∫ (2e2+2e8x+8e6xx−4ex2+2x4+e4x(−4e+12x2−8 log(5))−4x log(5)+e2x(−8ex+8x3+(−4−8x) log(5))) log( ex−e4xx−2e2xx2−x3−log(5)_______ e4x log(5)+2e2xx log(5)+(−e+x2) log(5)) ____________________________________________________________________________________________________________________________________________________________________________________________e2 x+e8x x+4e6x x2 −2ex3 +x5 +(−e+x2 ) log (5)+e4x (−2ex+6x3 +log (5))+e2x (−4ex2 +4x4 +2xlog (5)) dx

3.8.75 \(\int \frac {(2 e^2+2 e^{8 x}+8 e^{6 x} x-4 e x^2+2 x^4+e^{4 x} (-4 e+12 x^2-8 \log (5))-4 x \log (5)+e^{2 x} (-8 e x+8 x^3+(-4-8 x) \log (5))) \log (\frac {e x-e^{4 x} x-2 e^{2 x} x^2-x^3-\log (5)}{e^{4 x} \log (5)+2 e^{2 x} x \log (5)+(-e+x^2) \log (5)})}{e^2 x+e^{8 x} x+4 e^{6 x} x^2-2 e x^3+x^5+(-e+x^2) \log (5)+e^{4 x} (-2 e x+6 x^3+\log (5))+e^{2 x} (-4 e x^2+4 x^4+2 x \log (5))} \, dx\)

Optimal. Leaf size=26 \[ \log ^2\left (\frac {1}{e-\left (e^{2 x}+x\right )^2}-\frac {x}{\log (5)}\right ) \]

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Rubi [F] time = 88.12, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {\left (2 e^2+2 e^{8 x}+8 e^{6 x} x-4 e x^2+2 x^4+e^{4 x} \left (-4 e+12 x^2-8 \log (5)\right )-4 x \log (5)+e^{2 x} \left (-8 e x+8 x^3+(-4-8 x) \log (5)\right )\right ) \log \left (\frac {e x-e^{4 x} x-2 e^{2 x} x^2-x^3-\log (5)}{e^{4 x} \log (5)+2 e^{2 x} x \log (5)+\left (-e+x^2\right ) \log (5)}\right )}{e^2 x+e^{8 x} x+4 e^{6 x} x^2-2 e x^3+x^5+\left (-e+x^2\right ) \log (5)+e^{4 x} \left (-2 e x+6 x^3+\log (5)\right )+e^{2 x} \left (-4 e x^2+4 x^4+2 x \log (5)\right )} \, dx \end {gather*}

Veriﬁcation is not applicable to the result.

[In]

Int[((2*E^2 + 2*E^(8*x) + 8*E^(6*x)*x - 4*E*x^2 + 2*x^4 + E^(4*x)*(-4*E + 12*x^2 - 8*Log[5]) - 4*x*Log[5] + E^

(2*x)*(-8*E*x + 8*x^3 + (-4 - 8*x)*Log[5]))*Log[(E*x - E^(4*x)*x - 2*E^(2*x)*x^2 - x^3 - Log[5])/(E^(4*x)*Log[

5] + 2*E^(2*x)*x*Log[5] + (-E + x^2)*Log[5])])/(E^2*x + E^(8*x)*x + 4*E^(6*x)*x^2 - 2*E*x^3 + x^5 + (-E + x^2)

*Log[5] + E^(4*x)*(-2*E*x + 6*x^3 + Log[5]) + E^(2*x)*(-4*E*x^2 + 4*x^4 + 2*x*Log[5])),x]

[Out]

8*E*Log[-((E*x - E^(4*x)*x - 2*E^(2*x)*x^2 - x^3 - Log[5])/((E - E^(4*x) - 2*E^(2*x)*x - x^2)*Log[5]))]*Defer[

Int][(E - E^(4*x) - 2*E^(2*x)*x - x^2)^(-1), x] - 4*Log[-((E*x - E^(4*x)*x - 2*E^(2*x)*x^2 - x^3 - Log[5])/((E

- E^(4*x) - 2*E^(2*x)*x - x^2)*Log[5]))]*Defer[Int][E^(2*x)/(-E + E^(4*x) + 2*E^(2*x)*x + x^2), x] - 4*Log[-(

(E*x - E^(4*x)*x - 2*E^(2*x)*x^2 - x^3 - Log[5])/((E - E^(4*x) - 2*E^(2*x)*x - x^2)*Log[5]))]*Defer[Int][x/(-E

+ E^(4*x) + 2*E^(2*x)*x + x^2), x] + 8*Log[-((E*x - E^(4*x)*x - 2*E^(2*x)*x^2 - x^3 - Log[5])/((E - E^(4*x) -

2*E^(2*x)*x - x^2)*Log[5]))]*Defer[Int][(E^(2*x)*x)/(-E + E^(4*x) + 2*E^(2*x)*x + x^2), x] + 8*Log[-((E*x - E

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

4*x) + 2*E^(2*x)*x + x^2), x] - 8*E*Log[-((E*x - E^(4*x)*x - 2*E^(2*x)*x^2 - x^3 - Log[5])/((E - E^(4*x) - 2*E

^(2*x)*x - x^2)*Log[5]))]*Defer[Int][x/(E*x - E^(4*x)*x - 2*E^(2*x)*x^2 - x^3 - Log[5]), x] - 8*Log[5]*Log[-((

E*x - E^(4*x)*x - 2*E^(2*x)*x^2 - x^3 - Log[5])/((E - E^(4*x) - 2*E^(2*x)*x - x^2)*Log[5]))]*Defer[Int][(-(E*x

) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5])^(-1), x] - 2*Log[5]*Log[-((E*x - E^(4*x)*x - 2*E^(2*x)*x^2 - x^3

- Log[5])/((E - E^(4*x) - 2*E^(2*x)*x - x^2)*Log[5]))]*Defer[Int][1/(x*(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 +

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

2)*Log[5]))]*Defer[Int][(E^(2*x)*x)/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x] + 4*Log[-((E*x - E

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

E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x] - 8*Log[-((E*x - E^(4*x)*x - 2*E^(2*x)*x^2 - x^3 - Log[5])/((E

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

Log[5]), x] - 8*Log[-((E*x - E^(4*x)*x - 2*E^(2*x)*x^2 - x^3 - Log[5])/((E - E^(4*x) - 2*E^(2*x)*x - x^2)*Log[

