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\(\int \frac {8 x+32 x^3+e^{e^5} (-4-24 x^2)+4 (i \pi +\log (5))}{x^4+4 x^6+4 x^8+(2 x^3+4 x^5) (i \pi +\log (5))+x^2 (i \pi +\log (5))^2+e^{2 e^5} (x^2+4 x^4+4 x^6+(2 x+4 x^3) (i \pi +\log (5))+(i \pi +\log (5))^2)+e^{e^5} (-2 x^3-8 x^5-8 x^7+(-4 x^2-8 x^4) (i \pi +\log (5))-2 x (i \pi +\log (5))^2)} \, dx\) [7905]

   Optimal result
   Rubi [B] (warning: unable to verify)
   Mathematica [A] (verified)
   Maple [B] (verified)
   Fricas [A] (verification not implemented)
   Sympy [F(-1)]
   Maxima [A] (verification not implemented)
   Giac [F(-1)]
   Mupad [B] (verification not implemented)

Optimal result

Integrand size = 188, antiderivative size = 29 \[ \int \frac {8 x+32 x^3+e^{e^5} \left (-4-24 x^2\right )+4 (i \pi +\log (5))}{x^4+4 x^6+4 x^8+\left (2 x^3+4 x^5\right ) (i \pi +\log (5))+x^2 (i \pi +\log (5))^2+e^{2 e^5} \left (x^2+4 x^4+4 x^6+\left (2 x+4 x^3\right ) (i \pi +\log (5))+(i \pi +\log (5))^2\right )+e^{e^5} \left (-2 x^3-8 x^5-8 x^7+\left (-4 x^2-8 x^4\right ) (i \pi +\log (5))-2 x (i \pi +\log (5))^2\right )} \, dx=\frac {4}{\left (e^{e^5}-x\right ) \left (i \pi +x+2 x^3+\log (5)\right )} \]

[Out]

4/(exp(exp(5))-x)/(ln(5)+I*Pi+2*x^3+x)

Rubi [B] (warning: unable to verify)

Both result and optimal contain complex but leaf count is larger than twice the leaf count of optimal. \(16160\) vs. \(2(29)=58\).

Time = 177.35 (sec) , antiderivative size = 16160, normalized size of antiderivative = 557.24, number of steps used = 18, number of rules used = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.053, Rules used = {2099, 2104, 814, 648, 632, 210, 642, 2126, 836, 212} \[ \int \frac {8 x+32 x^3+e^{e^5} \left (-4-24 x^2\right )+4 (i \pi +\log (5))}{x^4+4 x^6+4 x^8+\left (2 x^3+4 x^5\right ) (i \pi +\log (5))+x^2 (i \pi +\log (5))^2+e^{2 e^5} \left (x^2+4 x^4+4 x^6+\left (2 x+4 x^3\right ) (i \pi +\log (5))+(i \pi +\log (5))^2\right )+e^{e^5} \left (-2 x^3-8 x^5-8 x^7+\left (-4 x^2-8 x^4\right ) (i \pi +\log (5))-2 x (i \pi +\log (5))^2\right )} \, dx =\text {Too large to display} \]

[In]

Int[(8*x + 32*x^3 + E^E^5*(-4 - 24*x^2) + 4*(I*Pi + Log[5]))/(x^4 + 4*x^6 + 4*x^8 + (2*x^3 + 4*x^5)*(I*Pi + Lo
g[5]) + x^2*(I*Pi + Log[5])^2 + E^(2*E^5)*(x^2 + 4*x^4 + 4*x^6 + (2*x + 4*x^3)*(I*Pi + Log[5]) + (I*Pi + Log[5
])^2) + E^E^5*(-2*x^3 - 8*x^5 - 8*x^7 + (-4*x^2 - 8*x^4)*(I*Pi + Log[5]) - 2*x*(I*Pi + Log[5])^2)),x]

[Out]

