∫ 180x3−120x4 log(3)+e2x(200x−600x2+200x3 log(3))+ex(360x2−120x3−180x4+(−200x3+60x4+60x5) log(3))+(−60x2+180x3−60x4 log(3)+ex(−200x+700x2−300x3+(−200x3+100x4) log(3))) log(1−3x+x2 log(3))________________________________________________________________________________________________________________________________________________________ 9x2−27x3+9x4 log(3)+e2x(25−75x+25x2 log(3))+ex(30x−90x2+30x3 log(3)) dx

3.74.87 \(\int \frac {180 x^3-120 x^4 \log (3)+e^{2 x} (200 x-600 x^2+200 x^3 \log (3))+e^x (360 x^2-120 x^3-180 x^4+(-200 x^3+60 x^4+60 x^5) \log (3))+(-60 x^2+180 x^3-60 x^4 \log (3)+e^x (-200 x+700 x^2-300 x^3+(-200 x^3+100 x^4) \log (3))) \log (1-3 x+x^2 \log (3))}{9 x^2-27 x^3+9 x^4 \log (3)+e^{2 x} (25-75 x+25 x^2 \log (3))+e^x (30 x-90 x^2+30 x^3 \log (3))} \, dx\)

Optimal. Leaf size=33 \[ \frac {4 x \left (e^x-\log (1+x (-3+x \log (3)))\right )}{\frac {3}{5}+\frac {e^x}{x}} \]

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Rubi [F] time = 79.61, 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 {180 x^3-120 x^4 \log (3)+e^{2 x} \left (200 x-600 x^2+200 x^3 \log (3)\right )+e^x \left (360 x^2-120 x^3-180 x^4+\left (-200 x^3+60 x^4+60 x^5\right ) \log (3)\right )+\left (-60 x^2+180 x^3-60 x^4 \log (3)+e^x \left (-200 x+700 x^2-300 x^3+\left (-200 x^3+100 x^4\right ) \log (3)\right )\right ) \log \left (1-3 x+x^2 \log (3)\right )}{9 x^2-27 x^3+9 x^4 \log (3)+e^{2 x} \left (25-75 x+25 x^2 \log (3)\right )+e^x \left (30 x-90 x^2+30 x^3 \log (3)\right )} \, dx \end {gather*}

Veriﬁcation is not applicable to the result.

[In]

Int[(180*x^3 - 120*x^4*Log[3] + E^(2*x)*(200*x - 600*x^2 + 200*x^3*Log[3]) + E^x*(360*x^2 - 120*x^3 - 180*x^4

+ (-200*x^3 + 60*x^4 + 60*x^5)*Log[3]) + (-60*x^2 + 180*x^3 - 60*x^4*Log[3] + E^x*(-200*x + 700*x^2 - 300*x^3

+ (-200*x^3 + 100*x^4)*Log[3]))*Log[1 - 3*x + x^2*Log[3]])/(9*x^2 - 27*x^3 + 9*x^4*Log[3] + E^(2*x)*(25 - 75*x

+ 25*x^2*Log[3]) + E^x*(30*x - 90*x^2 + 30*x^3*Log[3])),x]

[Out]

4*x^2 + (36*((3 - Log[3])*Log[27] + 9*(9 - Log[81]))*Defer[Int][(5*E^x + 3*x)^(-2), x])/Log[3]^4 - (12*(9 - Lo

g[3])*Log[27]*(9 - Log[81])*Defer[Int][(5*E^x + 3*x)^(-2), x])/Log[3]^5 - (108*(3 + (Log[3]*(9 - Log[2187]))/L

og[27])*Defer[Int][(5*E^x + 3*x)^(-2), x])/Log[3]^3 - (60*(3 - Log[3])*Log[1 - 3*x + x^2*Log[3]]*Defer[Int][(5

*E^x + 3*x)^(-2), x])/Log[3]^2 - (36*(9 - Log[81])*Log[243]*Log[1 - 3*x + x^2*Log[3]]*Defer[Int][(5*E^x + 3*x)

^(-2), x])/Log[3]^4 + (12*(135 - 15*Log[81] + (3 - Log[3])*Log[243])*Log[1 - 3*x + x^2*Log[3]]*Defer[Int][(5*E