5]))]*Defer[Int][x^3/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x] + 2*Defer[Int][Log[-((-(E*x) + E^

(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5])/((-E + E^(4*x) + 2*E^(2*x)*x + x^2)*Log[5]))]/x, x] - 8*E*Defer[Int][D

efer[Int][-(-E + E^(4*x) + 2*E^(2*x)*x + x^2)^(-1), x]/x, x] - 32*E^2*Defer[Int][Defer[Int][-(-E + E^(4*x) + 2

*E^(2*x)*x + x^2)^(-1), x]/(E - E^(4*x) - 2*E^(2*x)*x - x^2), x] - 16*E*Defer[Int][(x*Defer[Int][-(-E + E^(4*x

) + 2*E^(2*x)*x + x^2)^(-1), x])/(E - E^(4*x) - 2*E^(2*x)*x - x^2), x] + 32*E*Defer[Int][(x^2*Defer[Int][-(-E

+ E^(4*x) + 2*E^(2*x)*x + x^2)^(-1), x])/(E - E^(4*x) - 2*E^(2*x)*x - x^2), x] + 16*Defer[Int][(E^(1 + 2*x)*De

fer[Int][-(-E + E^(4*x) + 2*E^(2*x)*x + x^2)^(-1), x])/(-E + E^(4*x) + 2*E^(2*x)*x + x^2), x] - 32*Defer[Int][

(E^(1 + 2*x)*x*Defer[Int][-(-E + E^(4*x) + 2*E^(2*x)*x + x^2)^(-1), x])/(-E + E^(4*x) + 2*E^(2*x)*x + x^2), x]

- 32*E*Log[5]*Defer[Int][Defer[Int][-(-E + E^(4*x) + 2*E^(2*x)*x + x^2)^(-1), x]/(E*x - E^(4*x)*x - 2*E^(2*x)

*x^2 - x^3 - Log[5]), x] - 8*E*Log[5]*Defer[Int][Defer[Int][-(-E + E^(4*x) + 2*E^(2*x)*x + x^2)^(-1), x]/(x*(E

*x - E^(4*x)*x - 2*E^(2*x)*x^2 - x^3 - Log[5])), x] + 32*E^2*Defer[Int][(x*Defer[Int][-(-E + E^(4*x) + 2*E^(2*

x)*x + x^2)^(-1), x])/(E*x - E^(4*x)*x - 2*E^(2*x)*x^2 - x^3 - Log[5]), x] + 16*E*Defer[Int][(x^2*Defer[Int][-

(-E + E^(4*x) + 2*E^(2*x)*x + x^2)^(-1), x])/(E*x - E^(4*x)*x - 2*E^(2*x)*x^2 - x^3 - Log[5]), x] - 32*E*Defer

[Int][(x^3*Defer[Int][-(-E + E^(4*x) + 2*E^(2*x)*x + x^2)^(-1), x])/(E*x - E^(4*x)*x - 2*E^(2*x)*x^2 - x^3 - L

og[5]), x] - 16*Defer[Int][(E^(1 + 2*x)*x*Defer[Int][-(-E + E^(4*x) + 2*E^(2*x)*x + x^2)^(-1), x])/(-(E*x) + E

^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x] + 32*Defer[Int][(E^(1 + 2*x)*x^2*Defer[Int][-(-E + E^(4*x) + 2*E^

(2*x)*x + x^2)^(-1), x])/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x] + 4*Defer[Int][Defer[Int][E^(

2*x)/(-E + E^(4*x) + 2*E^(2*x)*x + x^2), x]/x, x] + 16*E*Defer[Int][Defer[Int][E^(2*x)/(-E + E^(4*x) + 2*E^(2*

x)*x + x^2), x]/(E - E^(4*x) - 2*E^(2*x)*x - x^2), x] - 8*Defer[Int][(E^(2*x)*Defer[Int][E^(2*x)/(-E + E^(4*x)

+ 2*E^(2*x)*x + x^2), x])/(-E + E^(4*x) + 2*E^(2*x)*x + x^2), x] - 8*Defer[Int][(x*Defer[Int][E^(2*x)/(-E + E

^(4*x) + 2*E^(2*x)*x + x^2), x])/(-E + E^(4*x) + 2*E^(2*x)*x + x^2), x] + 16*Defer[Int][(E^(2*x)*x*Defer[Int][

E^(2*x)/(-E + E^(4*x) + 2*E^(2*x)*x + x^2), x])/(-E + E^(4*x) + 2*E^(2*x)*x + x^2), x] + 16*Defer[Int][(x^2*De

fer[Int][E^(2*x)/(-E + E^(4*x) + 2*E^(2*x)*x + x^2), x])/(-E + E^(4*x) + 2*E^(2*x)*x + x^2), x] - 16*E*Defer[I

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

[5]), x] - 16*Log[5]*Defer[Int][Defer[Int][E^(2*x)/(-E + E^(4*x) + 2*E^(2*x)*x + x^2), x]/(-(E*x) + E^(4*x)*x

+ 2*E^(2*x)*x^2 + x^3 + Log[5]), x] - 4*Log[5]*Defer[Int][Defer[Int][E^(2*x)/(-E + E^(4*x) + 2*E^(2*x)*x + x^2

), x]/(x*(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5])), x] + 8*Defer[Int][(E^(2*x)*x*Defer[Int][E^(2*x)

/(-E + E^(4*x) + 2*E^(2*x)*x + x^2), x])/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x] + 8*Defer[Int

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

Log[5]), x] - 16*Defer[Int][(E^(2*x)*x^2*Defer[Int][E^(2*x)/(-E + E^(4*x) + 2*E^(2*x)*x + x^2), x])/(-(E*x) +

E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x] - 16*Defer[Int][(x^3*Defer[Int][E^(2*x)/(-E + E^(4*x) + 2*E^(2*x

)*x + x^2), x])/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x] + 4*Defer[Int][Defer[Int][x/(-E + E^(4

*x) + 2*E^(2*x)*x + x^2), x]/x, x] + 16*E*Defer[Int][Defer[Int][x/(-E + E^(4*x) + 2*E^(2*x)*x + x^2), x]/(E -

E^(4*x) - 2*E^(2*x)*x - x^2), x] - 8*Defer[Int][(E^(2*x)*Defer[Int][x/(-E + E^(4*x) + 2*E^(2*x)*x + x^2), x])/