4/((E^E^5 - x)*(E^E^5 + 2*E^(3*E^5) + I*Pi + Log[5])) - (4*(1 + 6*E^(2*E^5)))/(3*(Pi - I*x - (2*I)*x^3 - I*Log
[5])*(Pi - I*(E^E^5 + 2*E^(3*E^5) + Log[5]))) - (8*2^(5/6)*3^(1/6)*ArcTan[(12*x*((-9*I)*Pi - 9*Log[5] + Sqrt[6
 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2])^(2/3) - 6^(1/3)*((9*I)*Pi + 9*Log[5] - Sqrt[6 - 81*Pi^2 + (162*
I)*Pi*Log[5] + 81*Log[5]^2] + (6*((-9*I)*Pi - 9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))
^(1/3)))/(3*Sqrt[2*(6^(2/3) - 27*6^(2/3)*Pi^2 + (54*I)*6^(2/3)*Pi*Log[5] + 27*6^(2/3)*Log[5]^2 - 9*2^(2/3)*3^(
1/6)*(I*Pi + Log[5])*Sqrt[2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2] - (18*I)*Pi*((-9*I)*Pi - 9*Log[5] + Sq
rt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2])^(1/3) - 18*Log[5]*((-9*I)*Pi - 9*Log[5] + Sqrt[6 - 81*Pi^2
+ (162*I)*Pi*Log[5] + 81*Log[5]^2])^(1/3) + 2*Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]*((-9*I)*Pi -
 9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2])^(1/3) + 6^(1/3)*((-9*I)*Pi - 9*Log[5] + Sqrt[
6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2])^(2/3))])]*(2^(1/3)*Sqrt[3] - 27*2^(1/3)*Sqrt[3]*Pi^2 + 27*2^(1
/3)*Sqrt[3]*Log[5]^2 - 9*2^(1/3)*Log[5]*Sqrt[2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2] + (9*I)*2^(1/3)*Pi*
(6*Sqrt[3]*Log[5] - Sqrt[2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2]) + 3^(1/6)*((-9*I)*Pi - 9*Log[5] + Sqrt
[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2])^(2/3) - 2*E^E^5*((9*I)*3^(1/6)*Pi*(6^(1/3) - ((-9*I)*Pi - 9*L
og[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2])^(2/3)) + 9*3^(1/6)*Log[5]*(6^(1/3) - ((-9*I)*Pi -
 9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2])^(2/3)) - Sqrt[2 - 27*Pi^2 + (54*I)*Pi*Log[5]
+ 27*Log[5]^2]*(3*2^(1/3) - (3*((-9*I)*Pi - 9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(
2/3)))))/((E^E^5 + 2*E^(3*E^5) + I*Pi + Log[5])*(2*6^(1/3) - (3*I)*6^(2/3)*Pi*((-9*I)*Pi - 9*Log[5] + Sqrt[6 -
 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2])^(1/3) - 3*6^(2/3)*Log[5]*((-9*I)*Pi - 9*Log[5] + Sqrt[6 - 81*Pi^2
 + (162*I)*Pi*Log[5] + 81*Log[5]^2])^(1/3) + 2^(2/3)*3^(1/6)*Sqrt[2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2
]*((-9*I)*Pi - 9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2])^(1/3) - 2*((-9*I)*Pi - 9*Log[5]
 + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2])^(2/3))*Sqrt[6^(2/3) - 27*6^(2/3)*Pi^2 + 27*6^(2/3)*Log
[5]^2 + 2*Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]*((-9*I)*Pi - 9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*
I)*Pi*Log[5] + 81*Log[5]^2])^(1/3) + 6^(1/3)*((-9*I)*Pi - 9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81
*Log[5]^2])^(2/3) + (9*I)*Pi*(6*6^(2/3)*Log[5] - 2^(2/3)*3^(1/6)*Sqrt[2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[
5]^2] - 2*((-9*I)*Pi - 9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2])^(1/3)) - 9*Log[5]*(2^(2
/3)*3^(1/6)*Sqrt[2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2] + 2*((-9*I)*Pi - 9*Log[5] + Sqrt[6 - 81*Pi^2 +
(162*I)*Pi*Log[5] + 81*Log[5]^2])^(1/3))]) + (24*(9*Pi - I*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] +
81*Log[5]^2]))^(1/3)*(2 - 27*Pi^2 + 9*Log[5]*Log[125] + (9*I)*Pi*Log[15625]))/((E^E^5 + 2*E^(3*E^5) + I*Pi + L
og[5])*(54*Pi*Log[5] - I*(2 - 27*Pi^2 + 27*Log[5]^2))*((6*I)*x*(9*Pi - I*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I
)*Pi*Log[5] + 81*Log[5]^2]))^(1/3) + 6^(1/3)*(6^(1/3) + (9*Pi - I*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Lo
g[5] + 81*Log[5]^2]))^(2/3)))) + (24*6^(2/3)*(9*Pi - I*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*L
og[5]^2]))^(4/3)*(x*((2*(I + 9*E^E^5*(Pi - I*Log[5]))*(6^(1/3) + (9*Pi - I*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162
*I)*Pi*Log[5] + 81*Log[5]^2]))^(2/3)))/((9*Pi - I*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]
^2]))/6)^(1/3) - ((3*I)*2^(1/3)*(6 + 6^(1/3)*(9*Pi - I*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*L
og[5]^2]))^(4/3))*(3*Pi - I*(2*E^E^5 + Log[125])))/(27*Pi - (3*I)*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Lo
g[5] + 81*Log[5]^2]))^(2/3)) - 2*(2 - 27*Pi^2 + 9*Log[5]*Log[125] + (9*I)*Pi*Log[15625])))/((E^E^5 + 2*E^(3*E^
5) + I*Pi + Log[5])*(3*Pi*(18*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]) - I*(2 - 27*Pi^2 +
 27*Log[5]^2 + 3*Log[5]*Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))*(6^(1/3) - (9*Pi - I*(9*Log[5] +
 Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(2/3))*((6*I)*x + (6^(1/3) + (9*Pi - I*(9*Log[5] + Sqrt
[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(2/3))/((9*Pi - I*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*
Log[5] + 81*Log[5]^2]))/6)^(1/3))*(6 + 36*x^2 - (6*6^(1/3))/(9*Pi - I*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*P
i*Log[5] + 81*Log[5]^2]))^(2/3) - (54*Pi - (6*I)*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^
2]))^(2/3) + ((6*I)*x*(6^(1/3) + (9*Pi - I*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(
2/3)))/((9*Pi - I*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))/6)^(1/3))) + (((512*I)/9)*
Sqrt[2]*ArcTanh[(12*x*(9*Pi - I*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(2/3) + 6^(1
/3)*((9*I)*Pi + 9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2] + I*(54*Pi - (6*I)*(9*Log[5] +
Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(1/3)))/(3*Sqrt[2*(-6^(2/3) + 27*6^(2/3)*Pi^2 - (54*I)*6
^(2/3)*Pi*Log[5] - 27*6^(2/3)*Log[5]^2 - 9*2^(2/3)*3^(1/6)*(I*Pi + Log[5])*Sqrt[2 - 27*Pi^2 + (54*I)*Pi*Log[5]
 + 27*Log[5]^2] - 18*Pi*(9*Pi - I*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(1/3) + (1
8*I)*Log[5]*(9*Pi - I*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(1/3) + (2*I)*Sqrt[6 -
 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]*(9*Pi - I*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Lo
g[5]^2]))^(1/3) + 6^(1/3)*(9*Pi - I*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(2/3))])
]*(-24*(9*Pi - I*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(2/3)*(-48*6^(1/3)*E^E^5 -
(18*I)*6^(1/3)*Pi + 1944*6^(1/3)*E^E^5*Pi^2 + (243*I)*6^(1/3)*Pi^3 - 17496*6^(1/3)*E^E^5*Pi^4 + 54*6^(1/3)*Log
[5] - (3888*I)*6^(1/3)*E^E^5*Pi*Log[5] - 1458*6^(1/3)*Pi^2*Log[5] + (69984*I)*6^(1/3)*E^E^5*Pi^3*Log[5] - 1944
*6^(1/3)*E^E^5*Log[5]^2 + (3645*I)*6^(1/3)*Pi*Log[5]^2 + 104976*6^(1/3)*E^E^5*Pi^2*Log[5]^2 + 1944*6^(1/3)*Log
[5]^3 - (69984*I)*6^(1/3)*E^E^5*Pi*Log[5]^3 - 17496*6^(1/3)*E^E^5*Log[5]^4 - 2*2^(1/3)*3^(5/6)*Sqrt[2 - 27*Pi^
2 + (54*I)*Pi*Log[5] + 27*Log[5]^2] - (144*I)*2^(1/3)*3^(5/6)*E^E^5*Pi*Sqrt[2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 2
7*Log[5]^2] + 27*2^(1/3)*3^(5/6)*Pi^2*Sqrt[2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2] + (1944*I)*2^(1/3)*3^
(5/6)*E^E^5*Pi^3*Sqrt[2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2] - 144*2^(1/3)*3^(5/6)*E^E^5*Log[5]*Sqrt[2
- 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2] + (189*I)*2^(1/3)*3^(5/6)*Pi*Log[5]*Sqrt[2 - 27*Pi^2 + (54*I)*Pi*L
og[5] + 27*Log[5]^2] + 5832*2^(1/3)*3^(5/6)*E^E^5*Pi^2*Log[5]*Sqrt[2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^
2] + 216*2^(1/3)*3^(5/6)*Log[5]^2*Sqrt[2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2] - (5832*I)*2^(1/3)*3^(5/6
)*E^E^5*Pi*Log[5]^2*Sqrt[2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2] - 1944*2^(1/3)*3^(5/6)*E^E^5*Log[5]^3*S
qrt[2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2] + (2*I)*6^(2/3)*(9*Pi - (9*I)*Log[5] - I*Sqrt[3*(2 - 27*Pi^2
 + (54*I)*Pi*Log[5] + 27*Log[5]^2)])^(1/3) + 72*6^(2/3)*E^E^5*Pi*(9*Pi - (9*I)*Log[5] - I*Sqrt[3*(2 - 27*Pi^2
+ (54*I)*Pi*Log[5] + 27*Log[5]^2)])^(1/3) - (81*I)*6^(2/3)*Pi^2*(9*Pi - (9*I)*Log[5] - I*Sqrt[3*(2 - 27*Pi^2 +
 (54*I)*Pi*Log[5] + 27*Log[5]^2)])^(1/3) - 972*6^(2/3)*E^E^5*Pi^3*(9*Pi - (9*I)*Log[5] - I*Sqrt[3*(2 - 27*Pi^2
 + (54*I)*Pi*Log[5] + 27*Log[5]^2)])^(1/3) + (729*I)*6^(2/3)*Pi^4*(9*Pi - (9*I)*Log[5] - I*Sqrt[3*(2 - 27*Pi^2
 + (54*I)*Pi*Log[5] + 27*Log[5]^2)])^(1/3) - (72*I)*6^(2/3)*E^E^5*Log[5]*(9*Pi - (9*I)*Log[5] - I*Sqrt[3*(2 -
27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2)])^(1/3) - 243*6^(2/3)*Pi*Log[5]*(9*Pi - (9*I)*Log[5] - I*Sqrt[3*(2 -
 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2)])^(1/3) + (2916*I)*6^(2/3)*E^E^5*Pi^2*Log[5]*(9*Pi - (9*I)*Log[5] -
 I*Sqrt[3*(2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2)])^(1/3) + 2187*6^(2/3)*Pi^3*Log[5]*(9*Pi - (9*I)*Log[
5] - I*Sqrt[3*(2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2)])^(1/3) + (162*I)*6^(2/3)*Log[5]^2*(9*Pi - (9*I)*
Log[5] - I*Sqrt[3*(2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2)])^(1/3) + 2916*6^(2/3)*E^E^5*Pi*Log[5]^2*(9*P
i - (9*I)*Log[5] - I*Sqrt[3*(2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2)])^(1/3) - (2187*I)*6^(2/3)*Pi^2*Log
