*
z^4*exp(12*exp(-3)*(exp(3) + 1))*log(2)^3 + 13824*z^4*exp(4*exp(-3)*(exp(3) + 1))*log(2)^3 + 12288*z^4*exp(8*e
xp(-3)*(exp(3) + 1))*log(2)^3 + 8448*z^4*exp(8*exp(-3)*(exp(3) + 1))*log(2)^2 + 8192*z^4*exp(12*exp(-3)*(exp(3
) + 1))*log(2)^2 + 6144*z^4*exp(4*exp(-3)*(exp(3) + 1))*log(2)^4 - 4096*z^4*exp(16*exp(-3)*(exp(3) + 1))*log(2
)^2 - 512*z^4*exp(12*exp(-3)*(exp(3) + 1))*log(16)^2 - 432*z^4*exp(8*exp(-3)*(exp(3) + 1))*log(16)^2 - 256*z^4
*exp(16*exp(-3)*(exp(3) + 1))*log(16)^2 - 192*z^4*exp(8*exp(-3)*(exp(3) + 1))*log(16)^3 - 192*z^4*exp(4*exp(-3
)*(exp(3) + 1))*log(16)^2 - 128*z^4*exp(12*exp(-3)*(exp(3) + 1))*log(16)^3 - 104*z^4*exp(4*exp(-3)*(exp(3) + 1
))*log(16)^3 - 40*z^4*exp(4*exp(-3)*(exp(3) + 1))*log(16)^4 - 16*z^4*exp(8*exp(-3)*(exp(3) + 1))*log(16)^4 + 2
048*z^4*log(2)^4*log(16)^2 - 480*z^4*log(2)^2*log(16)^2 - 128*z^4*log(2)^2*log(16)^3 - 64*z^4*log(2)^2*log(16)
^4 + 2048*z^4*exp(16*exp(-3)*(exp(3) + 1))*log(2) + 1536*z^4*exp(12*exp(-3)*(exp(3) + 1))*log(2) - 896*z^4*exp
(12*exp(-3)*(exp(3) + 1))*log(16) - 512*z^4*exp(16*exp(-3)*(exp(3) + 1))*log(16) - 384*z^4*exp(8*exp(-3)*(exp(
3) + 1))*log(16) + 3072*z^4*log(2)^4*log(16) - 256*z^4*exp(16*exp(-3)*(exp(3) + 1)) - 256*z^4*exp(12*exp(-3)*(
exp(3) + 1)) - 16384*z^4*log(2)^6 + 6912*z^4*log(2)^4 - 32*z^4*log(16)^3 - 13*z^4*log(16)^4 - 4*z^4*log(16)^5
+ 512*z^2*exp(4*exp(-3)*(exp(3) + 1))*log(2)^2*log(16)*log(256) + 256*z^2*exp(4*exp(-3)*(exp(3) + 1))*log(2)*l
og(16)^2*log(256) - 64*z^2*exp(4*exp(-3)*(exp(3) + 1))*log(2)*log(16)*log(256)^2 + 512*z^2*exp(8*exp(-3)*(exp(
3) + 1))*log(2)*log(16)*log(256) + 128*z^2*exp(4*exp(-3)*(exp(3) + 1))*log(2)*log(16)*log(256) + 128*z^2*log(2
)^2*log(16)*log(256) + 2560*z^2*exp(4*exp(-3)*(exp(3) + 1))*log(2)^2*log(16)^2 - 128*z^2*exp(4*exp(-3)*(exp(3)
 + 1))*log(2)^2*log(256)^2 + 24*z^2*exp(4*exp(-3)*(exp(3) + 1))*log(16)^2*log(256)^2 - 8192*z^2*exp(4*exp(-3)*
(exp(3) + 1))*log(2)^3*log(256) - 8192*z^2*exp(4*exp(-3)*(exp(3) + 1))*log(2)^3*log(16) - 6144*z^2*exp(8*exp(-
3)*(exp(3) + 1))*log(2)^2*log(256) + 6144*z^2*exp(4*exp(-3)*(exp(3) + 1))*log(2)^2*log(16) + 2560*z^2*exp(8*ex
p(-3)*(exp(3) + 1))*log(2)*log(16)^2 + 1408*z^2*exp(4*exp(-3)*(exp(3) + 1))*log(2)*log(16)^2 - 512*z^2*exp(4*e
xp(-3)*(exp(3) + 1))*log(2)^2*log(256) + 256*z^2*exp(8*exp(-3)*(exp(3) + 1))*log(16)^2*log(256) + 256*z^2*exp(
4*exp(-3)*(exp(3) + 1))*log(16)^2*log(256) - 128*z^2*exp(8*exp(-3)*(exp(3) + 1))*log(2)*log(256)^2 - 96*z^2*ex
p(4*exp(-3)*(exp(3) + 1))*log(2)*log(256)^2 + 56*z^2*exp(4*exp(-3)*(exp(3) + 1))*log(16)*log(256)^2 + 32*z^2*e
xp(8*exp(-3)*(exp(3) + 1))*log(16)*log(256)^2 + 32*z^2*exp(4*exp(-3)*(exp(3) + 1))*log(16)^3*log(256) + 256*z^
2*exp(4*exp(-3)*(exp(3) + 1))*log(2)*log(16)^3 + 256*z^2*log(2)^2*log(16)^2*log(256) - 64*z^2*log(2)^2*log(16)
*log(256)^2 + 6144*z^2*exp(8*exp(-3)*(exp(3) + 1))*log(2)*log(16) + 4096*z^2*exp(12*exp(-3)*(exp(3) + 1))*log(
2)*log(16) - 2048*z^2*exp(12*exp(-3)*(exp(3) + 1))*log(2)*log(256) + 768*z^2*exp(8*exp(-3)*(exp(3) + 1))*log(1
6)*log(256) + 512*z^2*exp(12*exp(-3)*(exp(3) + 1))*log(16)*log(256) - 512*z^2*exp(8*exp(-3)*(exp(3) + 1))*log(