(-E + E^(4*x) + 2*E^(2*x)*x + x^2), x] - 8*Defer[Int][(x*Defer[Int][x/(-E + E^(4*x) + 2*E^(2*x)*x + x^2), x])/

(-E + E^(4*x) + 2*E^(2*x)*x + x^2), x] + 16*Defer[Int][(E^(2*x)*x*Defer[Int][x/(-E + E^(4*x) + 2*E^(2*x)*x + x

^2), x])/(-E + E^(4*x) + 2*E^(2*x)*x + x^2), x] + 16*Defer[Int][(x^2*Defer[Int][x/(-E + E^(4*x) + 2*E^(2*x)*x

+ x^2), x])/(-E + E^(4*x) + 2*E^(2*x)*x + x^2), x] - 16*E*Defer[Int][(x*Defer[Int][x/(-E + E^(4*x) + 2*E^(2*x)

*x + x^2), x])/(E*x - E^(4*x)*x - 2*E^(2*x)*x^2 - x^3 - Log[5]), x] - 16*Log[5]*Defer[Int][Defer[Int][x/(-E +

E^(4*x) + 2*E^(2*x)*x + x^2), x]/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x] - 4*Log[5]*Defer[Int]

[Defer[Int][x/(-E + E^(4*x) + 2*E^(2*x)*x + x^2), x]/(x*(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5])),

x] + 8*Defer[Int][(E^(2*x)*x*Defer[Int][x/(-E + E^(4*x) + 2*E^(2*x)*x + x^2), x])/(-(E*x) + E^(4*x)*x + 2*E^(2

*x)*x^2 + x^3 + Log[5]), x] + 8*Defer[Int][(x^2*Defer[Int][x/(-E + E^(4*x) + 2*E^(2*x)*x + x^2), x])/(-(E*x) +

E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x] - 16*Defer[Int][(E^(2*x)*x^2*Defer[Int][x/(-E + E^(4*x) + 2*E^(

2*x)*x + x^2), x])/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x] - 16*Defer[Int][(x^3*Defer[Int][x/(

-E + E^(4*x) + 2*E^(2*x)*x + x^2), x])/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x] - 8*Defer[Int][

Defer[Int][(E^(2*x)*x)/(-E + E^(4*x) + 2*E^(2*x)*x + x^2), x]/x, x] - 32*E*Defer[Int][Defer[Int][(E^(2*x)*x)/(

-E + E^(4*x) + 2*E^(2*x)*x + x^2), x]/(E - E^(4*x) - 2*E^(2*x)*x - x^2), x] + 16*Defer[Int][(E^(2*x)*Defer[Int

][(E^(2*x)*x)/(-E + E^(4*x) + 2*E^(2*x)*x + x^2), x])/(-E + E^(4*x) + 2*E^(2*x)*x + x^2), x] + 16*Defer[Int][(

x*Defer[Int][(E^(2*x)*x)/(-E + E^(4*x) + 2*E^(2*x)*x + x^2), x])/(-E + E^(4*x) + 2*E^(2*x)*x + x^2), x] - 32*D

efer[Int][(E^(2*x)*x*Defer[Int][(E^(2*x)*x)/(-E + E^(4*x) + 2*E^(2*x)*x + x^2), x])/(-E + E^(4*x) + 2*E^(2*x)*

x + x^2), x] - 32*Defer[Int][(x^2*Defer[Int][(E^(2*x)*x)/(-E + E^(4*x) + 2*E^(2*x)*x + x^2), x])/(-E + E^(4*x)

+ 2*E^(2*x)*x + x^2), x] + 32*E*Defer[Int][(x*Defer[Int][(E^(2*x)*x)/(-E + E^(4*x) + 2*E^(2*x)*x + x^2), x])/

(E*x - E^(4*x)*x - 2*E^(2*x)*x^2 - x^3 - Log[5]), x] + 32*Log[5]*Defer[Int][Defer[Int][(E^(2*x)*x)/(-E + E^(4*

x) + 2*E^(2*x)*x + x^2), x]/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x] + 8*Log[5]*Defer[Int][Defe

r[Int][(E^(2*x)*x)/(-E + E^(4*x) + 2*E^(2*x)*x + x^2), x]/(x*(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5

])), x] - 16*Defer[Int][(E^(2*x)*x*Defer[Int][(E^(2*x)*x)/(-E + E^(4*x) + 2*E^(2*x)*x + x^2), x])/(-(E*x) + E^

(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x] - 16*Defer[Int][(x^2*Defer[Int][(E^(2*x)*x)/(-E + E^(4*x) + 2*E^(2

*x)*x + x^2), x])/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x] + 32*Defer[Int][(E^(2*x)*x^2*Defer[I

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

] + 32*Defer[Int][(x^3*Defer[Int][(E^(2*x)*x)/(-E + E^(4*x) + 2*E^(2*x)*x + x^2), x])/(-(E*x) + E^(4*x)*x + 2*

E^(2*x)*x^2 + x^3 + Log[5]), x] - 8*Defer[Int][Defer[Int][x^2/(-E + E^(4*x) + 2*E^(2*x)*x + x^2), x]/x, x] - 3

2*E*Defer[Int][Defer[Int][x^2/(-E + E^(4*x) + 2*E^(2*x)*x + x^2), x]/(E - E^(4*x) - 2*E^(2*x)*x - x^2), x] + 1

6*Defer[Int][(E^(2*x)*Defer[Int][x^2/(-E + E^(4*x) + 2*E^(2*x)*x + x^2), x])/(-E + E^(4*x) + 2*E^(2*x)*x + x^2

), x] + 16*Defer[Int][(x*Defer[Int][x^2/(-E + E^(4*x) + 2*E^(2*x)*x + x^2), x])/(-E + E^(4*x) + 2*E^(2*x)*x +

x^2), x] - 32*Defer[Int][(E^(2*x)*x*Defer[Int][x^2/(-E + E^(4*x) + 2*E^(2*x)*x + x^2), x])/(-E + E^(4*x) + 2*E

^(2*x)*x + x^2), x] - 32*Defer[Int][(x^2*Defer[Int][x^2/(-E + E^(4*x) + 2*E^(2*x)*x + x^2), x])/(-E + E^(4*x)

+ 2*E^(2*x)*x + x^2), x] + 32*E*Defer[Int][(x*Defer[Int][x^2/(-E + E^(4*x) + 2*E^(2*x)*x + x^2), x])/(E*x - E^