^x + 3*x)^(-2), x])/Log[3]^3 - (36*(3 - Log[3])*Defer[Int][x/(5*E^x + 3*x)^2, x])/Log[3]^2 + (12*((3 - Log[3])

*Log[27] + 9*(9 - Log[81]))*Defer[Int][x/(5*E^x + 3*x)^2, x])/Log[3]^3 - (36*Log[27]*(9 - Log[81])*Defer[Int][

x/(5*E^x + 3*x)^2, x])/Log[3]^4 + (180*(3 - Log[3])*Log[1 - 3*x + x^2*Log[3]]*Defer[Int][x/(5*E^x + 3*x)^2, x]

)/Log[3]^2 - (60*Log[1 - 3*x + x^2*Log[3]]*Defer[Int][x/(5*E^x + 3*x)^2, x])/Log[3] - (12*(9 - Log[81])*Log[24

3]*Log[1 - 3*x + x^2*Log[3]]*Defer[Int][x/(5*E^x + 3*x)^2, x])/Log[3]^3 + (108*(3 - Log[3])*Defer[Int][x^2/(5*

E^x + 3*x)^2, x])/Log[3]^2 - (36*Defer[Int][x^2/(5*E^x + 3*x)^2, x])/Log[3] - (12*Log[27]*(9 - Log[81])*Defer[

Int][x^2/(5*E^x + 3*x)^2, x])/Log[3]^3 + (180*Log[1 - 3*x + x^2*Log[3]]*Defer[Int][x^2/(5*E^x + 3*x)^2, x])/Lo

g[3] - (12*(3 - Log[3])*Log[243]*Log[1 - 3*x + x^2*Log[3]]*Defer[Int][x^2/(5*E^x + 3*x)^2, x])/Log[3]^2 + (108

*Defer[Int][x^3/(5*E^x + 3*x)^2, x])/Log[3] - (12*(3 - Log[3])*Log[27]*Defer[Int][x^3/(5*E^x + 3*x)^2, x])/Log

[3]^2 - (12*Log[243]*Log[1 - 3*x + x^2*Log[3]]*Defer[Int][x^3/(5*E^x + 3*x)^2, x])/Log[3] - (12*Log[27]*Defer[

Int][x^4/(5*E^x + 3*x)^2, x])/Log[3] + (120*(3 - Log[3])*Defer[Int][(5*E^x + 3*x)^(-1), x])/Log[3]^2 - (36*(9

- Log[3])*(1 + Log[3])*Defer[Int][(5*E^x + 3*x)^(-1), x])/Log[3]^3 + (12*(9 - Log[9])*Log[27]*Defer[Int][(5*E^

x + 3*x)^(-1), x])/Log[3]^4 + (20*(9 - Log[3])*Log[1 - 3*x + x^2*Log[3]]*Defer[Int][(5*E^x + 3*x)^(-1), x])/Lo

g[3]^2 - (60*(3 + Log[9])*Log[1 - 3*x + x^2*Log[3]]*Defer[Int][(5*E^x + 3*x)^(-1), x])/Log[3]^2 - (108*(1 + Lo

g[3])*Defer[Int][x/(5*E^x + 3*x), x])/Log[3]^2 + (4*(9 - Log[3])*Log[27]*Defer[Int][x/(5*E^x + 3*x), x])/Log[3

]^3 + (60*Log[1 - 3*x + x^2*Log[3]]*Defer[Int][x/(5*E^x + 3*x), x])/Log[3] + (12*Log[27]*Defer[Int][x^2/(5*E^x

+ 3*x), x])/Log[3]^2 + (36*(1 + 3/Sqrt[9 - 4*Log[3]])*(3 - Log[3])*Defer[Int][1/((5*E^x + 3*x)^2*(-3 - Sqrt[9

- 4*Log[3]] + 2*x*Log[3])), x])/Log[3]^2 + (12*(1 + 3/Sqrt[9 - 4*Log[3]])*(9 - Log[3])*((3 - Log[3])*Log[27]

+ 9*(9 - Log[81]))*Defer[Int][1/((5*E^x + 3*x)^2*(-3 - Sqrt[9 - 4*Log[3]] + 2*x*Log[3])), x])/Log[3]^4 - (36*(