[5]^2*(9*Pi - (9*I)*Log[5] - I*Sqrt[3*(2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2)])^(1/3) - (972*I)*6^(2/3)
*E^E^5*Log[5]^3*(9*Pi - (9*I)*Log[5] - I*Sqrt[3*(2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2)])^(1/3) - 729*6
^(2/3)*Pi*Log[5]^3*(9*Pi - (9*I)*Log[5] - I*Sqrt[3*(2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2)])^(1/3) - (2
4*I)*2^(2/3)*3^(1/6)*E^E^5*Sqrt[2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2]*(9*Pi - (9*I)*Log[5] - I*Sqrt[3*
(2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2)])^(1/3) - 18*2^(2/3)*3^(1/6)*Pi*Sqrt[2 - 27*Pi^2 + (54*I)*Pi*Lo
g[5] + 27*Log[5]^2]*(9*Pi - (9*I)*Log[5] - I*Sqrt[3*(2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2)])^(1/3) + (
324*I)*2^(2/3)*3^(1/6)*E^E^5*Pi^2*Sqrt[2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2]*(9*Pi - (9*I)*Log[5] - I*
Sqrt[3*(2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2)])^(1/3) + 243*2^(2/3)*3^(1/6)*Pi^3*Sqrt[2 - 27*Pi^2 + (5
4*I)*Pi*Log[5] + 27*Log[5]^2]*(9*Pi - (9*I)*Log[5] - I*Sqrt[3*(2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2)])
^(1/3) + (54*I)*2^(2/3)*3^(1/6)*Log[5]*Sqrt[2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2]*(9*Pi - (9*I)*Log[5]
 - I*Sqrt[3*(2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2)])^(1/3) + 648*2^(2/3)*3^(1/6)*E^E^5*Pi*Log[5]*Sqrt[
2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2]*(9*Pi - (9*I)*Log[5] - I*Sqrt[3*(2 - 27*Pi^2 + (54*I)*Pi*Log[5]
+ 27*Log[5]^2)])^(1/3) - (486*I)*2^(2/3)*3^(1/6)*Pi^2*Log[5]*Sqrt[2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2
]*(9*Pi - (9*I)*Log[5] - I*Sqrt[3*(2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2)])^(1/3) - (324*I)*2^(2/3)*3^(
1/6)*E^E^5*Log[5]^2*Sqrt[2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2]*(9*Pi - (9*I)*Log[5] - I*Sqrt[3*(2 - 27
*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2)])^(1/3) - 243*2^(2/3)*3^(1/6)*Pi*Log[5]^2*Sqrt[2 - 27*Pi^2 + (54*I)*Pi
*Log[5] + 27*Log[5]^2]*(9*Pi - (9*I)*Log[5] - I*Sqrt[3*(2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2)])^(1/3)
+ (18*I)*Pi*(9*Pi - (9*I)*Log[5] - I*Sqrt[3*(2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2)])^(2/3) - (243*I)*P
i^3*(9*Pi - (9*I)*Log[5] - I*Sqrt[3*(2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2)])^(2/3) + 18*Log[5]*(9*Pi -
 (9*I)*Log[5] - I*Sqrt[3*(2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2)])^(2/3) - 486*Pi^2*Log[5]*(9*Pi - (9*I
)*Log[5] - I*Sqrt[3*(2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2)])^(2/3) + (243*I)*Pi*Log[5]^2*(9*Pi - (9*I)
*Log[5] - I*Sqrt[3*(2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2)])^(2/3) + 2*Sqrt[3*(2 - 27*Pi^2 + (54*I)*Pi*
Log[5] + 27*Log[5]^2)]*(9*Pi - (9*I)*Log[5] - I*Sqrt[3*(2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2)])^(2/3)
- 27*Pi^2*Sqrt[3*(2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2)]*(9*Pi - (9*I)*Log[5] - I*Sqrt[3*(2 - 27*Pi^2
+ (54*I)*Pi*Log[5] + 27*Log[5]^2)])^(2/3) + (27*I)*Pi*Log[5]*Sqrt[3*(2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5
]^2)]*(9*Pi - (9*I)*Log[5] - I*Sqrt[3*(2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2)])^(2/3) - 24*6^(1/3)*Log[
125] + 729*6^(1/3)*Pi^2*Log[125] - (1458*I)*6^(1/3)*Pi*Log[5]*Log[125] - 729*6^(1/3)*Log[5]^2*Log[125] - (81*I
)*2^(1/3)*3^(5/6)*Pi*Sqrt[2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2]*Log[125] - 81*2^(1/3)*3^(5/6)*Log[5]*S
qrt[2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2]*Log[125] + 27*6^(2/3)*Pi*(9*Pi - (9*I)*Log[5] - I*Sqrt[3*(2
- 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2)])^(1/3)*Log[125] + 243*6^(2/3)*Pi^3*(9*Pi - (9*I)*Log[5] - I*Sqrt[
3*(2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2)])^(1/3)*Log[125] - (27*I)*6^(2/3)*Log[5]*(9*Pi - (9*I)*Log[5]
 - I*Sqrt[3*(2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2)])^(1/3)*Log[125] - (729*I)*6^(2/3)*Pi^2*Log[5]*(9*P
i - (9*I)*Log[5] - I*Sqrt[3*(2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2)])^(1/3)*Log[125] - 729*6^(2/3)*Pi*L
og[5]^2*(9*Pi - (9*I)*Log[5] - I*Sqrt[3*(2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2)])^(1/3)*Log[125] + (243
*I)*6^(2/3)*Log[5]^3*(9*Pi - (9*I)*Log[5] - I*Sqrt[3*(2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2)])^(1/3)*Lo
g[125] - (12*I)*2^(2/3)*3^(1/6)*Sqrt[2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2]*(9*Pi - (9*I)*Log[5] - I*Sq
rt[3*(2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2)])^(1/3)*Log[125] - (81*I)*2^(2/3)*3^(1/6)*Pi^2*Sqrt[2 - 27
*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2]*(9*Pi - (9*I)*Log[5] - I*Sqrt[3*(2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*L
og[5]^2)])^(1/3)*Log[125] - 162*2^(2/3)*3^(1/6)*Pi*Log[5]*Sqrt[2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2]*(
9*Pi - (9*I)*Log[5] - I*Sqrt[3*(2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2)])^(1/3)*Log[125] + (81*I)*2^(2/3
)*3^(1/6)*Log[5]^2*Sqrt[2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2]*(9*Pi - (9*I)*Log[5] - I*Sqrt[3*(2 - 27*
Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2)])^(1/3)*Log[125] - 81*Pi^2*(9*Pi - (9*I)*Log[5] - I*Sqrt[3*(2 - 27*Pi^2
 + (54*I)*Pi*Log[5] + 27*Log[5]^2)])^(2/3)*Log[125] + (162*I)*Pi*Log[5]*(9*Pi - (9*I)*Log[5] - I*Sqrt[3*(2 - 2
7*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2)])^(2/3)*Log[125] + 81*Log[5]^2*(9*Pi - (9*I)*Log[5] - I*Sqrt[3*(2 - 2
7*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2)])^(2/3)*Log[125] + (9*I)*Pi*Sqrt[3*(2 - 27*Pi^2 + (54*I)*Pi*Log[5] +
27*Log[5]^2)]*(9*Pi - (9*I)*Log[5] - I*Sqrt[3*(2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2)])^(2/3)*Log[125]
+ 9*Log[5]*Sqrt[3*(2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2)]*(9*Pi - (9*I)*Log[5] - I*Sqrt[3*(2 - 27*Pi^2
 + (54*I)*Pi*Log[5] + 27*Log[5]^2)])^(2/3)*Log[125]) + 2*6^(1/3)*((9*I)*Pi + 9*Log[5] + Sqrt[6 - 81*Pi^2 + (16
2*I)*Pi*Log[5] + 81*Log[5]^2] + I*(54*Pi - (6*I)*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^
2]))^(1/3))*(-12*6^(1/3) + 486*6^(1/3)*Pi^2 - 4374*6^(1/3)*Pi^4 - (810*I)*6^(1/3)*Pi*Log[5] + (13122*I)*6^(1/3
)*Pi^3*Log[5] - 324*6^(1/3)*Log[5]^2 + 13122*6^(1/3)*Pi^2*Log[5]^2 - (4374*I)*6^(1/3)*Pi*Log[5]^3 - (36*I)*2^(
1/3)*3^(5/6)*Pi*Sqrt[2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2] + (486*I)*2^(1/3)*3^(5/6)*Pi^3*Sqrt[2 - 27*
Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2] - 36*2^(1/3)*3^(5/6)*Log[5]*Sqrt[2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Lo
g[5]^2] + 972*2^(1/3)*3^(5/6)*Pi^2*Log[5]*Sqrt[2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2] - (486*I)*2^(1/3)
*3^(5/6)*Pi*Log[5]^2*Sqrt[2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2] + 18*6^(2/3)*Pi*(9*Pi - (9*I)*Log[5] -
 I*Sqrt[3*(2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2)])^(1/3) - 243*6^(2/3)*Pi^3*(9*Pi - (9*I)*Log[5] - I*S
qrt[3*(2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2)])^(1/3) - (18*I)*6^(2/3)*Log[5]*(9*Pi - (9*I)*Log[5] - I*
Sqrt[3*(2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2)])^(1/3) + (486*I)*6^(2/3)*Pi^2*Log[5]*(9*Pi - (9*I)*Log[
5] - I*Sqrt[3*(2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2)])^(1/3) + 243*6^(2/3)*Pi*Log[5]^2*(9*Pi - (9*I)*L
og[5] - I*Sqrt[3*(2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2)])^(1/3) - (6*I)*2^(2/3)*3^(1/6)*Sqrt[2 - 27*Pi
^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2]*(9*Pi - (9*I)*Log[5] - I*Sqrt[3*(2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[
5]^2)])^(1/3) + (81*I)*2^(2/3)*3^(1/6)*Pi^2*Sqrt[2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2]*(9*Pi - (9*I)*L
og[5] - I*Sqrt[3*(2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2)])^(1/3) - (216*I)*E^E^5*Pi*(9*Pi - (9*I)*Log[5
] - I*Sqrt[3*(2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2)])^(2/3) + (2916*I)*E^E^5*Pi^3*(9*Pi - (9*I)*Log[5]
 - I*Sqrt[3*(2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2)])^(2/3) - 216*E^E^5*Log[5]*(9*Pi - (9*I)*Log[5] - I
*Sqrt[3*(2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2)])^(2/3) + (324*I)*Pi*Log[5]*(9*Pi - (9*I)*Log[5] - I*Sq
rt[3*(2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2)])^(2/3) + 8748*E^E^5*Pi^2*Log[5]*(9*Pi - (9*I)*Log[5] - I*
Sqrt[3*(2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2)])^(2/3) + 324*Log[5]^2*(9*Pi - (9*I)*Log[5] - I*Sqrt[3*(
2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2)])^(2/3) - (8748*I)*E^E^5*Pi*Log[5]^2*(9*Pi - (9*I)*Log[5] - I*Sq
rt[3*(2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2)])^(2/3) - 2916*E^E^5*Log[5]^3*(9*Pi - (9*I)*Log[5] - I*Sqr