2)*log(256) + 320*z^2*exp(4*exp(-3)*(exp(3) + 1))*log(16)*log(256) - 49152*z^2*exp(8*exp(-3)*(exp(3) + 1))*log
(2)^3 - 36864*z^2*exp(4*exp(-3)*(exp(3) + 1))*log(2)^3 - 32768*z^2*exp(12*exp(-3)*(exp(3) + 1))*log(2)^2 - 245
76*z^2*exp(4*exp(-3)*(exp(3) + 1))*log(2)^4 - 22528*z^2*exp(8*exp(-3)*(exp(3) + 1))*log(2)^2 + 1536*z^2*exp(8*
exp(-3)*(exp(3) + 1))*log(16)^2 + 1024*z^2*exp(12*exp(-3)*(exp(3) + 1))*log(16)^2 + 704*z^2*exp(4*exp(-3)*(exp
(3) + 1))*log(16)^2 + 48*z^2*exp(4*exp(-3)*(exp(3) + 1))*log(256)^2 + 32*z^2*exp(8*exp(-3)*(exp(3) + 1))*log(2
56)^2 + 224*z^2*exp(4*exp(-3)*(exp(3) + 1))*log(16)^3 + 128*z^2*exp(8*exp(-3)*(exp(3) + 1))*log(16)^3 + 1408*z
^2*log(2)^2*log(16)^2 - 96*z^2*log(2)^2*log(256)^2 + 14*z^2*log(16)^2*log(256)^2 + 4*z^2*log(16)^3*log(256)^2
+ 256*z^2*log(2)^2*log(16)^3 - 8192*z^2*exp(16*exp(-3)*(exp(3) + 1))*log(2) + 4096*z^2*exp(12*exp(-3)*(exp(3)
+ 1))*log(16) - 4096*z^2*exp(12*exp(-3)*(exp(3) + 1))*log(2) + 2048*z^2*exp(16*exp(-3)*(exp(3) + 1))*log(16) +
 2048*z^2*exp(8*exp(-3)*(exp(3) + 1))*log(16) + 512*z^2*exp(12*exp(-3)*(exp(3) + 1))*log(256) + 512*z^2*exp(8*
exp(-3)*(exp(3) + 1))*log(256) - 4096*z^2*log(2)^4*log(256) - 4096*z^2*log(2)^4*log(16) + 32*z^2*log(16)^2*log
(256) + 24*z^2*log(16)^3*log(256) + 24*z^2*log(16)*log(256)^2 + 2048*z^2*exp(16*exp(-3)*(exp(3) + 1)) + 2048*z
^2*exp(12*exp(-3)*(exp(3) + 1)) - 18432*z^2*log(2)^4 + 96*z^2*log(16)^3 + 16*z^2*log(16)^4 + 4096*z*exp(8*exp(
-3)*(exp(3) + 1))*log(2)*log(16) + 2048*z*exp(8*exp(-3)*(exp(3) + 1))*log(2)*log(256) - 512*z*exp(8*exp(-3)*(e
xp(3) + 1))*log(16)*log(256) - 256*z*exp(4*exp(-3)*(exp(3) + 1))*log(16)*log(256) + 4096*z*exp(4*exp(-3)*(exp(
3) + 1))*log(2)^2*log(16) + 2048*z*exp(4*exp(-3)*(exp(3) + 1))*log(2)^2*log(256) + 1024*z*exp(4*exp(-3)*(exp(3
) + 1))*log(2)*log(16)^2 + 256*z*exp(4*exp(-3)*(exp(3) + 1))*log(2)*log(256)^2 - 128*z*exp(4*exp(-3)*(exp(3) +
 1))*log(16)^2*log(256) - 64*z*exp(4*exp(-3)*(exp(3) + 1))*log(16)*log(256)^2 - 32768*z*exp(4*exp(-3)*(exp(3)
+ 1))*log(2)^3 - 16384*z*exp(8*exp(-3)*(exp(3) + 1))*log(2)^2 + 64*z*exp(4*exp(-3)*(exp(3) + 1))*log(256)^2 +
256*z*exp(4*exp(-3)*(exp(3) + 1))*log(16)^2 + 1024*z*log(2)^2*log(16)^2 + 256*z*log(2)^2*log(256)^2 - 16*z*log
(16)^2*log(256)^2 - 32*z*log(16)^2*log(256) - 16*z*log(16)*log(256)^2 - 16384*z*log(2)^4 + 8*z*log(256)^3 + 64
*z*log(16)^3 - 512*exp(4*exp(-3)*(exp(3) + 1))*log(2)*log(16)*log(256) - 2048*exp(4*exp(-3)*(exp(3) + 1))*log(
2)^2*log(256) - 2048*exp(4*exp(-3)*(exp(3) + 1))*log(2)^2*log(16) - 160*exp(4*exp(-3)*(exp(3) + 1))*log(16)*lo
g(256)^2 - 128*exp(4*exp(-3)*(exp(3) + 1))*log(16)^2*log(256) - 128*exp(4*exp(-3)*(exp(3) + 1))*log(2)*log(256
)^2 - 2048*exp(8*exp(-3)*(exp(3) + 1))*log(2)*log(256) - 2048*exp(8*exp(-3)*(exp(3) + 1))*log(2)*log(16) - 102
4*exp(8*exp(-3)*(exp(3) + 1))*log(16)*log(256) - 768*exp(4*exp(-3)*(exp(3) + 1))*log(16)*log(256) - 512*log(2)
^2*log(16)*log(256) - 128*log(2)^2*log(256)^2 - 16*log(16)^2*log(256)^2 - 8192*exp(12*exp(-3)*(exp(3) + 1))*lo
g(2) - 2048*exp(12*exp(-3)*(exp(3) + 1))*log(256) - 2048*exp(8*exp(-3)*(exp(3) + 1))*log(256) - 2048*exp(12*ex