1 + 3/Sqrt[9 - 4*Log[3]])*(9 - Log[9])*Log[27]*(9 - Log[81])*Defer[Int][1/((5*E^x + 3*x)^2*(-3 - Sqrt[9 - 4*Lo

g[3]] + 2*x*Log[3])), x])/Log[3]^5 - (324*(1 + 3/Sqrt[9 - 4*Log[3]])*(3 + (Log[3]*(9 - Log[2187]))/Log[27])*De

fer[Int][1/((5*E^x + 3*x)^2*(-3 - Sqrt[9 - 4*Log[3]] + 2*x*Log[3])), x])/Log[3]^3 - (12*(1 + 3/Sqrt[9 - 4*Log[

3]])*(9 - Log[3])*(9 - Log[81])*Log[243]*Log[1 - 3*x + x^2*Log[3]]*Defer[Int][1/((5*E^x + 3*x)^2*(-3 - Sqrt[9

- 4*Log[3]] + 2*x*Log[3])), x])/Log[3]^4 + (36*(1 + 3/Sqrt[9 - 4*Log[3]])*(135 - 15*Log[81] + (3 - Log[3])*Log

[243])*Log[1 - 3*x + x^2*Log[3]]*Defer[Int][1/((5*E^x + 3*x)^2*(-3 - Sqrt[9 - 4*Log[3]] + 2*x*Log[3])), x])/Lo

g[3]^3 - (180*(1 + 3/Sqrt[9 - 4*Log[3]])*(3 + (Log[3]*(9 - Log[2187]))/Log[27])*Log[1 - 3*x + x^2*Log[3]]*Defe

r[Int][1/((5*E^x + 3*x)^2*(-3 - Sqrt[9 - 4*Log[3]] + 2*x*Log[3])), x])/Log[3]^2 + (40*(1 + 3/Sqrt[9 - 4*Log[3]

])*(3 - Log[3])*(9 - Log[3])*Defer[Int][1/((5*E^x + 3*x)*(-3 - Sqrt[9 - 4*Log[3]] + 2*x*Log[3])), x])/Log[3]^2

+ (72*(1 + 3/Sqrt[9 - 4*Log[3]])*Defer[Int][1/((5*E^x + 3*x)*(-3 - Sqrt[9 - 4*Log[3]] + 2*x*Log[3])), x])/Log

[3] - (108*(1 + 3/Sqrt[9 - 4*Log[3]])*(1 + Log[3])*(9 - Log[9])*Defer[Int][1/((5*E^x + 3*x)*(-3 - Sqrt[9 - 4*L

og[3]] + 2*x*Log[3])), x])/Log[3]^3 + (4*(1 + 3/Sqrt[9 - 4*Log[3]])*(81 - 27*Log[3] + Log[3]^2)*Log[27]*Defer[

Int][1/((5*E^x + 3*x)*(-3 - Sqrt[9 - 4*Log[3]] + 2*x*Log[3])), x])/Log[3]^4 - 40*(1 + 3/Sqrt[9 - 4*Log[3]])*Lo

g[1 - 3*x + x^2*Log[3]]*Defer[Int][1/((5*E^x + 3*x)*(-3 - Sqrt[9 - 4*Log[3]] + 2*x*Log[3])), x] + (420*(1 + 3/

Sqrt[9 - 4*Log[3]])*Log[1 - 3*x + x^2*Log[3]]*Defer[Int][1/((5*E^x + 3*x)*(-3 - Sqrt[9 - 4*Log[3]] + 2*x*Log[3

])), x])/Log[3] + (60*(1 + 3/Sqrt[9 - 4*Log[3]])*(9 - Log[9])*Log[1 - 3*x + x^2*Log[3]]*Defer[Int][1/((5*E^x +

3*x)*(-3 - Sqrt[9 - 4*Log[3]] + 2*x*Log[3])), x])/Log[3]^2 - (20*(1 + 3/Sqrt[9 - 4*Log[3]])*(9 - Log[3])*(3 +