t[3*(2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2)])^(2/3) - 24*E^E^5*Sqrt[3*(2 - 27*Pi^2 + (54*I)*Pi*Log[5] +
 27*Log[5]^2)]*(9*Pi - (9*I)*Log[5] - I*Sqrt[3*(2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2)])^(2/3) + 324*E^
E^5*Pi^2*Sqrt[3*(2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2)]*(9*Pi - (9*I)*Log[5] - I*Sqrt[3*(2 - 27*Pi^2 +
 (54*I)*Pi*Log[5] + 27*Log[5]^2)])^(2/3) + 36*Log[5]*Sqrt[3*(2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2)]*(9
*Pi - (9*I)*Log[5] - I*Sqrt[3*(2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2)])^(2/3) - (648*I)*E^E^5*Pi*Log[5]
*Sqrt[3*(2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2)]*(9*Pi - (9*I)*Log[5] - I*Sqrt[3*(2 - 27*Pi^2 + (54*I)*
Pi*Log[5] + 27*Log[5]^2)])^(2/3) - 324*E^E^5*Log[5]^2*Sqrt[3*(2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2)]*(
9*Pi - (9*I)*Log[5] - I*Sqrt[3*(2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2)])^(2/3) - (54*I)*6^(1/3)*Pi*Log[
125] + (1458*I)*6^(1/3)*Pi^3*Log[125] - 54*6^(1/3)*Log[5]*Log[125] + 4374*6^(1/3)*Pi^2*Log[5]*Log[125] - (4374
*I)*6^(1/3)*Pi*Log[5]^2*Log[125] - 1458*6^(1/3)*Log[5]^3*Log[125] + 162*2^(1/3)*3^(5/6)*Pi^2*Sqrt[2 - 27*Pi^2
+ (54*I)*Pi*Log[5] + 27*Log[5]^2]*Log[125] - (324*I)*2^(1/3)*3^(5/6)*Pi*Log[5]*Sqrt[2 - 27*Pi^2 + (54*I)*Pi*Lo
g[5] + 27*Log[5]^2]*Log[125] - 162*2^(1/3)*3^(5/6)*Log[5]^2*Sqrt[2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2]
*Log[125] + (81*I)*6^(2/3)*Pi^2*(9*Pi - (9*I)*Log[5] - I*Sqrt[3*(2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2)
])^(1/3)*Log[125] - (81*I)*6^(2/3)*Log[5]^2*(9*Pi - (9*I)*Log[5] - I*Sqrt[3*(2 - 27*Pi^2 + (54*I)*Pi*Log[5] +
27*Log[5]^2)])^(1/3)*Log[125] - (27*I)*2^(2/3)*3^(1/6)*Log[5]*Sqrt[2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^
2]*(9*Pi - (9*I)*Log[5] - I*Sqrt[3*(2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2)])^(1/3)*Log[125] - (108*I)*P
i*(9*Pi - (9*I)*Log[5] - I*Sqrt[3*(2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2)])^(2/3)*Log[125] - 108*Log[5]
*(9*Pi - (9*I)*Log[5] - I*Sqrt[3*(2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2)])^(2/3)*Log[125] - 12*Sqrt[3*(
2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2)]*(9*Pi - (9*I)*Log[5] - I*Sqrt[3*(2 - 27*Pi^2 + (54*I)*Pi*Log[5]
 + 27*Log[5]^2)])^(2/3)*Log[125] + 18*2^(2/3)*3^(1/6)*Pi*Sqrt[2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2]*(9
*Pi - (9*I)*Log[5] - I*Sqrt[3*(2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2)])^(1/3)*Log[1953125] + 9*6^(2/3)*
Pi*(9*Pi - (9*I)*Log[5] - I*Sqrt[3*(2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2)])^(1/3)*Log[125]*Log[3814697
265625])))/((E^E^5 + 2*E^(3*E^5) + I*Pi + Log[5])*(9*Pi - I*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] +
 81*Log[5]^2]))^(1/3)*(2*6^(1/3) + 3*6^(2/3)*Pi*(9*Pi - I*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 8
1*Log[5]^2]))^(1/3) - (3*I)*6^(2/3)*Log[5]*(9*Pi - I*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log
[5]^2]))^(1/3) - I*2^(2/3)*3^(1/6)*Sqrt[2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2]*(9*Pi - I*(9*Log[5] + Sq
rt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(1/3) + 2*(9*Pi - I*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)
*Pi*Log[5] + 81*Log[5]^2]))^(2/3))^2*Sqrt[-6^(2/3) + 27*6^(2/3)*Pi^2 - (54*I)*6^(2/3)*Pi*Log[5] - 27*6^(2/3)*L
og[5]^2 - 9*2^(2/3)*3^(1/6)*(I*Pi + Log[5])*Sqrt[2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2] - 18*Pi*(9*Pi -
 I*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(1/3) + (18*I)*Log[5]*(9*Pi - I*(9*Log[5]
 + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(1/3) + (2*I)*Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] +
81*Log[5]^2]*(9*Pi - I*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(1/3) + 6^(1/3)*(9*Pi
 - I*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(2/3)]*((-8*(6^(1/3) + (9*Pi - I*(9*Log
[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(2/3))^2)/(3*3^(1/3)*((9*Pi - I*(9*Log[5] + Sqrt[6
 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))/2)^(2/3)) - (4*(-6 + (6*6^(1/3))/(9*Pi - I*(9*Log[5] + Sqrt[6
- 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(2/3) + (54*Pi - (6*I)*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*P
i*Log[5] + 81*Log[5]^2]))^(2/3)))/9)*((-4*(6^(1/3) + (9*Pi - I*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5
] + 81*Log[5]^2]))^(2/3))^2)/(3*3^(1/3)*((9*Pi - I*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5
]^2]))/2)^(2/3)) + (16*(-6 + (6*6^(1/3))/(9*Pi - I*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5
]^2]))^(2/3) + (54*Pi - (6*I)*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(2/3)))/9)) +
(8*((-9*I)*Pi - 9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2])^(1/3)*(6^(2/3) - 12*E^E^5*((-9
*I)*Pi - 9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2])^(1/3) - 6^(1/3)*((-9*I)*Pi - 9*Log[5]
 + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2])^(2/3))*Log[6^(1/3) + 6^(2/3)*x*((-9*I)*Pi - 9*Log[5] +
 Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2])^(1/3) - ((-9*I)*Pi - 9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*
I)*Pi*Log[5] + 81*Log[5]^2])^(2/3)])/(3*(E^E^5 + 2*E^(3*E^5) + I*Pi + Log[5])*(2*6^(1/3) - (3*I)*6^(2/3)*Pi*((
-9*I)*Pi - 9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2])^(1/3) - 3*6^(2/3)*Log[5]*((-9*I)*Pi
 - 9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2])^(1/3) + 2^(2/3)*3^(1/6)*Sqrt[2 - 27*Pi^2 +
(54*I)*Pi*Log[5] + 27*Log[5]^2]*((-9*I)*Pi - 9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2])^(
1/3) - 2*((-9*I)*Pi - 9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2])^(2/3))) - (4*((9*I)*6^(1
/3)*Pi - 12*E^E^5*((-9*I)*Pi - 9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2])^(2/3) + 6^(1/3)
*(9*Log[5] - Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2] + (6*((-9*I)*Pi - 9*Log[5] + Sqrt[6 - 81*Pi^2
 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(1/3)))*Log[2*6^(1/3) - (3*I)*6^(2/3)*Pi*((-9*I)*Pi - 9*Log[5] + Sqrt[6
- 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2])^(1/3) - 3*6^(2/3)*Log[5]*((-9*I)*Pi - 9*Log[5] + Sqrt[6 - 81*Pi^
2 + (162*I)*Pi*Log[5] + 81*Log[5]^2])^(1/3) + 2^(2/3)*3^(1/6)*Sqrt[2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^
2]*((-9*I)*Pi - 9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2])^(1/3) + 2*((-9*I)*Pi - 9*Log[5
] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2])^(2/3) + 12*x^2*((-9*I)*Pi - 9*Log[5] + Sqrt[6 - 81*Pi
^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2])^(2/3) - 2*6^(1/3)*x*((9*I)*Pi + 9*Log[5] - Sqrt[6 - 81*Pi^2 + (162*I)*P
i*Log[5] + 81*Log[5]^2] + (6*((-9*I)*Pi - 9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(1/
3))])/(3*(E^E^5 + 2*E^(3*E^5) + I*Pi + Log[5])*(2*6^(1/3) - (3*I)*6^(2/3)*Pi*((-9*I)*Pi - 9*Log[5] + Sqrt[6 -
81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2])^(1/3) - 3*6^(2/3)*Log[5]*((-9*I)*Pi - 9*Log[5] + Sqrt[6 - 81*Pi^2
+ (162*I)*Pi*Log[5] + 81*Log[5]^2])^(1/3) + 2^(2/3)*3^(1/6)*Sqrt[2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2]
*((-9*I)*Pi - 9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2])^(1/3) - 2*((-9*I)*Pi - 9*Log[5]
+ Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2])^(2/3))) - (128*((9*I)*Pi + 9*Log[5] + Sqrt[6 - 81*Pi^2
+ (162*I)*Pi*Log[5] + 81*Log[5]^2])*(4*6^(1/3) + 1458*6^(1/3)*Pi^4 + 108*6^(1/3)*Log[5]^2 + 12*2^(1/3)*3^(5/6)
*Log[5]*Sqrt[2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2] + (6*I)*6^(2/3)*Log[5]*(9*Pi - I*(9*Log[5] + Sqrt[6
 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(1/3) + (2*I)*2^(2/3)*3^(1/6)*Sqrt[2 - 27*Pi^2 + (54*I)*Pi*Log
[5] + 27*Log[5]^2]*(9*Pi - I*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(1/3) - 108*Log
[5]^2*(9*Pi - I*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(2/3) + 4*E^E^5*(2 + 27*Log[
5]^2)*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2])*(9*Pi - I*(9*Log[5] + Sqrt[6 - 81*Pi^2
+ (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(2/3) - 81*Pi^3*((12*I)*E^E^5*(9*Pi - I*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (1
62*I)*Pi*Log[5] + 81*Log[5]^2]))^(2/3) + 6^(1/3)*((54*I)*Log[5] + (2*I)*Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] +
 81*Log[5]^2] - (54*Pi - (6*I)*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(1/3) + (6*I)
*Log[125])) + 18*6^(1/3)*Log[5]*Log[125] + 486*6^(1/3)*Log[5]^3*Log[125] + 54*2^(1/3)*3^(5/6)*Log[5]^2*Sqrt[2
- 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2]*Log[125] + (27*I)*6^(2/3)*Log[5]^2*(9*Pi - I*(9*Log[5] + Sqrt[6 -
81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(1/3)*Log[125] + (9*I)*2^(2/3)*3^(1/6)*Log[5]*Sqrt[2 - 27*Pi^2 +
(54*I)*Pi*Log[5] + 27*Log[5]^2]*(9*Pi - I*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(1