p(-3)*(exp(3) + 1))*log(16) - 2048*exp(8*exp(-3)*(exp(3) + 1))*log(16) - 64*log(16)^2*log(256) - 64*log(16)*lo
g(256)^2 - 8*log(16)*log(256)^3 - 12288*exp(8*exp(-3)*(exp(3) + 1))*log(2)^2 - 8192*exp(4*exp(-3)*(exp(3) + 1)
)*log(2)^3 - 384*exp(8*exp(-3)*(exp(3) + 1))*log(256)^2 - 320*exp(4*exp(-3)*(exp(3) + 1))*log(256)^2 - 32*exp(
4*exp(-3)*(exp(3) + 1))*log(256)^3 - 256*exp(8*exp(-3)*(exp(3) + 1))*log(16)^2 - 256*exp(4*exp(-3)*(exp(3) + 1
))*log(16)^2 - log(256)^4 - 4096*exp(16*exp(-3)*(exp(3) + 1)) - 4096*exp(12*exp(-3)*(exp(3) + 1)) - 4096*log(2
)^4 - 16*log(256)^3, z, k)*(64*exp(8*exp(-3) + 8) + root(4096*z^4*exp(4*exp(-3)*(exp(3) + 1))*log(2)^3*log(16)
^2 + 1536*z^4*exp(8*exp(-3)*(exp(3) + 1))*log(2)^2*log(16)^2 - 768*z^4*exp(4*exp(-3)*(exp(3) + 1))*log(2)^2*lo
g(16)^2 - 512*z^4*exp(4*exp(-3)*(exp(3) + 1))*log(2)^2*log(16)^3 + 16384*z^4*exp(8*exp(-3)*(exp(3) + 1))*log(2
)^3*log(16) + 10240*z^4*exp(12*exp(-3)*(exp(3) + 1))*log(2)^2*log(16) + 8192*z^4*exp(4*exp(-3)*(exp(3) + 1))*l
og(2)^4*log(16) + 6144*z^4*exp(4*exp(-3)*(exp(3) + 1))*log(2)^3*log(16) + 3072*z^4*exp(8*exp(-3)*(exp(3) + 1))
*log(2)^2*log(16) - 1920*z^4*exp(4*exp(-3)*(exp(3) + 1))*log(2)^2*log(16) - 768*z^4*exp(8*exp(-3)*(exp(3) + 1)
)*log(2)*log(16)^2 - 512*z^4*exp(12*exp(-3)*(exp(3) + 1))*log(2)*log(16)^2 - 512*z^4*exp(8*exp(-3)*(exp(3) + 1
))*log(2)*log(16)^3 - 480*z^4*exp(4*exp(-3)*(exp(3) + 1))*log(2)*log(16)^2 - 128*z^4*exp(4*exp(-3)*(exp(3) + 1
))*log(2)*log(16)^3 - 64*z^4*exp(4*exp(-3)*(exp(3) + 1))*log(2)*log(16)^4 + 2048*z^4*exp(16*exp(-3)*(exp(3) +
1))*log(2)*log(16) - 1920*z^4*exp(8*exp(-3)*(exp(3) + 1))*log(2)*log(16) - 53248*z^4*exp(8*exp(-3)*(exp(3) + 1
))*log(2)^4 - 49152*z^4*exp(4*exp(-3)*(exp(3) + 1))*log(2)^5 - 24576*z^4*exp(12*exp(-3)*(exp(3) + 1))*log(2)^3
 + 13824*z^4*exp(4*exp(-3)*(exp(3) + 1))*log(2)^3 + 12288*z^4*exp(8*exp(-3)*(exp(3) + 1))*log(2)^3 + 8448*z^4*
exp(8*exp(-3)*(exp(3) + 1))*log(2)^2 + 8192*z^4*exp(12*exp(-3)*(exp(3) + 1))*log(2)^2 + 6144*z^4*exp(4*exp(-3)
*(exp(3) + 1))*log(2)^4 - 4096*z^4*exp(16*exp(-3)*(exp(3) + 1))*log(2)^2 - 512*z^4*exp(12*exp(-3)*(exp(3) + 1)
)*log(16)^2 - 432*z^4*exp(8*exp(-3)*(exp(3) + 1))*log(16)^2 - 256*z^4*exp(16*exp(-3)*(exp(3) + 1))*log(16)^2 -
 192*z^4*exp(8*exp(-3)*(exp(3) + 1))*log(16)^3 - 192*z^4*exp(4*exp(-3)*(exp(3) + 1))*log(16)^2 - 128*z^4*exp(1
2*exp(-3)*(exp(3) + 1))*log(16)^3 - 104*z^4*exp(4*exp(-3)*(exp(3) + 1))*log(16)^3 - 40*z^4*exp(4*exp(-3)*(exp(
3) + 1))*log(16)^4 - 16*z^4*exp(8*exp(-3)*(exp(3) + 1))*log(16)^4 + 2048*z^4*log(2)^4*log(16)^2 - 480*z^4*log(
2)^2*log(16)^2 - 128*z^4*log(2)^2*log(16)^3 - 64*z^4*log(2)^2*log(16)^4 + 2048*z^4*exp(16*exp(-3)*(exp(3) + 1)
)*log(2) + 1536*z^4*exp(12*exp(-3)*(exp(3) + 1))*log(2) - 896*z^4*exp(12*exp(-3)*(exp(3) + 1))*log(16) - 512*z
^4*exp(16*exp(-3)*(exp(3) + 1))*log(16) - 384*z^4*exp(8*exp(-3)*(exp(3) + 1))*log(16) + 3072*z^4*log(2)^4*log(
16) - 256*z^4*exp(16*exp(-3)*(exp(3) + 1)) - 256*z^4*exp(12*exp(-3)*(exp(3) + 1)) - 16384*z^4*log(2)^6 + 6912*
z^4*log(2)^4 - 32*z^4*log(16)^3 - 13*z^4*log(16)^4 - 4*z^4*log(16)^5 + 512*z^2*exp(4*exp(-3)*(exp(3) + 1))*log
(2)^2*log(16)*log(256) + 256*z^2*exp(4*exp(-3)*(exp(3) + 1))*log(2)*log(16)^2*log(256) - 64*z^2*exp(4*exp(-3)*