(4*x)*x - 2*E^(2*x)*x^2 - x^3 - Log[5]), x] + 32*Log[5]*Defer[Int][Defer[Int][x^2/(-E + E^(4*x) + 2*E^(2*x)*x

+ x^2), x]/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x] + 8*Log[5]*Defer[Int][Defer[Int][x^2/(-E +

E^(4*x) + 2*E^(2*x)*x + x^2), x]/(x*(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5])), x] - 16*Defer[Int][(

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

og[5]), x] - 16*Defer[Int][(x^2*Defer[Int][x^2/(-E + E^(4*x) + 2*E^(2*x)*x + x^2), x])/(-(E*x) + E^(4*x)*x + 2

*E^(2*x)*x^2 + x^3 + Log[5]), x] + 32*Defer[Int][(E^(2*x)*x^2*Defer[Int][x^2/(-E + E^(4*x) + 2*E^(2*x)*x + x^2

), x])/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x] + 32*Defer[Int][(x^3*Defer[Int][x^2/(-E + E^(4*

x) + 2*E^(2*x)*x + x^2), x])/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x] + 8*Log[5]*Defer[Int][Def

er[Int][(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5])^(-1), x]/x, x] + 32*E*Log[5]*Defer[Int][Defer[Int]

[(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5])^(-1), x]/(E - E^(4*x) - 2*E^(2*x)*x - x^2), x] - 16*Log[5

]*Defer[Int][(E^(2*x)*Defer[Int][(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5])^(-1), x])/(-E + E^(4*x) +

2*E^(2*x)*x + x^2), x] - 16*Log[5]*Defer[Int][(x*Defer[Int][(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5

])^(-1), x])/(-E + E^(4*x) + 2*E^(2*x)*x + x^2), x] + 32*Log[5]*Defer[Int][(E^(2*x)*x*Defer[Int][(-(E*x) + E^(

4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5])^(-1), x])/(-E + E^(4*x) + 2*E^(2*x)*x + x^2), x] + 32*Log[5]*Defer[Int]

[(x^2*Defer[Int][(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5])^(-1), x])/(-E + E^(4*x) + 2*E^(2*x)*x + x

^2), x] - 32*E*Log[5]*Defer[Int][(x*Defer[Int][(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5])^(-1), x])/(

E*x - E^(4*x)*x - 2*E^(2*x)*x^2 - x^3 - Log[5]), x] - 32*Log[5]^2*Defer[Int][Defer[Int][(-(E*x) + E^(4*x)*x +

2*E^(2*x)*x^2 + x^3 + Log[5])^(-1), x]/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x] - 8*Log[5]^2*De

fer[Int][Defer[Int][(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5])^(-1), x]/(x*(-(E*x) + E^(4*x)*x + 2*E^

(2*x)*x^2 + x^3 + Log[5])), x] + 16*Log[5]*Defer[Int][(E^(2*x)*x*Defer[Int][(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^

2 + x^3 + Log[5])^(-1), x])/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x] + 16*Log[5]*Defer[Int][(x^

2*Defer[Int][(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5])^(-1), x])/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2

+ x^3 + Log[5]), x] - 32*Log[5]*Defer[Int][(E^(2*x)*x^2*Defer[Int][(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3

+ Log[5])^(-1), x])/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x] - 32*Log[5]*Defer[Int][(x^3*Defer[

Int][(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5])^(-1), x])/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 +

Log[5]), x] + 2*Log[5]*Defer[Int][Defer[Int][1/(x*(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5])), x]/x,

x] + 8*E*Log[5]*Defer[Int][Defer[Int][1/(x*(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5])), x]/(E - E^(4

*x) - 2*E^(2*x)*x - x^2), x] - 4*Log[5]*Defer[Int][(E^(2*x)*Defer[Int][1/(x*(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^

2 + x^3 + Log[5])), x])/(-E + E^(4*x) + 2*E^(2*x)*x + x^2), x] - 4*Log[5]*Defer[Int][(x*Defer[Int][1/(x*(-(E*x

) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5])), x])/(-E + E^(4*x) + 2*E^(2*x)*x + x^2), x] + 8*Log[5]*Defer[In

t][(E^(2*x)*x*Defer[Int][1/(x*(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5])), x])/(-E + E^(4*x) + 2*E^(2

*x)*x + x^2), x] + 8*Log[5]*Defer[Int][(x^2*Defer[Int][1/(x*(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5]

)), x])/(-E + E^(4*x) + 2*E^(2*x)*x + x^2), x] - 8*E*Log[5]*Defer[Int][(x*Defer[Int][1/(x*(-(E*x) + E^(4*x)*x

+ 2*E^(2*x)*x^2 + x^3 + Log[5])), x])/(E*x - E^(4*x)*x - 2*E^(2*x)*x^2 - x^3 - Log[5]), x] - 8*Log[5]^2*Defer[

Int][Defer[Int][1/(x*(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5])), x]/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*

x^2 + x^3 + Log[5]), x] - 2*Log[5]^2*Defer[Int][Defer[Int][1/(x*(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Lo

g[5])), x]/(x*(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5])), x] + 4*Log[5]*Defer[Int][(E^(2*x)*x*Defer[

Int][1/(x*(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5])), x])/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3

+ Log[5]), x] + 4*Log[5]*Defer[Int][(x^2*Defer[Int][1/(x*(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5])),

x])/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x] - 8*Log[5]*Defer[Int][(E^(2*x)*x^2*Defer[Int][1/(

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

), x] - 8*Log[5]*Defer[Int][(x^3*Defer[Int][1/(x*(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5])), x])/(-(

E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x] + 8*E*Defer[Int][Defer[Int][-(x/(-(E*x) + E^(4*x)*x + 2*E

^(2*x)*x^2 + x^3 + Log[5])), x]/x, x] + 32*E^2*Defer[Int][Defer[Int][-(x/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 +

x^3 + Log[5])), x]/(E - E^(4*x) - 2*E^(2*x)*x - x^2), x] + 16*E*Defer[Int][(x*Defer[Int][-(x/(-(E*x) + E^(4*x

)*x + 2*E^(2*x)*x^2 + x^3 + Log[5])), x])/(E - E^(4*x) - 2*E^(2*x)*x - x^2), x] - 32*E*Defer[Int][(x^2*Defer[I

nt][-(x/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5])), x])/(E - E^(4*x) - 2*E^(2*x)*x - x^2), x] - 16*D

efer[Int][(E^(1 + 2*x)*Defer[Int][-(x/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5])), x])/(-E + E^(4*x)