/3)*Log[125] + 36*Log[5]*(9*Pi - I*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(2/3)*Log
[125] - 27*Pi^2*(162*6^(1/3)*Log[5]^2 + 4*E^E^5*(27*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^
2])*(9*Pi - I*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(2/3) + 6*6^(1/3)*Log[5]*(2*Sq
rt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2] + I*(54*Pi - (6*I)*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi
*Log[5] + 81*Log[5]^2]))^(1/3) + 9*Log[125]) + 2^(1/3)*3^(1/6)*Sqrt[2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]
^2]*(I*(18*Pi - (2*I)*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(1/3) + 2*3^(2/3)*Log[
125]) + 6^(1/3)*(6 + I*(54*Pi - (6*I)*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(1/3)*
Log[125])) + 3*Pi*((486*I)*6^(1/3)*Log[5]^3 + (4*I)*2^(1/3)*3^(5/6)*Sqrt[2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*L
og[5]^2] - 2*6^(2/3)*(9*Pi - I*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(1/3) + (12*I
)*E^E^5*(2 + 81*Log[5]^2 + 6*Log[5]*Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2])*(9*Pi - I*(9*Log[5] +
 Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(2/3) + 27*6^(1/3)*Log[5]^2*((2*I)*Sqrt[6 - 81*Pi^2 + (
162*I)*Pi*Log[5] + 81*Log[5]^2] - (54*Pi - (6*I)*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^
2]))^(1/3) + (18*I)*Log[125]) + (6*I)*6^(1/3)*Log[125] + (12*I)*(9*Pi - I*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*
I)*Pi*Log[5] + 81*Log[5]^2]))^(2/3)*Log[125] - (18*I)*Log[5]*(2*(9*Pi - I*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*
I)*Pi*Log[5] + 81*Log[5]^2]))^(2/3) - 6^(1/3)*(5 + 2*Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]*Log[1
25])) - 2*2^(2/3)*3^(1/6)*Sqrt[2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2]*(9*Pi - I*(9*Log[5] + Sqrt[6 - 81
*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(1/3)*Log[1953125] - 6^(2/3)*(9*Pi - I*(9*Log[5] + Sqrt[6 - 81*Pi^2
 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(1/3)*Log[125]*Log[3814697265625]))*Log[(6*I)*x*(9*Pi - I*(9*Log[5] + Sq
rt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(1/3) + 6^(1/3)*(6^(1/3) + (9*Pi - I*(9*Log[5] + Sqrt[6 -
81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(2/3))])/((E^E^5 + 2*E^(3*E^5) + I*Pi + Log[5])*(2*6^(1/3) + 3*6^
(2/3)*Pi*(9*Pi - I*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(1/3) - (3*I)*6^(2/3)*Log
[5]*(9*Pi - I*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(1/3) - I*2^(2/3)*3^(1/6)*Sqrt
[2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2]*(9*Pi - I*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81
*Log[5]^2]))^(1/3) - 4*(9*Pi - I*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(2/3))*(2*6
^(1/3) + 3*6^(2/3)*Pi*(9*Pi - I*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(1/3) - (3*I
)*6^(2/3)*Log[5]*(9*Pi - I*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(1/3) - I*2^(2/3)
*3^(1/6)*Sqrt[2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2]*(9*Pi - I*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*P
i*Log[5] + 81*Log[5]^2]))^(1/3) + 2*(9*Pi - I*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2])
)^(2/3))^3) + (64*((9*I)*Pi + 9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2])*(4*6^(1/3) + 145
8*6^(1/3)*Pi^4 + 108*6^(1/3)*Log[5]^2 + 12*2^(1/3)*3^(5/6)*Log[5]*Sqrt[2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log
[5]^2] + (6*I)*6^(2/3)*Log[5]*(9*Pi - I*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(1/3
) + (2*I)*2^(2/3)*3^(1/6)*Sqrt[2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2]*(9*Pi - I*(9*Log[5] + Sqrt[6 - 81
*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(1/3) - 108*Log[5]^2*(9*Pi - I*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*
I)*Pi*Log[5] + 81*Log[5]^2]))^(2/3) - 12*Log[5]*Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]*(9*Pi - I*
(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(2/3) + 4*E^E^5*(2 + 27*Log[5]^2)*(9*Log[5]
+ Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2])*(9*Pi - I*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log
[5] + 81*Log[5]^2]))^(2/3) + 18*6^(1/3)*Log[5]*Log[125] + 486*6^(1/3)*Log[5]^3*Log[125] + 54*2^(1/3)*3^(5/6)*L
og[5]^2*Sqrt[2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2]*Log[125] + (27*I)*6^(2/3)*Log[5]^2*(9*Pi - I*(9*Log
[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(1/3)*Log[125] + (9*I)*2^(2/3)*3^(1/6)*Log[5]*Sqrt
[2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2]*(9*Pi - I*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81
*Log[5]^2]))^(1/3)*Log[125] + 36*Log[5]*(9*Pi - I*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]
^2]))^(2/3)*Log[125] + 4*Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]*(9*Pi - I*(9*Log[5] + Sqrt[6 - 81
*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(2/3)*Log[125] - 81*Pi^3*((12*I)*E^E^5*(9*Pi - I*(9*Log[5] + Sqrt[6
 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(2/3) + I*6^(1/3)*(54*Log[5] + 2*Sqrt[6 - 81*Pi^2 + (162*I)*Pi
*Log[5] + 81*Log[5]^2] + I*(54*Pi - (6*I)*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(1
/3) + 6*Log[125])) - 27*Pi^2*(162*6^(1/3)*Log[5]^2 + 4*E^E^5*(27*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5]
 + 81*Log[5]^2])*(9*Pi - I*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(2/3) + 6*6^(1/3)
*Log[5]*(2*Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2] + I*(54*Pi - (6*I)*(9*Log[5] + Sqrt[6 - 81*Pi^2
 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(1/3) + 9*Log[125]) + 2^(1/3)*3^(1/6)*Sqrt[2 - 27*Pi^2 + (54*I)*Pi*Log[5
] + 27*Log[5]^2]*(I*(18*Pi - (2*I)*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(1/3) + 2
*3^(2/3)*Log[125]) + 6^(1/3)*(6 + I*(54*Pi - (6*I)*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5
]^2]))^(1/3)*Log[125])) + 3*Pi*((486*I)*6^(1/3)*Log[5]^3 + (4*I)*2^(1/3)*3^(5/6)*Sqrt[2 - 27*Pi^2 + (54*I)*Pi*
Log[5] + 27*Log[5]^2] - 2*6^(2/3)*(9*Pi - I*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^
(1/3) + (12*I)*E^E^5*(2 + 81*Log[5]^2 + 6*Log[5]*Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2])*(9*Pi -
I*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(2/3) + 27*6^(1/3)*Log[5]^2*((2*I)*Sqrt[6
- 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2] - (54*Pi - (6*I)*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5]
 + 81*Log[5]^2]))^(1/3) + (18*I)*Log[125]) + (6*I)*6^(1/3)*Log[125] + (12*I)*(9*Pi - I*(9*Log[5] + Sqrt[6 - 81
*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(2/3)*Log[125] - (18*I)*Log[5]*(2*(9*Pi - I*(9*Log[5] + Sqrt[6 - 81
*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(2/3) - 6^(1/3)*(5 + 2*Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Lo
g[5]^2]*Log[125])) - 2*2^(2/3)*3^(1/6)*Sqrt[2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2]*(9*Pi - I*(9*Log[5]
+ Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(1/3)*Log[1953125] - 6^(2/3)*(9*Pi - I*(9*Log[5] + Sqr
t[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(1/3)*Log[125]*Log[3814697265625]))*Log[2*6^(1/3) + 3*6^(2/
3)*Pi*(9*Pi - I*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(1/3) - (3*I)*6^(2/3)*Log[5]
*(9*Pi - I*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(1/3) - I*2^(2/3)*3^(1/6)*Sqrt[2
- 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2]*(9*Pi - I*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Lo
g[5]^2]))^(1/3) - 2*(9*Pi - I*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(2/3) - 12*x^2
*(9*Pi - I*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(2/3) - 2*6^(1/3)*x*((9*I)*Pi + 9
*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2] + I*(54*Pi - (6*I)*(9*Log[5] + Sqrt[6 - 81*Pi^2
+ (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(1/3))])/((E^E^5 + 2*E^(3*E^5) + I*Pi + Log[5])*(2*6^(1/3) + 3*6^(2/3)*Pi
*(9*Pi - I*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(1/3) - (3*I)*6^(2/3)*Log[5]*(9*P
i - I*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(1/3) - I*2^(2/3)*3^(1/6)*Sqrt[2 - 27*
Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2]*(9*Pi - I*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^
2]))^(1/3) - 4*(9*Pi - I*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(2/3))*(2*6^(1/3) +
 3*6^(2/3)*Pi*(9*Pi - I*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(1/3) - (3*I)*6^(2/3
)*Log[5]*(9*Pi - I*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(1/3) - I*2^(2/3)*3^(1/6)
*Sqrt[2 - 27*Pi^2 + (54*I)*Pi*Log[5] + 27*Log[5]^2]*(9*Pi - I*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5]
 + 81*Log[5]^2]))^(1/3) + 2*(9*Pi - I*(9*Log[5] + Sqrt[6 - 81*Pi^2 + (162*I)*Pi*Log[5] + 81*Log[5]^2]))^(2/3))
^3)