(exp(3) + 1))*log(2)*log(16)*log(256)^2 + 512*z^2*exp(8*exp(-3)*(exp(3) + 1))*log(2)*log(16)*log(256) + 128*z^
2*exp(4*exp(-3)*(exp(3) + 1))*log(2)*log(16)*log(256) + 128*z^2*log(2)^2*log(16)*log(256) + 2560*z^2*exp(4*exp
(-3)*(exp(3) + 1))*log(2)^2*log(16)^2 - 128*z^2*exp(4*exp(-3)*(exp(3) + 1))*log(2)^2*log(256)^2 + 24*z^2*exp(4
*exp(-3)*(exp(3) + 1))*log(16)^2*log(256)^2 - 8192*z^2*exp(4*exp(-3)*(exp(3) + 1))*log(2)^3*log(256) - 8192*z^
2*exp(4*exp(-3)*(exp(3) + 1))*log(2)^3*log(16) - 6144*z^2*exp(8*exp(-3)*(exp(3) + 1))*log(2)^2*log(256) + 6144
*z^2*exp(4*exp(-3)*(exp(3) + 1))*log(2)^2*log(16) + 2560*z^2*exp(8*exp(-3)*(exp(3) + 1))*log(2)*log(16)^2 + 14
08*z^2*exp(4*exp(-3)*(exp(3) + 1))*log(2)*log(16)^2 - 512*z^2*exp(4*exp(-3)*(exp(3) + 1))*log(2)^2*log(256) +
256*z^2*exp(8*exp(-3)*(exp(3) + 1))*log(16)^2*log(256) + 256*z^2*exp(4*exp(-3)*(exp(3) + 1))*log(16)^2*log(256
) - 128*z^2*exp(8*exp(-3)*(exp(3) + 1))*log(2)*log(256)^2 - 96*z^2*exp(4*exp(-3)*(exp(3) + 1))*log(2)*log(256)
^2 + 56*z^2*exp(4*exp(-3)*(exp(3) + 1))*log(16)*log(256)^2 + 32*z^2*exp(8*exp(-3)*(exp(3) + 1))*log(16)*log(25
6)^2 + 32*z^2*exp(4*exp(-3)*(exp(3) + 1))*log(16)^3*log(256) + 256*z^2*exp(4*exp(-3)*(exp(3) + 1))*log(2)*log(
16)^3 + 256*z^2*log(2)^2*log(16)^2*log(256) - 64*z^2*log(2)^2*log(16)*log(256)^2 + 6144*z^2*exp(8*exp(-3)*(exp
(3) + 1))*log(2)*log(16) + 4096*z^2*exp(12*exp(-3)*(exp(3) + 1))*log(2)*log(16) - 2048*z^2*exp(12*exp(-3)*(exp
(3) + 1))*log(2)*log(256) + 768*z^2*exp(8*exp(-3)*(exp(3) + 1))*log(16)*log(256) + 512*z^2*exp(12*exp(-3)*(exp
(3) + 1))*log(16)*log(256) - 512*z^2*exp(8*exp(-3)*(exp(3) + 1))*log(2)*log(256) + 320*z^2*exp(4*exp(-3)*(exp(
3) + 1))*log(16)*log(256) - 49152*z^2*exp(8*exp(-3)*(exp(3) + 1))*log(2)^3 - 36864*z^2*exp(4*exp(-3)*(exp(3) +
 1))*log(2)^3 - 32768*z^2*exp(12*exp(-3)*(exp(3) + 1))*log(2)^2 - 24576*z^2*exp(4*exp(-3)*(exp(3) + 1))*log(2)
^4 - 22528*z^2*exp(8*exp(-3)*(exp(3) + 1))*log(2)^2 + 1536*z^2*exp(8*exp(-3)*(exp(3) + 1))*log(16)^2 + 1024*z^
2*exp(12*exp(-3)*(exp(3) + 1))*log(16)^2 + 704*z^2*exp(4*exp(-3)*(exp(3) + 1))*log(16)^2 + 48*z^2*exp(4*exp(-3
)*(exp(3) + 1))*log(256)^2 + 32*z^2*exp(8*exp(-3)*(exp(3) + 1))*log(256)^2 + 224*z^2*exp(4*exp(-3)*(exp(3) + 1
))*log(16)^3 + 128*z^2*exp(8*exp(-3)*(exp(3) + 1))*log(16)^3 + 1408*z^2*log(2)^2*log(16)^2 - 96*z^2*log(2)^2*l
og(256)^2 + 14*z^2*log(16)^2*log(256)^2 + 4*z^2*log(16)^3*log(256)^2 + 256*z^2*log(2)^2*log(16)^3 - 8192*z^2*e
xp(16*exp(-3)*(exp(3) + 1))*log(2) + 4096*z^2*exp(12*exp(-3)*(exp(3) + 1))*log(16) - 4096*z^2*exp(12*exp(-3)*(
exp(3) + 1))*log(2) + 2048*z^2*exp(16*exp(-3)*(exp(3) + 1))*log(16) + 2048*z^2*exp(8*exp(-3)*(exp(3) + 1))*log
(16) + 512*z^2*exp(12*exp(-3)*(exp(3) + 1))*log(256) + 512*z^2*exp(8*exp(-3)*(exp(3) + 1))*log(256) - 4096*z^2
*log(2)^4*log(256) - 4096*z^2*log(2)^4*log(16) + 32*z^2*log(16)^2*log(256) + 24*z^2*log(16)^3*log(256) + 24*z^
2*log(16)*log(256)^2 + 2048*z^2*exp(16*exp(-3)*(exp(3) + 1)) + 2048*z^2*exp(12*exp(-3)*(exp(3) + 1)) - 18432*z
^2*log(2)^4 + 96*z^2*log(16)^3 + 16*z^2*log(16)^4 + 4096*z*exp(8*exp(-3)*(exp(3) + 1))*log(2)*log(16) + 2048*z