+ 2*E^(2*x)*x + x^2), x] + 32*Defer[Int][(E^(1 + 2*x)*x*Defer[Int][-(x/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x

^3 + Log[5])), x])/(-E + E^(4*x) + 2*E^(2*x)*x + x^2), x] + 32*E*Log[5]*Defer[Int][Defer[Int][-(x/(-(E*x) + E^

(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5])), x]/(E*x - E^(4*x)*x - 2*E^(2*x)*x^2 - x^3 - Log[5]), x] + 8*E*Log[5]

*Defer[Int][Defer[Int][-(x/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5])), x]/(x*(E*x - E^(4*x)*x - 2*E^

(2*x)*x^2 - x^3 - Log[5])), x] - 32*E^2*Defer[Int][(x*Defer[Int][-(x/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3

+ Log[5])), x])/(E*x - E^(4*x)*x - 2*E^(2*x)*x^2 - x^3 - Log[5]), x] - 16*E*Defer[Int][(x^2*Defer[Int][-(x/(-

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

32*E*Defer[Int][(x^3*Defer[Int][-(x/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5])), x])/(E*x - E^(4*x)*

x - 2*E^(2*x)*x^2 - x^3 - Log[5]), x] + 16*Defer[Int][(E^(1 + 2*x)*x*Defer[Int][-(x/(-(E*x) + E^(4*x)*x + 2*E^

(2*x)*x^2 + x^3 + Log[5])), x])/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x] - 32*Defer[Int][(E^(1

+ 2*x)*x^2*Defer[Int][-(x/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5])), x])/(-(E*x) + E^(4*x)*x + 2*E^

(2*x)*x^2 + x^3 + Log[5]), x] - 4*Defer[Int][Defer[Int][(E^(2*x)*x)/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3

+ Log[5]), x]/x, x] - 16*E*Defer[Int][Defer[Int][(E^(2*x)*x)/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5

]), x]/(E - E^(4*x) - 2*E^(2*x)*x - x^2), x] + 8*Defer[Int][(E^(2*x)*Defer[Int][(E^(2*x)*x)/(-(E*x) + E^(4*x)*

x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x])/(-E + E^(4*x) + 2*E^(2*x)*x + x^2), x] + 8*Defer[Int][(x*Defer[Int][(E^

(2*x)*x)/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x])/(-E + E^(4*x) + 2*E^(2*x)*x + x^2), x] - 16*

Defer[Int][(E^(2*x)*x*Defer[Int][(E^(2*x)*x)/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x])/(-E + E^

(4*x) + 2*E^(2*x)*x + x^2), x] - 16*Defer[Int][(x^2*Defer[Int][(E^(2*x)*x)/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2

+ x^3 + Log[5]), x])/(-E + E^(4*x) + 2*E^(2*x)*x + x^2), x] + 16*E*Defer[Int][(x*Defer[Int][(E^(2*x)*x)/(-(E*

x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x])/(E*x - E^(4*x)*x - 2*E^(2*x)*x^2 - x^3 - Log[5]), x] + 16*

Log[5]*Defer[Int][Defer[Int][(E^(2*x)*x)/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x]/(-(E*x) + E^(

4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x] + 4*Log[5]*Defer[Int][Defer[Int][(E^(2*x)*x)/(-(E*x) + E^(4*x)*x +

2*E^(2*x)*x^2 + x^3 + Log[5]), x]/(x*(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5])), x] - 8*Defer[Int][(

E^(2*x)*x*Defer[Int][(E^(2*x)*x)/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x])/(-(E*x) + E^(4*x)*x

+ 2*E^(2*x)*x^2 + x^3 + Log[5]), x] - 8*Defer[Int][(x^2*Defer[Int][(E^(2*x)*x)/(-(E*x) + E^(4*x)*x + 2*E^(2*x)

*x^2 + x^3 + Log[5]), x])/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x] + 16*Defer[Int][(E^(2*x)*x^2

*Defer[Int][(E^(2*x)*x)/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x])/(-(E*x) + E^(4*x)*x + 2*E^(2*

x)*x^2 + x^3 + Log[5]), x] + 16*Defer[Int][(x^3*Defer[Int][(E^(2*x)*x)/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x

^3 + Log[5]), x])/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x] - 4*Defer[Int][Defer[Int][x^2/(-(E*x

) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x]/x, x] - 16*E*Defer[Int][Defer[Int][x^2/(-(E*x) + E^(4*x)*x +

2*E^(2*x)*x^2 + x^3 + Log[5]), x]/(E - E^(4*x) - 2*E^(2*x)*x - x^2), x] + 8*Defer[Int][(E^(2*x)*Defer[Int][x^

2/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x])/(-E + E^(4*x) + 2*E^(2*x)*x + x^2), x] + 8*Defer[In

t][(x*Defer[Int][x^2/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x])/(-E + E^(4*x) + 2*E^(2*x)*x + x^

2), x] - 16*Defer[Int][(E^(2*x)*x*Defer[Int][x^2/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x])/(-E

+ E^(4*x) + 2*E^(2*x)*x + x^2), x] - 16*Defer[Int][(x^2*Defer[Int][x^2/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x

^3 + Log[5]), x])/(-E + E^(4*x) + 2*E^(2*x)*x + x^2), x] + 16*E*Defer[Int][(x*Defer[Int][x^2/(-(E*x) + E^(4*x)

*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x])/(E*x - E^(4*x)*x - 2*E^(2*x)*x^2 - x^3 - Log[5]), x] + 16*Log[5]*Defer

[Int][Defer[Int][x^2/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x]/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x

^2 + x^3 + Log[5]), x] + 4*Log[5]*Defer[Int][Defer[Int][x^2/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5]

), x]/(x*(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5])), x] - 8*Defer[Int][(E^(2*x)*x*Defer[Int][x^2/(-(

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

- 8*Defer[Int][(x^2*Defer[Int][x^2/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x])/(-(E*x) + E^(4*x)*

x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x] + 16*Defer[Int][(E^(2*x)*x^2*Defer[Int][x^2/(-(E*x) + E^(4*x)*x + 2*E^(2

*x)*x^2 + x^3 + Log[5]), x])/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x] + 16*Defer[Int][(x^3*Defe

r[Int][x^2/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x])/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3