Rule 210

Int[((a_) + (b_.)*(x_)^2)^(-1), x_Symbol] :> Simp[(-(Rt[-a, 2]*Rt[-b, 2])^(-1))*ArcTan[Rt[-b, 2]*(x/Rt[-a, 2])
], x] /; FreeQ[{a, b}, x] && PosQ[a/b] && (LtQ[a, 0] || LtQ[b, 0])

Rule 212

Int[((a_) + (b_.)*(x_)^2)^(-1), x_Symbol] :> Simp[(1/(Rt[a, 2]*Rt[-b, 2]))*ArcTanh[Rt[-b, 2]*(x/Rt[a, 2])], x]
 /; FreeQ[{a, b}, x] && NegQ[a/b] && (GtQ[a, 0] || LtQ[b, 0])

Rule 632

Int[((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(-1), x_Symbol] :> Dist[-2, Subst[Int[1/Simp[b^2 - 4*a*c - x^2, x], x]
, x, b + 2*c*x], x] /; FreeQ[{a, b, c}, x] && NeQ[b^2 - 4*a*c, 0]

Rule 642

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 648

Int[((d_.) + (e_.)*(x_))/((a_) + (b_.)*(x_) + (c_.)*(x_)^2), x_Symbol] :> Dist[(2*c*d - b*e)/(2*c), Int[1/(a +
 b*x + c*x^2), x], x] + Dist[e/(2*c), Int[(b + 2*c*x)/(a + b*x + c*x^2), x], x] /; FreeQ[{a, b, c, d, e}, x] &
& NeQ[2*c*d - b*e, 0] && NeQ[b^2 - 4*a*c, 0] &&  !NiceSqrtQ[b^2 - 4*a*c]

Rule 814

Int[(((d_.) + (e_.)*(x_))^(m_)*((f_.) + (g_.)*(x_)))/((a_.) + (b_.)*(x_) + (c_.)*(x_)^2), x_Symbol] :> Int[Exp
andIntegrand[(d + e*x)^m*((f + g*x)/(a + b*x + c*x^2)), x], x] /; FreeQ[{a, b, c, d, e, f, g}, x] && NeQ[b^2 -
 4*a*c, 0] && NeQ[c*d^2 - b*d*e + a*e^2, 0] && IntegerQ[m]

Rule 836

Int[((d_.) + (e_.)*(x_))^(m_)*((f_.) + (g_.)*(x_))*((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_), x_Symbol] :> Simp
[(d + e*x)^(m + 1)*(f*(b*c*d - b^2*e + 2*a*c*e) - a*g*(2*c*d - b*e) + c*(f*(2*c*d - b*e) - g*(b*d - 2*a*e))*x)
*((a + b*x + c*x^2)^(p + 1)/((p + 1)*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2))), x] + Dist[1/((p + 1)*(b^2 - 4*a*
c)*(c*d^2 - b*d*e + a*e^2)), Int[(d + e*x)^m*(a + b*x + c*x^2)^(p + 1)*Simp[f*(b*c*d*e*(2*p - m + 2) + b^2*e^2
*(p + m + 2) - 2*c^2*d^2*(2*p + 3) - 2*a*c*e^2*(m + 2*p + 3)) - g*(a*e*(b*e - 2*c*d*m + b*e*m) - b*d*(3*c*d -
b*e + 2*c*d*p - b*e*p)) + c*e*(g*(b*d - 2*a*e) - f*(2*c*d - b*e))*(m + 2*p + 4)*x, x], x], x] /; FreeQ[{a, b,
c, d, e, f, g, m}, x] && NeQ[b^2 - 4*a*c, 0] && NeQ[c*d^2 - b*d*e + a*e^2, 0] && LtQ[p, -1] && (IntegerQ[m] ||
 IntegerQ[p] || IntegersQ[2*m, 2*p])