*exp(8*exp(-3)*(exp(3) + 1))*log(2)*log(256) - 512*z*exp(8*exp(-3)*(exp(3) + 1))*log(16)*log(256) - 256*z*exp(
4*exp(-3)*(exp(3) + 1))*log(16)*log(256) + 4096*z*exp(4*exp(-3)*(exp(3) + 1))*log(2)^2*log(16) + 2048*z*exp(4*
exp(-3)*(exp(3) + 1))*log(2)^2*log(256) + 1024*z*exp(4*exp(-3)*(exp(3) + 1))*log(2)*log(16)^2 + 256*z*exp(4*ex
p(-3)*(exp(3) + 1))*log(2)*log(256)^2 - 128*z*exp(4*exp(-3)*(exp(3) + 1))*log(16)^2*log(256) - 64*z*exp(4*exp(
-3)*(exp(3) + 1))*log(16)*log(256)^2 - 32768*z*exp(4*exp(-3)*(exp(3) + 1))*log(2)^3 - 16384*z*exp(8*exp(-3)*(e
xp(3) + 1))*log(2)^2 + 64*z*exp(4*exp(-3)*(exp(3) + 1))*log(256)^2 + 256*z*exp(4*exp(-3)*(exp(3) + 1))*log(16)
^2 + 1024*z*log(2)^2*log(16)^2 + 256*z*log(2)^2*log(256)^2 - 16*z*log(16)^2*log(256)^2 - 32*z*log(16)^2*log(25
6) - 16*z*log(16)*log(256)^2 - 16384*z*log(2)^4 + 8*z*log(256)^3 + 64*z*log(16)^3 - 512*exp(4*exp(-3)*(exp(3)
+ 1))*log(2)*log(16)*log(256) - 2048*exp(4*exp(-3)*(exp(3) + 1))*log(2)^2*log(256) - 2048*exp(4*exp(-3)*(exp(3
) + 1))*log(2)^2*log(16) - 160*exp(4*exp(-3)*(exp(3) + 1))*log(16)*log(256)^2 - 128*exp(4*exp(-3)*(exp(3) + 1)
)*log(16)^2*log(256) - 128*exp(4*exp(-3)*(exp(3) + 1))*log(2)*log(256)^2 - 2048*exp(8*exp(-3)*(exp(3) + 1))*lo
g(2)*log(256) - 2048*exp(8*exp(-3)*(exp(3) + 1))*log(2)*log(16) - 1024*exp(8*exp(-3)*(exp(3) + 1))*log(16)*log
(256) - 768*exp(4*exp(-3)*(exp(3) + 1))*log(16)*log(256) - 512*log(2)^2*log(16)*log(256) - 128*log(2)^2*log(25
6)^2 - 16*log(16)^2*log(256)^2 - 8192*exp(12*exp(-3)*(exp(3) + 1))*log(2) - 2048*exp(12*exp(-3)*(exp(3) + 1))*
log(256) - 2048*exp(8*exp(-3)*(exp(3) + 1))*log(256) - 2048*exp(12*exp(-3)*(exp(3) + 1))*log(16) - 2048*exp(8*
exp(-3)*(exp(3) + 1))*log(16) - 64*log(16)^2*log(256) - 64*log(16)*log(256)^2 - 8*log(16)*log(256)^3 - 12288*e
xp(8*exp(-3)*(exp(3) + 1))*log(2)^2 - 8192*exp(4*exp(-3)*(exp(3) + 1))*log(2)^3 - 384*exp(8*exp(-3)*(exp(3) +
1))*log(256)^2 - 320*exp(4*exp(-3)*(exp(3) + 1))*log(256)^2 - 32*exp(4*exp(-3)*(exp(3) + 1))*log(256)^3 - 256*
exp(8*exp(-3)*(exp(3) + 1))*log(16)^2 - 256*exp(4*exp(-3)*(exp(3) + 1))*log(16)^2 - log(256)^4 - 4096*exp(16*e
xp(-3)*(exp(3) + 1)) - 4096*exp(12*exp(-3)*(exp(3) + 1)) - 4096*log(2)^4 - 16*log(256)^3, z, k)*(32*exp(8*exp(
-3) + 8) + 288*exp(4*exp(-3) + 4)*log(2) + 128*exp(8*exp(-3) + 8)*log(2) - 40*exp(4*exp(-3) + 4)*log(16) - 32*
exp(8*exp(-3) + 8)*log(16) + x*(48*log(16) + 96*exp(4*exp(-3) + 4) + 64*exp(8*exp(-3) + 8) - 192*exp(4*exp(-3)
 + 4)*log(2) - 256*exp(8*exp(-3) + 8)*log(2) + 112*exp(4*exp(-3) + 4)*log(16) + 64*exp(8*exp(-3) + 8)*log(16)
- 128*log(2)^2*log(16) - 256*exp(4*exp(-3) + 4)*log(2)^2 + 48*exp(4*exp(-3) + 4)*log(16)^2 - 192*log(2)^2 + 28
*log(16)^2 + 8*log(16)^3 - 128*exp(4*exp(-3) + 4)*log(2)*log(16)) + 64*log(2)^2*log(16) + 128*exp(4*exp(-3) +
4)*log(2)^2 - 24*exp(4*exp(-3) + 4)*log(16)^2 + 288*log(2)^2 - 10*log(16)^2 - 4*log(16)^3 + 64*exp(4*exp(-3) +
 4)*log(2)*log(16)) + 8*log(16)*log(256) - 192*exp(4*exp(-3) + 4)*log(2) - 256*exp(8*exp(-3) + 8)*log(2) + 80*
exp(4*exp(-3) + 4)*log(16) + 64*exp(8*exp(-3) + 8)*log(16) + 16*exp(4*exp(-3) + 4)*log(256) - 64*log(2)^2*log(