+ Log[5]), x] + 8*Defer[Int][Defer[Int][(E^(2*x)*x^2)/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x]/

x, x] + 32*E*Defer[Int][Defer[Int][(E^(2*x)*x^2)/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x]/(E -

E^(4*x) - 2*E^(2*x)*x - x^2), x] - 16*Defer[Int][(E^(2*x)*Defer[Int][(E^(2*x)*x^2)/(-(E*x) + E^(4*x)*x + 2*E^(

2*x)*x^2 + x^3 + Log[5]), x])/(-E + E^(4*x) + 2*E^(2*x)*x + x^2), x] - 16*Defer[Int][(x*Defer[Int][(E^(2*x)*x^

2)/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x])/(-E + E^(4*x) + 2*E^(2*x)*x + x^2), x] + 32*Defer[

Int][(E^(2*x)*x*Defer[Int][(E^(2*x)*x^2)/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x])/(-E + E^(4*x

) + 2*E^(2*x)*x + x^2), x] + 32*Defer[Int][(x^2*Defer[Int][(E^(2*x)*x^2)/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 +

x^3 + Log[5]), x])/(-E + E^(4*x) + 2*E^(2*x)*x + x^2), x] - 32*E*Defer[Int][(x*Defer[Int][(E^(2*x)*x^2)/(-(E*

x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x])/(E*x - E^(4*x)*x - 2*E^(2*x)*x^2 - x^3 - Log[5]), x] - 32*

Log[5]*Defer[Int][Defer[Int][(E^(2*x)*x^2)/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x]/(-(E*x) + E

^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x] - 8*Log[5]*Defer[Int][Defer[Int][(E^(2*x)*x^2)/(-(E*x) + E^(4*x)*

x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x]/(x*(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5])), x] + 16*Defer[I

nt][(E^(2*x)*x*Defer[Int][(E^(2*x)*x^2)/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x])/(-(E*x) + E^(

4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x] + 16*Defer[Int][(x^2*Defer[Int][(E^(2*x)*x^2)/(-(E*x) + E^(4*x)*x +

2*E^(2*x)*x^2 + x^3 + Log[5]), x])/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x] - 32*Defer[Int][(E

^(2*x)*x^2*Defer[Int][(E^(2*x)*x^2)/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x])/(-(E*x) + E^(4*x)

*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x] - 32*Defer[Int][(x^3*Defer[Int][(E^(2*x)*x^2)/(-(E*x) + E^(4*x)*x + 2*E

^(2*x)*x^2 + x^3 + Log[5]), x])/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x] + 8*Defer[Int][Defer[I

nt][x^3/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x]/x, x] + 32*E*Defer[Int][Defer[Int][x^3/(-(E*x)

+ E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x]/(E - E^(4*x) - 2*E^(2*x)*x - x^2), x] - 16*Defer[Int][(E^(2*x

)*Defer[Int][x^3/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x])/(-E + E^(4*x) + 2*E^(2*x)*x + x^2),

x] - 16*Defer[Int][(x*Defer[Int][x^3/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x])/(-E + E^(4*x) +

2*E^(2*x)*x + x^2), x] + 32*Defer[Int][(E^(2*x)*x*Defer[Int][x^3/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + L

og[5]), x])/(-E + E^(4*x) + 2*E^(2*x)*x + x^2), x] + 32*Defer[Int][(x^2*Defer[Int][x^3/(-(E*x) + E^(4*x)*x + 2

*E^(2*x)*x^2 + x^3 + Log[5]), x])/(-E + E^(4*x) + 2*E^(2*x)*x + x^2), x] - 32*E*Defer[Int][(x*Defer[Int][x^3/(

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

32*Log[5]*Defer[Int][Defer[Int][x^3/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x]/(-(E*x) + E^(4*x)

*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x] - 8*Log[5]*Defer[Int][Defer[Int][x^3/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^

2 + x^3 + Log[5]), x]/(x*(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5])), x] + 16*Defer[Int][(E^(2*x)*x*D

efer[Int][x^3/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x])/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x

^3 + Log[5]), x] + 16*Defer[Int][(x^2*Defer[Int][x^3/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x])/

(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x] - 32*Defer[Int][(E^(2*x)*x^2*Defer[Int][x^3/(-(E*x) +

E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x])/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x] - 32*De

fer[Int][(x^3*Defer[Int][x^3/(-(E*x) + E^(4*x)*x + 2*E^(2*x)*x^2 + x^3 + Log[5]), x])/(-(E*x) + E^(4*x)*x + 2*

E^(2*x)*x^2 + x^3 + Log[5]), x]

Rubi steps

Aborted

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Mathematica [B] time = 0.16, size = 58, normalized size = 2.23 \begin {gather*} \log ^2\left (-\frac {-e x+e^{4 x} x+2 e^{2 x} x^2+x^3+\log (5)}{\left (-e+e^{4 x}+2 e^{2 x} x+x^2\right ) \log (5)}\right ) \end {gather*}

Antiderivative was successfully veriﬁed.

[In]

Integrate[((2*E^2 + 2*E^(8*x) + 8*E^(6*x)*x - 4*E*x^2 + 2*x^4 + E^(4*x)*(-4*E + 12*x^2 - 8*Log[5]) - 4*x*Log[5

] + E^(2*x)*(-8*E*x + 8*x^3 + (-4 - 8*x)*Log[5]))*Log[(E*x - E^(4*x)*x - 2*E^(2*x)*x^2 - x^3 - Log[5])/(E^(4*x

)*Log[5] + 2*E^(2*x)*x*Log[5] + (-E + x^2)*Log[5])])/(E^2*x + E^(8*x)*x + 4*E^(6*x)*x^2 - 2*E*x^3 + x^5 + (-E

+ x^2)*Log[5] + E^(4*x)*(-2*E*x + 6*x^3 + Log[5]) + E^(2*x)*(-4*E*x^2 + 4*x^4 + 2*x*Log[5])),x]

[Out]

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

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fricas [B] time = 0.84, size = 61, normalized size = 2.35 \begin {gather*} \log \left (-\frac {x^{3} + 2 \, x^{2} e^{\left (2 \, x\right )} - x e + x e^{\left (4 \, x\right )} + \log \relax (5)}{2 \, x e^{\left (2 \, x\right )} \log \relax (5) + {\left (x^{2} - e\right )} \log \relax (5) + e^{\left (4 \, x\right )} \log \relax (5)}\right )^{2} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*exp(x)^8+8*x*exp(x)^6+(-8*log(5)-4*exp(1)+12*x^2)*exp(x)^4+((-8*x-4)*log(5)-8*x*exp(1)+8*x^3)*exp