Rule 2099

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]

Rule 2104

Int[((e_.) + (f_.)*(x_))^(m_.)*((a_) + (b_.)*(x_) + (d_.)*(x_)^3)^(p_), x_Symbol] :> With[{r = Rt[-9*a*d^2 + S
qrt[3]*d*Sqrt[4*b^3*d + 27*a^2*d^2], 3]}, Dist[1/d^(2*p), Int[(e + f*x)^m*Simp[18^(1/3)*b*(d/(3*r)) - r/18^(1/
3) + d*x, x]^p*Simp[b*(d/3) + 12^(1/3)*b^2*(d^2/(3*r^2)) + r^2/(3*12^(1/3)) - d*(2^(1/3)*b*(d/(3^(1/3)*r)) - r
/18^(1/3))*x + d^2*x^2, x]^p, x], x]] /; FreeQ[{a, b, d, e, f, m}, x] && NeQ[4*b^3 + 27*a^2*d, 0] && ILtQ[p, 0
]

Rule 2126

Int[(Pm_)*(Qn_)^(p_), x_Symbol] :> With[{m = Expon[Pm, x], n = Expon[Qn, x]}, Simp[Coeff[Pm, x, m]*(Qn^(p + 1)
/(n*(p + 1)*Coeff[Qn, x, n])), x] + Dist[1/(n*Coeff[Qn, x, n]), Int[ExpandToSum[n*Coeff[Qn, x, n]*Pm - Coeff[P
m, x, m]*D[Qn, x], x]*Qn^p, x], x] /; EqQ[m, n - 1]] /; FreeQ[p, x] && PolyQ[Pm, x] && PolyQ[Qn, x] && NeQ[p,
-1]

Rubi steps Aborted

Mathematica [A] (verified)

Time = 0.28 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.00 \[ \int \frac {8 x+32 x^3+e^{e^5} \left (-4-24 x^2\right )+4 (i \pi +\log (5))}{x^4+4 x^6+4 x^8+\left (2 x^3+4 x^5\right ) (i \pi +\log (5))+x^2 (i \pi +\log (5))^2+e^{2 e^5} \left (x^2+4 x^4+4 x^6+\left (2 x+4 x^3\right ) (i \pi +\log (5))+(i \pi +\log (5))^2\right )+e^{e^5} \left (-2 x^3-8 x^5-8 x^7+\left (-4 x^2-8 x^4\right ) (i \pi +\log (5))-2 x (i \pi +\log (5))^2\right )} \, dx=\frac {4}{\left (e^{e^5}-x\right ) \left (i \pi +x+2 x^3+\log (5)\right )} \]

[In]

Integrate[(8*x + 32*x^3 + E^E^5*(-4 - 24*x^2) + 4*(I*Pi + Log[5]))/(x^4 + 4*x^6 + 4*x^8 + (2*x^3 + 4*x^5)*(I*P
i + Log[5]) + x^2*(I*Pi + Log[5])^2 + E^(2*E^5)*(x^2 + 4*x^4 + 4*x^6 + (2*x + 4*x^3)*(I*Pi + Log[5]) + (I*Pi +
 Log[5])^2) + E^E^5*(-2*x^3 - 8*x^5 - 8*x^7 + (-4*x^2 - 8*x^4)*(I*Pi + Log[5]) - 2*x*(I*Pi + Log[5])^2)),x]

[Out]

4/((E^E^5 - x)*(I*Pi + x + 2*x^3 + Log[5]))

Maple [B] (verified)

Both result and optimal contain complex but leaf count of result is larger than twice the leaf count of optimal. 57 vs. \(2 (26 ) = 52\).

Time = 6.38 (sec) , antiderivative size = 58, normalized size of antiderivative = 2.00

method result size
risch \(-\frac {4 i}{-2 i {\mathrm e}^{{\mathrm e}^{5}} x^{3}+2 i x^{4}-i \ln \left (5\right ) {\mathrm e}^{{\mathrm e}^{5}}+i x \ln \left (5\right )-i {\mathrm e}^{{\mathrm e}^{5}} x +i x^{2}+\pi \,{\mathrm e}^{{\mathrm e}^{5}}-\pi x}\) \(58\)
parallelrisch \(-\frac {4 i}{-2 i {\mathrm e}^{{\mathrm e}^{5}} x^{3}+2 i x^{4}-i \ln \left (5\right ) {\mathrm e}^{{\mathrm e}^{5}}+i x \ln \left (5\right )-i {\mathrm e}^{{\mathrm e}^{5}} x +i x^{2}+\pi \,{\mathrm e}^{{\mathrm e}^{5}}-\pi x}\) \(58\)
norman \(\frac {8 x^{3}+4 x -4 i \pi +4 \ln \left (5\right )}{\left ({\mathrm e}^{{\mathrm e}^{5}}-x \right ) \left (4 x^{6}+4 x^{3} \ln \left (5\right )+4 x^{4}+\pi ^{2}+\ln \left (5\right )^{2}+2 x \ln \left (5\right )+x^{2}\right )}\) \(63\)
gosper \(-\frac {4 \left (-6 x^{2} {\mathrm e}^{{\mathrm e}^{5}}+8 x^{3}+i \pi +\ln \left (5\right )-{\mathrm e}^{{\mathrm e}^{5}}+2 x \right ) \left (-2 i x^{3}-i \ln \left (5\right )-i x +\pi \right )}{\left (-4 \,{\mathrm e}^{{\mathrm e}^{5}} x^{6}+4 x^{7}+4 i x^{4} \pi +2 i x^{2} \pi -4 \ln \left (5\right ) {\mathrm e}^{{\mathrm e}^{5}} x^{3}+4 x^{4} \ln \left (5\right )-4 \,{\mathrm e}^{{\mathrm e}^{5}} x^{4}+4 x^{5}-2 i \pi \,{\mathrm e}^{{\mathrm e}^{5}} x +2 i x \ln \left (5\right ) \pi -4 i \pi \,{\mathrm e}^{{\mathrm e}^{5}} x^{3}-2 i \pi \ln \left (5\right ) {\mathrm e}^{{\mathrm e}^{5}}+\pi ^{2} {\mathrm e}^{{\mathrm e}^{5}}-x \,\pi ^{2}-\ln \left (5\right )^{2} {\mathrm e}^{{\mathrm e}^{5}}+x \ln \left (5\right )^{2}-2 \ln \left (5\right ) {\mathrm e}^{{\mathrm e}^{5}} x +2 x^{2} \ln \left (5\right )-x^{2} {\mathrm e}^{{\mathrm e}^{5}}+x^{3}\right ) \left (6 i {\mathrm e}^{{\mathrm e}^{5}} x^{2}-8 i x^{3}+\pi +i {\mathrm e}^{{\mathrm e}^{5}}-i \ln \left (5\right )-2 i x \right )}\) \(230\)

[In]

int(((-24*x^2-4)*exp(exp(5))+4*ln(5)+4*I*Pi+32*x^3+8*x)/(((ln(5)+I*Pi)^2+(4*x^3+2*x)*(ln(5)+I*Pi)+4*x^6+4*x^4+
x^2)*exp(exp(5))^2+(-2*x*(ln(5)+I*Pi)^2+(-8*x^4-4*x^2)*(ln(5)+I*Pi)-8*x^7-8*x^5-2*x^3)*exp(exp(5))+x^2*(ln(5)+
I*Pi)^2+(4*x^5+2*x^3)*(ln(5)+I*Pi)+4*x^8+4*x^6+x^4),x,method=_RETURNVERBOSE)

[Out]

-4*I/(-2*I*exp(exp(5))*x^3+2*I*x^4-I*ln(5)*exp(exp(5))+I*x*ln(5)-I*exp(exp(5))*x+I*x^2+Pi*exp(exp(5))-Pi*x)

Fricas [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 38, normalized size of antiderivative = 1.31 \[ \int \frac {8 x+32 x^3+e^{e^5} \left (-4-24 x^2\right )+4 (i \pi +\log (5))}{x^4+4 x^6+4 x^8+\left (2 x^3+4 x^5\right ) (i \pi +\log (5))+x^2 (i \pi +\log (5))^2+e^{2 e^5} \left (x^2+4 x^4+4 x^6+\left (2 x+4 x^3\right ) (i \pi +\log (5))+(i \pi +\log (5))^2\right )+e^{e^5} \left (-2 x^3-8 x^5-8 x^7+\left (-4 x^2-8 x^4\right ) (i \pi +\log (5))-2 x (i \pi +\log (5))^2\right )} \, dx=-\frac {4}{2 \, x^{4} + i \, \pi x + x^{2} - {\left (i \, \pi + 2 \, x^{3} + x + \log \left (5\right )\right )} e^{\left (e^{5}\right )} + x \log \left (5\right )} \]