256) + 4*log(16)^2*log(256) - 256*exp(4*exp(-3) + 4)*log(2)^2 + 16*exp(4*exp(-3) + 4)*log(16)^2 + x*(24*log(25
6) - 16*log(16) + 64*exp(4*exp(-3) + 4) + 256*exp(4*exp(-3) + 4)*log(2) - 64*exp(4*exp(-3) + 4)*log(16) + 256*
log(2)^2 - 16*log(16)^2) - 192*log(2)^2 + 12*log(16)^2 - 64*exp(4*exp(-3) + 4)*log(2)*log(256) + 16*exp(4*exp(
-3) + 4)*log(16)*log(256)) + 8*log(16)*log(256) + 640*exp(4*exp(-3) + 4)*log(2) - 32*exp(4*exp(-3) + 4)*log(16
) + x*(128*log(16) + 32*log(256) + 384*exp(4*exp(-3) + 4) + 256*exp(8*exp(-3) + 8) + 16*log(16)*log(256) - 256
*exp(4*exp(-3) + 4)*log(2) + 192*exp(4*exp(-3) + 4)*log(16) + 64*exp(4*exp(-3) + 4)*log(256) - 256*log(2)^2 +
32*log(16)^2 + 4*log(256)^2) + 640*log(2)^2 - 16*log(16)^2 - 2*log(256)^2))*root(4096*z^4*exp(4*exp(-3)*(exp(3
) + 1))*log(2)^3*log(16)^2 + 1536*z^4*exp(8*exp(-3)*(exp(3) + 1))*log(2)^2*log(16)^2 - 768*z^4*exp(4*exp(-3)*(
exp(3) + 1))*log(2)^2*log(16)^2 - 512*z^4*exp(4*exp(-3)*(exp(3) + 1))*log(2)^2*log(16)^3 + 16384*z^4*exp(8*exp
(-3)*(exp(3) + 1))*log(2)^3*log(16) + 10240*z^4*exp(12*exp(-3)*(exp(3) + 1))*log(2)^2*log(16) + 8192*z^4*exp(4
*exp(-3)*(exp(3) + 1))*log(2)^4*log(16) + 6144*z^4*exp(4*exp(-3)*(exp(3) + 1))*log(2)^3*log(16) + 3072*z^4*exp
(8*exp(-3)*(exp(3) + 1))*log(2)^2*log(16) - 1920*z^4*exp(4*exp(-3)*(exp(3) + 1))*log(2)^2*log(16) - 768*z^4*ex
p(8*exp(-3)*(exp(3) + 1))*log(2)*log(16)^2 - 512*z^4*exp(12*exp(-3)*(exp(3) + 1))*log(2)*log(16)^2 - 512*z^4*e
xp(8*exp(-3)*(exp(3) + 1))*log(2)*log(16)^3 - 480*z^4*exp(4*exp(-3)*(exp(3) + 1))*log(2)*log(16)^2 - 128*z^4*e
xp(4*exp(-3)*(exp(3) + 1))*log(2)*log(16)^3 - 64*z^4*exp(4*exp(-3)*(exp(3) + 1))*log(2)*log(16)^4 + 2048*z^4*e
xp(16*exp(-3)*(exp(3) + 1))*log(2)*log(16) - 1920*z^4*exp(8*exp(-3)*(exp(3) + 1))*log(2)*log(16) - 53248*z^4*e
xp(8*exp(-3)*(exp(3) + 1))*log(2)^4 - 49152*z^4*exp(4*exp(-3)*(exp(3) + 1))*log(2)^5 - 24576*z^4*exp(12*exp(-3
)*(exp(3) + 1))*log(2)^3 + 13824*z^4*exp(4*exp(-3)*(exp(3) + 1))*log(2)^3 + 12288*z^4*exp(8*exp(-3)*(exp(3) +
1))*log(2)^3 + 8448*z^4*exp(8*exp(-3)*(exp(3) + 1))*log(2)^2 + 8192*z^4*exp(12*exp(-3)*(exp(3) + 1))*log(2)^2
+ 6144*z^4*exp(4*exp(-3)*(exp(3) + 1))*log(2)^4 - 4096*z^4*exp(16*exp(-3)*(exp(3) + 1))*log(2)^2 - 512*z^4*exp
(12*exp(-3)*(exp(3) + 1))*log(16)^2 - 432*z^4*exp(8*exp(-3)*(exp(3) + 1))*log(16)^2 - 256*z^4*exp(16*exp(-3)*(
exp(3) + 1))*log(16)^2 - 192*z^4*exp(8*exp(-3)*(exp(3) + 1))*log(16)^3 - 192*z^4*exp(4*exp(-3)*(exp(3) + 1))*l
og(16)^2 - 128*z^4*exp(12*exp(-3)*(exp(3) + 1))*log(16)^3 - 104*z^4*exp(4*exp(-3)*(exp(3) + 1))*log(16)^3 - 40
*z^4*exp(4*exp(-3)*(exp(3) + 1))*log(16)^4 - 16*z^4*exp(8*exp(-3)*(exp(3) + 1))*log(16)^4 + 2048*z^4*log(2)^4*
log(16)^2 - 480*z^4*log(2)^2*log(16)^2 - 128*z^4*log(2)^2*log(16)^3 - 64*z^4*log(2)^2*log(16)^4 + 2048*z^4*exp
(16*exp(-3)*(exp(3) + 1))*log(2) + 1536*z^4*exp(12*exp(-3)*(exp(3) + 1))*log(2) - 896*z^4*exp(12*exp(-3)*(exp(
3) + 1))*log(16) - 512*z^4*exp(16*exp(-3)*(exp(3) + 1))*log(16) - 384*z^4*exp(8*exp(-3)*(exp(3) + 1))*log(16)
+ 3072*z^4*log(2)^4*log(16) - 256*z^4*exp(16*exp(-3)*(exp(3) + 1)) - 256*z^4*exp(12*exp(-3)*(exp(3) + 1)) - 16