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

xp(x)^4+2*x*log(5)*exp(x)^2+(-exp(1)+x^2)*log(5)))/(x*exp(x)^8+4*x^2*exp(x)^6+(log(5)-2*x*exp(1)+6*x^3)*exp(x)

^4+(2*x*log(5)-4*x^2*exp(1)+4*x^4)*exp(x)^2+(-exp(1)+x^2)*log(5)+x*exp(1)^2-2*x^3*exp(1)+x^5),x, algorithm="fr

icas")

[Out]

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

)^2

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giac [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*exp(x)^8+8*x*exp(x)^6+(-8*log(5)-4*exp(1)+12*x^2)*exp(x)^4+((-8*x-4)*log(5)-8*x*exp(1)+8*x^3)*exp

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

xp(x)^4+2*x*log(5)*exp(x)^2+(-exp(1)+x^2)*log(5)))/(x*exp(x)^8+4*x^2*exp(x)^6+(log(5)-2*x*exp(1)+6*x^3)*exp(x)

^4+(2*x*log(5)-4*x^2*exp(1)+4*x^4)*exp(x)^2+(-exp(1)+x^2)*log(5)+x*exp(1)^2-2*x^3*exp(1)+x^5),x, algorithm="gi

ac")

[Out]

Timed out

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maple [F] time = 0.09, size = 0, normalized size = 0.00 \[\int \frac {\left (2 \,{\mathrm e}^{8 x}+8 x \,{\mathrm e}^{6 x}+\left (-8 \ln \relax (5)-4 \,{\mathrm e}+12 x^{2}\right ) {\mathrm e}^{4 x}+\left (\left (-8 x -4\right ) \ln \relax (5)-8 x \,{\mathrm e}+8 x^{3}\right ) {\mathrm e}^{2 x}-4 x \ln \relax (5)+2 \,{\mathrm e}^{2}-4 x^{2} {\mathrm e}+2 x^{4}\right ) \ln \left (\frac {-x \,{\mathrm e}^{4 x}-2 \,{\mathrm e}^{2 x} x^{2}-\ln \relax (5)+x \,{\mathrm e}-x^{3}}{\ln \relax (5) {\mathrm e}^{4 x}+2 x \ln \relax (5) {\mathrm e}^{2 x}+\left (-{\mathrm e}+x^{2}\right ) \ln \relax (5)}\right )}{x \,{\mathrm e}^{8 x}+4 x^{2} {\mathrm e}^{6 x}+\left (\ln \relax (5)-2 x \,{\mathrm e}+6 x^{3}\right ) {\mathrm e}^{4 x}+\left (2 x \ln \relax (5)-4 x^{2} {\mathrm e}+4 x^{4}\right ) {\mathrm e}^{2 x}+\left (-{\mathrm e}+x^{2}\right ) \ln \relax (5)+{\mathrm e}^{2} x -2 x^{3} {\mathrm e}+x^{5}}\, dx\]

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int((2*exp(x)^8+8*x*exp(x)^6+(-8*ln(5)-4*exp(1)+12*x^2)*exp(x)^4+((-8*x-4)*ln(5)-8*x*exp(1)+8*x^3)*exp(x)^2-4*

x*ln(5)+2*exp(1)^2-4*x^2*exp(1)+2*x^4)*ln((-x*exp(x)^4-2*exp(x)^2*x^2-ln(5)+x*exp(1)-x^3)/(ln(5)*exp(x)^4+2*x*

ln(5)*exp(x)^2+(-exp(1)+x^2)*ln(5)))/(x*exp(x)^8+4*x^2*exp(x)^6+(ln(5)-2*x*exp(1)+6*x^3)*exp(x)^4+(2*x*ln(5)-4

*x^2*exp(1)+4*x^4)*exp(x)^2+(-exp(1)+x^2)*ln(5)+x*exp(1)^2-2*x^3*exp(1)+x^5),x)

[Out]

int((2*exp(x)^8+8*x*exp(x)^6+(-8*ln(5)-4*exp(1)+12*x^2)*exp(x)^4+((-8*x-4)*ln(5)-8*x*exp(1)+8*x^3)*exp(x)^2-4*

x*ln(5)+2*exp(1)^2-4*x^2*exp(1)+2*x^4)*ln((-x*exp(x)^4-2*exp(x)^2*x^2-ln(5)+x*exp(1)-x^3)/(ln(5)*exp(x)^4+2*x*

ln(5)*exp(x)^2+(-exp(1)+x^2)*ln(5)))/(x*exp(x)^8+4*x^2*exp(x)^6+(ln(5)-2*x*exp(1)+6*x^3)*exp(x)^4+(2*x*ln(5)-4

*x^2*exp(1)+4*x^4)*exp(x)^2+(-exp(1)+x^2)*ln(5)+x*exp(1)^2-2*x^3*exp(1)+x^5),x)

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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} 2 \, \int \frac {{\left (x^{4} - 2 \, x^{2} e + 4 \, x e^{\left (6 \, x\right )} + 2 \, {\left (3 \, x^{2} - e - 2 \, \log \relax (5)\right )} e^{\left (4 \, x\right )} + 2 \, {\left (2 \, x^{3} - 2 \, x e - {\left (2 \, x + 1\right )} \log \relax (5)\right )} e^{\left (2 \, x\right )} - 2 \, x \log \relax (5) + e^{2} + e^{\left (8 \, x\right )}\right )} \log \left (-\frac {x^{3} + 2 \, x^{2} e^{\left (2 \, x\right )} - x e + x e^{\left (4 \, x\right )} + \log \relax (5)}{2 \, x e^{\left (2 \, x\right )} \log \relax (5) + {\left (x^{2} - e\right )} \log \relax (5) + e^{\left (4 \, x\right )} \log \relax (5)}\right )}{x^{5} - 2 \, x^{3} e + 4 \, x^{2} e^{\left (6 \, x\right )} + x e^{2} + x e^{\left (8 \, x\right )} + {\left (6 \, x^{3} - 2 \, x e + \log \relax (5)\right )} e^{\left (4 \, x\right )} + 2 \, {\left (2 \, x^{4} - 2 \, x^{2} e + x \log \relax (5)\right )} e^{\left (2 \, x\right )} + {\left (x^{2} - e\right )} \log \relax (5)}\,{d x} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*exp(x)^8+8*x*exp(x)^6+(-8*log(5)-4*exp(1)+12*x^2)*exp(x)^4+((-8*x-4)*log(5)-8*x*exp(1)+8*x^3)*exp