[In]

integrate(((-24*x^2-4)*exp(exp(5))+4*log(5)+4*I*pi+32*x^3+8*x)/(((log(5)+I*pi)^2+(4*x^3+2*x)*(log(5)+I*pi)+4*x
^6+4*x^4+x^2)*exp(exp(5))^2+(-2*x*(log(5)+I*pi)^2+(-8*x^4-4*x^2)*(log(5)+I*pi)-8*x^7-8*x^5-2*x^3)*exp(exp(5))+
x^2*(log(5)+I*pi)^2+(4*x^5+2*x^3)*(log(5)+I*pi)+4*x^8+4*x^6+x^4),x, algorithm="fricas")

[Out]

-4/(2*x^4 + I*pi*x + x^2 - (I*pi + 2*x^3 + x + log(5))*e^(e^5) + x*log(5))

Sympy [F(-1)]

Timed out. \[ \int \frac {8 x+32 x^3+e^{e^5} \left (-4-24 x^2\right )+4 (i \pi +\log (5))}{x^4+4 x^6+4 x^8+\left (2 x^3+4 x^5\right ) (i \pi +\log (5))+x^2 (i \pi +\log (5))^2+e^{2 e^5} \left (x^2+4 x^4+4 x^6+\left (2 x+4 x^3\right ) (i \pi +\log (5))+(i \pi +\log (5))^2\right )+e^{e^5} \left (-2 x^3-8 x^5-8 x^7+\left (-4 x^2-8 x^4\right ) (i \pi +\log (5))-2 x (i \pi +\log (5))^2\right )} \, dx=\text {Timed out} \]

[In]

integrate(((-24*x**2-4)*exp(exp(5))+4*ln(5)+4*I*pi+32*x**3+8*x)/(((ln(5)+I*pi)**2+(4*x**3+2*x)*(ln(5)+I*pi)+4*
x**6+4*x**4+x**2)*exp(exp(5))**2+(-2*x*(ln(5)+I*pi)**2+(-8*x**4-4*x**2)*(ln(5)+I*pi)-8*x**7-8*x**5-2*x**3)*exp
(exp(5))+x**2*(ln(5)+I*pi)**2+(4*x**5+2*x**3)*(ln(5)+I*pi)+4*x**8+4*x**6+x**4),x)

[Out]

Timed out

Maxima [A] (verification not implemented)

none

Time = 0.21 (sec) , antiderivative size = 47, normalized size of antiderivative = 1.62 \[ \int \frac {8 x+32 x^3+e^{e^5} \left (-4-24 x^2\right )+4 (i \pi +\log (5))}{x^4+4 x^6+4 x^8+\left (2 x^3+4 x^5\right ) (i \pi +\log (5))+x^2 (i \pi +\log (5))^2+e^{2 e^5} \left (x^2+4 x^4+4 x^6+\left (2 x+4 x^3\right ) (i \pi +\log (5))+(i \pi +\log (5))^2\right )+e^{e^5} \left (-2 x^3-8 x^5-8 x^7+\left (-4 x^2-8 x^4\right ) (i \pi +\log (5))-2 x (i \pi +\log (5))^2\right )} \, dx=-\frac {4}{2 \, x^{4} - 2 \, x^{3} e^{\left (e^{5}\right )} + {\left (i \, \pi - e^{\left (e^{5}\right )} + \log \left (5\right )\right )} x + x^{2} - i \, \pi e^{\left (e^{5}\right )} - e^{\left (e^{5}\right )} \log \left (5\right )} \]

[In]

integrate(((-24*x^2-4)*exp(exp(5))+4*log(5)+4*I*pi+32*x^3+8*x)/(((log(5)+I*pi)^2+(4*x^3+2*x)*(log(5)+I*pi)+4*x
^6+4*x^4+x^2)*exp(exp(5))^2+(-2*x*(log(5)+I*pi)^2+(-8*x^4-4*x^2)*(log(5)+I*pi)-8*x^7-8*x^5-2*x^3)*exp(exp(5))+
x^2*(log(5)+I*pi)^2+(4*x^5+2*x^3)*(log(5)+I*pi)+4*x^8+4*x^6+x^4),x, algorithm="maxima")

[Out]

-4/(2*x^4 - 2*x^3*e^(e^5) + (I*pi - e^(e^5) + log(5))*x + x^2 - I*pi*e^(e^5) - e^(e^5)*log(5))

Giac [F(-1)]

Timed out. \[ \int \frac {8 x+32 x^3+e^{e^5} \left (-4-24 x^2\right )+4 (i \pi +\log (5))}{x^4+4 x^6+4 x^8+\left (2 x^3+4 x^5\right ) (i \pi +\log (5))+x^2 (i \pi +\log (5))^2+e^{2 e^5} \left (x^2+4 x^4+4 x^6+\left (2 x+4 x^3\right ) (i \pi +\log (5))+(i \pi +\log (5))^2\right )+e^{e^5} \left (-2 x^3-8 x^5-8 x^7+\left (-4 x^2-8 x^4\right ) (i \pi +\log (5))-2 x (i \pi +\log (5))^2\right )} \, dx=\text {Timed out} \]

[In]

integrate(((-24*x^2-4)*exp(exp(5))+4*log(5)+4*I*pi+32*x^3+8*x)/(((log(5)+I*pi)^2+(4*x^3+2*x)*(log(5)+I*pi)+4*x
^6+4*x^4+x^2)*exp(exp(5))^2+(-2*x*(log(5)+I*pi)^2+(-8*x^4-4*x^2)*(log(5)+I*pi)-8*x^7-8*x^5-2*x^3)*exp(exp(5))+
x^2*(log(5)+I*pi)^2+(4*x^5+2*x^3)*(log(5)+I*pi)+4*x^8+4*x^6+x^4),x, algorithm="giac")

[Out]

Timed out

Mupad [B] (verification not implemented)

Time = 18.32 (sec) , antiderivative size = 53, normalized size of antiderivative = 1.83 \[ \int \frac {8 x+32 x^3+e^{e^5} \left (-4-24 x^2\right )+4 (i \pi +\log (5))}{x^4+4 x^6+4 x^8+\left (2 x^3+4 x^5\right ) (i \pi +\log (5))+x^2 (i \pi +\log (5))^2+e^{2 e^5} \left (x^2+4 x^4+4 x^6+\left (2 x+4 x^3\right ) (i \pi +\log (5))+(i \pi +\log (5))^2\right )+e^{e^5} \left (-2 x^3-8 x^5-8 x^7+\left (-4 x^2-8 x^4\right ) (i \pi +\log (5))-2 x (i \pi +\log (5))^2\right )} \, dx=\frac {2}{-x^4+{\mathrm {e}}^{{\mathrm {e}}^5}\,x^3-\frac {x^2}{2}+\left (\frac {{\mathrm {e}}^{{\mathrm {e}}^5}}{2}-\frac {\ln \left (5\right )}{2}-\frac {\Pi \,1{}\mathrm {i}}{2}\right )\,x+\frac {\Pi \,{\mathrm {e}}^{{\mathrm {e}}^5}\,1{}\mathrm {i}}{2}+\frac {{\mathrm {e}}^{{\mathrm {e}}^5}\,\ln \left (5\right )}{2}} \]

[In]

int((Pi*4i + 8*x + 4*log(5) - exp(exp(5))*(24*x^2 + 4) + 32*x^3)/(x^2*(Pi*1i + log(5))^2 + exp(2*exp(5))*((2*x
 + 4*x^3)*(Pi*1i + log(5)) + x^2 + 4*x^4 + 4*x^6 + (Pi*1i + log(5))^2) - exp(exp(5))*((Pi*1i + log(5))*(4*x^2
+ 8*x^4) + 2*x*(Pi*1i + log(5))^2 + 2*x^3 + 8*x^5 + 8*x^7) + (Pi*1i + log(5))*(2*x^3 + 4*x^5) + x^4 + 4*x^6 +
4*x^8),x)

[Out]

2/(x^3*exp(exp(5)) + (Pi*exp(exp(5))*1i)/2 + (exp(exp(5))*log(5))/2 - x^2/2 - x^4 - x*((Pi*1i)/2 + log(5)/2 -
exp(exp(5))/2))

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