384*z^4*log(2)^6 + 6912*z^4*log(2)^4 - 32*z^4*log(16)^3 - 13*z^4*log(16)^4 - 4*z^4*log(16)^5 + 512*z^2*exp(4*e
xp(-3)*(exp(3) + 1))*log(2)^2*log(16)*log(256) + 256*z^2*exp(4*exp(-3)*(exp(3) + 1))*log(2)*log(16)^2*log(256)
 - 64*z^2*exp(4*exp(-3)*(exp(3) + 1))*log(2)*log(16)*log(256)^2 + 512*z^2*exp(8*exp(-3)*(exp(3) + 1))*log(2)*l
og(16)*log(256) + 128*z^2*exp(4*exp(-3)*(exp(3) + 1))*log(2)*log(16)*log(256) + 128*z^2*log(2)^2*log(16)*log(2
56) + 2560*z^2*exp(4*exp(-3)*(exp(3) + 1))*log(2)^2*log(16)^2 - 128*z^2*exp(4*exp(-3)*(exp(3) + 1))*log(2)^2*l
og(256)^2 + 24*z^2*exp(4*exp(-3)*(exp(3) + 1))*log(16)^2*log(256)^2 - 8192*z^2*exp(4*exp(-3)*(exp(3) + 1))*log
(2)^3*log(256) - 8192*z^2*exp(4*exp(-3)*(exp(3) + 1))*log(2)^3*log(16) - 6144*z^2*exp(8*exp(-3)*(exp(3) + 1))*
log(2)^2*log(256) + 6144*z^2*exp(4*exp(-3)*(exp(3) + 1))*log(2)^2*log(16) + 2560*z^2*exp(8*exp(-3)*(exp(3) + 1
))*log(2)*log(16)^2 + 1408*z^2*exp(4*exp(-3)*(exp(3) + 1))*log(2)*log(16)^2 - 512*z^2*exp(4*exp(-3)*(exp(3) +
1))*log(2)^2*log(256) + 256*z^2*exp(8*exp(-3)*(exp(3) + 1))*log(16)^2*log(256) + 256*z^2*exp(4*exp(-3)*(exp(3)
 + 1))*log(16)^2*log(256) - 128*z^2*exp(8*exp(-3)*(exp(3) + 1))*log(2)*log(256)^2 - 96*z^2*exp(4*exp(-3)*(exp(
3) + 1))*log(2)*log(256)^2 + 56*z^2*exp(4*exp(-3)*(exp(3) + 1))*log(16)*log(256)^2 + 32*z^2*exp(8*exp(-3)*(exp
(3) + 1))*log(16)*log(256)^2 + 32*z^2*exp(4*exp(-3)*(exp(3) + 1))*log(16)^3*log(256) + 256*z^2*exp(4*exp(-3)*(
exp(3) + 1))*log(2)*log(16)^3 + 256*z^2*log(2)^2*log(16)^2*log(256) - 64*z^2*log(2)^2*log(16)*log(256)^2 + 614
4*z^2*exp(8*exp(-3)*(exp(3) + 1))*log(2)*log(16) + 4096*z^2*exp(12*exp(-3)*(exp(3) + 1))*log(2)*log(16) - 2048
*z^2*exp(12*exp(-3)*(exp(3) + 1))*log(2)*log(256) + 768*z^2*exp(8*exp(-3)*(exp(3) + 1))*log(16)*log(256) + 512
*z^2*exp(12*exp(-3)*(exp(3) + 1))*log(16)*log(256) - 512*z^2*exp(8*exp(-3)*(exp(3) + 1))*log(2)*log(256) + 320
*z^2*exp(4*exp(-3)*(exp(3) + 1))*log(16)*log(256) - 49152*z^2*exp(8*exp(-3)*(exp(3) + 1))*log(2)^3 - 36864*z^2
*exp(4*exp(-3)*(exp(3) + 1))*log(2)^3 - 32768*z^2*exp(12*exp(-3)*(exp(3) + 1))*log(2)^2 - 24576*z^2*exp(4*exp(
-3)*(exp(3) + 1))*log(2)^4 - 22528*z^2*exp(8*exp(-3)*(exp(3) + 1))*log(2)^2 + 1536*z^2*exp(8*exp(-3)*(exp(3) +
 1))*log(16)^2 + 1024*z^2*exp(12*exp(-3)*(exp(3) + 1))*log(16)^2 + 704*z^2*exp(4*exp(-3)*(exp(3) + 1))*log(16)
^2 + 48*z^2*exp(4*exp(-3)*(exp(3) + 1))*log(256)^2 + 32*z^2*exp(8*exp(-3)*(exp(3) + 1))*log(256)^2 + 224*z^2*e
xp(4*exp(-3)*(exp(3) + 1))*log(16)^3 + 128*z^2*exp(8*exp(-3)*(exp(3) + 1))*log(16)^3 + 1408*z^2*log(2)^2*log(1
6)^2 - 96*z^2*log(2)^2*log(256)^2 + 14*z^2*log(16)^2*log(256)^2 + 4*z^2*log(16)^3*log(256)^2 + 256*z^2*log(2)^
2*log(16)^3 - 8192*z^2*exp(16*exp(-3)*(exp(3) + 1))*log(2) + 4096*z^2*exp(12*exp(-3)*(exp(3) + 1))*log(16) - 4
096*z^2*exp(12*exp(-3)*(exp(3) + 1))*log(2) + 2048*z^2*exp(16*exp(-3)*(exp(3) + 1))*log(16) + 2048*z^2*exp(8*e
xp(-3)*(exp(3) + 1))*log(16) + 512*z^2*exp(12*exp(-3)*(exp(3) + 1))*log(256) + 512*z^2*exp(8*exp(-3)*(exp(3) +
 1))*log(256) - 4096*z^2*log(2)^4*log(256) - 4096*z^2*log(2)^4*log(16) + 32*z^2*log(16)^2*log(256) + 24*z^2*lo