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

xp(x)^4+2*x*log(5)*exp(x)^2+(-exp(1)+x^2)*log(5)))/(x*exp(x)^8+4*x^2*exp(x)^6+(log(5)-2*x*exp(1)+6*x^3)*exp(x)

^4+(2*x*log(5)-4*x^2*exp(1)+4*x^4)*exp(x)^2+(-exp(1)+x^2)*log(5)+x*exp(1)^2-2*x^3*exp(1)+x^5),x, algorithm="ma

xima")

[Out]

2*integrate((x^4 - 2*x^2*e + 4*x*e^(6*x) + 2*(3*x^2 - e - 2*log(5))*e^(4*x) + 2*(2*x^3 - 2*x*e - (2*x + 1)*log

(5))*e^(2*x) - 2*x*log(5) + e^2 + e^(8*x))*log(-(x^3 + 2*x^2*e^(2*x) - x*e + x*e^(4*x) + log(5))/(2*x*e^(2*x)*

log(5) + (x^2 - e)*log(5) + e^(4*x)*log(5)))/(x^5 - 2*x^3*e + 4*x^2*e^(6*x) + x*e^2 + x*e^(8*x) + (6*x^3 - 2*x

*e + log(5))*e^(4*x) + 2*(2*x^4 - 2*x^2*e + x*log(5))*e^(2*x) + (x^2 - e)*log(5)), x)

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mupad [F] time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {\ln \left (-\frac {\ln \relax (5)+x\,{\mathrm {e}}^{4\,x}-x\,\mathrm {e}+2\,x^2\,{\mathrm {e}}^{2\,x}+x^3}{{\mathrm {e}}^{4\,x}\,\ln \relax (5)-\ln \relax (5)\,\left (\mathrm {e}-x^2\right )+2\,x\,{\mathrm {e}}^{2\,x}\,\ln \relax (5)}\right )\,\left (2\,{\mathrm {e}}^{8\,x}+2\,{\mathrm {e}}^2+8\,x\,{\mathrm {e}}^{6\,x}-4\,x\,\ln \relax (5)-{\mathrm {e}}^{2\,x}\,\left (\ln \relax (5)\,\left (8\,x+4\right )+8\,x\,\mathrm {e}-8\,x^3\right )-4\,x^2\,\mathrm {e}-{\mathrm {e}}^{4\,x}\,\left (-12\,x^2+4\,\mathrm {e}+8\,\ln \relax (5)\right )+2\,x^4\right )}{{\mathrm {e}}^{2\,x}\,\left (4\,x^4-4\,\mathrm {e}\,x^2+2\,\ln \relax (5)\,x\right )+x\,{\mathrm {e}}^{8\,x}+x\,{\mathrm {e}}^2+4\,x^2\,{\mathrm {e}}^{6\,x}-2\,x^3\,\mathrm {e}-\ln \relax (5)\,\left (\mathrm {e}-x^2\right )+x^5+{\mathrm {e}}^{4\,x}\,\left (6\,x^3-2\,\mathrm {e}\,x+\ln \relax (5)\right )} \,d x \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

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

*x*exp(2*x)*log(5)))*(2*exp(8*x) + 2*exp(2) + 8*x*exp(6*x) - 4*x*log(5) - exp(2*x)*(log(5)*(8*x + 4) + 8*x*exp

(1) - 8*x^3) - 4*x^2*exp(1) - exp(4*x)*(4*exp(1) + 8*log(5) - 12*x^2) + 2*x^4))/(exp(2*x)*(2*x*log(5) - 4*x^2*

exp(1) + 4*x^4) + x*exp(8*x) + x*exp(2) + 4*x^2*exp(6*x) - 2*x^3*exp(1) - log(5)*(exp(1) - x^2) + x^5 + exp(4*

x)*(log(5) - 2*x*exp(1) + 6*x^3)),x)

[Out]

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

*x*exp(2*x)*log(5)))*(2*exp(8*x) + 2*exp(2) + 8*x*exp(6*x) - 4*x*log(5) - exp(2*x)*(log(5)*(8*x + 4) + 8*x*exp

(1) - 8*x^3) - 4*x^2*exp(1) - exp(4*x)*(4*exp(1) + 8*log(5) - 12*x^2) + 2*x^4))/(exp(2*x)*(2*x*log(5) - 4*x^2*

exp(1) + 4*x^4) + x*exp(8*x) + x*exp(2) + 4*x^2*exp(6*x) - 2*x^3*exp(1) - log(5)*(exp(1) - x^2) + x^5 + exp(4*

x)*(log(5) - 2*x*exp(1) + 6*x^3)), x)

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sympy [B] time = 1.19, size = 61, normalized size = 2.35 \begin {gather*} \log {\left (\frac {- x^{3} - 2 x^{2} e^{2 x} - x e^{4 x} + e x - \log {\relax (5 )}}{2 x e^{2 x} \log {\relax (5 )} + \left (x^{2} - e\right ) \log {\relax (5 )} + e^{4 x} \log {\relax (5 )}} \right )}^{2} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate((2*exp(x)**8+8*x*exp(x)**6+(-8*ln(5)-4*exp(1)+12*x**2)*exp(x)**4+((-8*x-4)*ln(5)-8*x*exp(1)+8*x**3)*

exp(x)**2-4*x*ln(5)+2*exp(1)**2-4*x**2*exp(1)+2*x**4)*ln((-x*exp(x)**4-2*exp(x)**2*x**2-ln(5)+x*exp(1)-x**3)/(

ln(5)*exp(x)**4+2*x*ln(5)*exp(x)**2+(-exp(1)+x**2)*ln(5)))/(x*exp(x)**8+4*x**2*exp(x)**6+(ln(5)-2*x*exp(1)+6*x

**3)*exp(x)**4+(2*x*ln(5)-4*x**2*exp(1)+4*x**4)*exp(x)**2+(-exp(1)+x**2)*ln(5)+x*exp(1)**2-2*x**3*exp(1)+x**5)

,x)

[Out]

log((-x**3 - 2*x**2*exp(2*x) - x*exp(4*x) + E*x - log(5))/(2*x*exp(2*x)*log(5) + (x**2 - E)*log(5) + exp(4*x)*

log(5)))**2

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