g(16)^3*log(256) + 24*z^2*log(16)*log(256)^2 + 2048*z^2*exp(16*exp(-3)*(exp(3) + 1)) + 2048*z^2*exp(12*exp(-3)
*(exp(3) + 1)) - 18432*z^2*log(2)^4 + 96*z^2*log(16)^3 + 16*z^2*log(16)^4 + 4096*z*exp(8*exp(-3)*(exp(3) + 1))
*log(2)*log(16) + 2048*z*exp(8*exp(-3)*(exp(3) + 1))*log(2)*log(256) - 512*z*exp(8*exp(-3)*(exp(3) + 1))*log(1
6)*log(256) - 256*z*exp(4*exp(-3)*(exp(3) + 1))*log(16)*log(256) + 4096*z*exp(4*exp(-3)*(exp(3) + 1))*log(2)^2
*log(16) + 2048*z*exp(4*exp(-3)*(exp(3) + 1))*log(2)^2*log(256) + 1024*z*exp(4*exp(-3)*(exp(3) + 1))*log(2)*lo
g(16)^2 + 256*z*exp(4*exp(-3)*(exp(3) + 1))*log(2)*log(256)^2 - 128*z*exp(4*exp(-3)*(exp(3) + 1))*log(16)^2*lo
g(256) - 64*z*exp(4*exp(-3)*(exp(3) + 1))*log(16)*log(256)^2 - 32768*z*exp(4*exp(-3)*(exp(3) + 1))*log(2)^3 -
16384*z*exp(8*exp(-3)*(exp(3) + 1))*log(2)^2 + 64*z*exp(4*exp(-3)*(exp(3) + 1))*log(256)^2 + 256*z*exp(4*exp(-
3)*(exp(3) + 1))*log(16)^2 + 1024*z*log(2)^2*log(16)^2 + 256*z*log(2)^2*log(256)^2 - 16*z*log(16)^2*log(256)^2
 - 32*z*log(16)^2*log(256) - 16*z*log(16)*log(256)^2 - 16384*z*log(2)^4 + 8*z*log(256)^3 + 64*z*log(16)^3 - 51
2*exp(4*exp(-3)*(exp(3) + 1))*log(2)*log(16)*log(256) - 2048*exp(4*exp(-3)*(exp(3) + 1))*log(2)^2*log(256) - 2
048*exp(4*exp(-3)*(exp(3) + 1))*log(2)^2*log(16) - 160*exp(4*exp(-3)*(exp(3) + 1))*log(16)*log(256)^2 - 128*ex
p(4*exp(-3)*(exp(3) + 1))*log(16)^2*log(256) - 128*exp(4*exp(-3)*(exp(3) + 1))*log(2)*log(256)^2 - 2048*exp(8*
exp(-3)*(exp(3) + 1))*log(2)*log(256) - 2048*exp(8*exp(-3)*(exp(3) + 1))*log(2)*log(16) - 1024*exp(8*exp(-3)*(
exp(3) + 1))*log(16)*log(256) - 768*exp(4*exp(-3)*(exp(3) + 1))*log(16)*log(256) - 512*log(2)^2*log(16)*log(25
6) - 128*log(2)^2*log(256)^2 - 16*log(16)^2*log(256)^2 - 8192*exp(12*exp(-3)*(exp(3) + 1))*log(2) - 2048*exp(1
2*exp(-3)*(exp(3) + 1))*log(256) - 2048*exp(8*exp(-3)*(exp(3) + 1))*log(256) - 2048*exp(12*exp(-3)*(exp(3) + 1
))*log(16) - 2048*exp(8*exp(-3)*(exp(3) + 1))*log(16) - 64*log(16)^2*log(256) - 64*log(16)*log(256)^2 - 8*log(
16)*log(256)^3 - 12288*exp(8*exp(-3)*(exp(3) + 1))*log(2)^2 - 8192*exp(4*exp(-3)*(exp(3) + 1))*log(2)^3 - 384*
exp(8*exp(-3)*(exp(3) + 1))*log(256)^2 - 320*exp(4*exp(-3)*(exp(3) + 1))*log(256)^2 - 32*exp(4*exp(-3)*(exp(3)
 + 1))*log(256)^3 - 256*exp(8*exp(-3)*(exp(3) + 1))*log(16)^2 - 256*exp(4*exp(-3)*(exp(3) + 1))*log(16)^2 - lo
g(256)^4 - 4096*exp(16*exp(-3)*(exp(3) + 1)) - 4096*exp(12*exp(-3)*(exp(3) + 1)) - 4096*log(2)^4 - 16*log(256)
^3, z, k), k, 1, 4)

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sympy [A]  time = 1.75, size = 46, normalized size = 1.70 \begin {gather*} - 2 \log {\left (x^{2} - e^{4} e^{\frac {4}{e^{3}}} - 2 \log {\relax (2 )} \right )} + 2 \log {\left (x^{2} - 2 x - e^{4} e^{\frac {4}{e^{3}}} - 2 \log {\relax (2 )} \right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((4*exp((4*exp(3)+4)/exp(3))+8*ln(2)+4*x**2)/(exp((4*exp(3)+4)/exp(3))**2+(4*ln(2)-2*x**2+2*x)*exp((4
*exp(3)+4)/exp(3))+4*ln(2)**2+2*(-2*x**2+2*x)*ln(2)+x**4-2*x**3),x)

[Out]

-2*log(x**2 - exp(4)*exp(4*exp(-3)) - 2*log(2)) + 2*log(x**2 - 2*x - exp(4)*exp(4*exp(-3)) - 2*log(2))

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