Log[9])*Log[1 - 3*x + x^2*Log[3]]*Defer[Int][1/((5*E^x + 3*x)*(-3 - Sqrt[9 - 4*Log[3]] + 2*x*Log[3])), x])/Lo

g[3]^2 + (36*(1 - 3/Sqrt[9 - 4*Log[3]])*(3 - Log[3])*Defer[Int][1/((5*E^x + 3*x)^2*(-3 + Sqrt[9 - 4*Log[3]] +

2*x*Log[3])), x])/Log[3]^2 + (12*(1 - 3/Sqrt[9 - 4*Log[3]])*(9 - Log[3])*((3 - Log[3])*Log[27] + 9*(9 - Log[81

]))*Defer[Int][1/((5*E^x + 3*x)^2*(-3 + Sqrt[9 - 4*Log[3]] + 2*x*Log[3])), x])/Log[3]^4 - (36*(1 - 3/Sqrt[9 -

4*Log[3]])*(9 - Log[9])*Log[27]*(9 - Log[81])*Defer[Int][1/((5*E^x + 3*x)^2*(-3 + Sqrt[9 - 4*Log[3]] + 2*x*Log

[3])), x])/Log[3]^5 - (324*(1 - 3/Sqrt[9 - 4*Log[3]])*(3 + (Log[3]*(9 - Log[2187]))/Log[27])*Defer[Int][1/((5*

E^x + 3*x)^2*(-3 + Sqrt[9 - 4*Log[3]] + 2*x*Log[3])), x])/Log[3]^3 - (12*(1 - 3/Sqrt[9 - 4*Log[3]])*(9 - Log[3

])*(9 - Log[81])*Log[243]*Log[1 - 3*x + x^2*Log[3]]*Defer[Int][1/((5*E^x + 3*x)^2*(-3 + Sqrt[9 - 4*Log[3]] + 2

*x*Log[3])), x])/Log[3]^4 + (36*(1 - 3/Sqrt[9 - 4*Log[3]])*(135 - 15*Log[81] + (3 - Log[3])*Log[243])*Log[1 -

3*x + x^2*Log[3]]*Defer[Int][1/((5*E^x + 3*x)^2*(-3 + Sqrt[9 - 4*Log[3]] + 2*x*Log[3])), x])/Log[3]^3 - (180*(

1 - 3/Sqrt[9 - 4*Log[3]])*(3 + (Log[3]*(9 - Log[2187]))/Log[27])*Log[1 - 3*x + x^2*Log[3]]*Defer[Int][1/((5*E^

x + 3*x)^2*(-3 + Sqrt[9 - 4*Log[3]] + 2*x*Log[3])), x])/Log[3]^2 + (40*(1 - 3/Sqrt[9 - 4*Log[3]])*(3 - Log[3])

*(9 - Log[3])*Defer[Int][1/((5*E^x + 3*x)*(-3 + Sqrt[9 - 4*Log[3]] + 2*x*Log[3])), x])/Log[3]^2 + (72*(1 - 3/S

qrt[9 - 4*Log[3]])*Defer[Int][1/((5*E^x + 3*x)*(-3 + Sqrt[9 - 4*Log[3]] + 2*x*Log[3])), x])/Log[3] - (108*(1 -

3/Sqrt[9 - 4*Log[3]])*(1 + Log[3])*(9 - Log[9])*Defer[Int][1/((5*E^x + 3*x)*(-3 + Sqrt[9 - 4*Log[3]] + 2*x*Lo

g[3])), x])/Log[3]^3 + (4*(1 - 3/Sqrt[9 - 4*Log[3]])*(81 - 27*Log[3] + Log[3]^2)*Log[27]*Defer[Int][1/((5*E^x

+ 3*x)*(-3 + Sqrt[9 - 4*Log[3]] + 2*x*Log[3])), x])/Log[3]^4 - 40*(1 - 3/Sqrt[9 - 4*Log[3]])*Log[1 - 3*x + x^2

*Log[3]]*Defer[Int][1/((5*E^x + 3*x)*(-3 + Sqrt[9 - 4*Log[3]] + 2*x*Log[3])), x] + (420*(1 - 3/Sqrt[9 - 4*Log[

3]])*Log[1 - 3*x + x^2*Log[3]]*Defer[Int][1/((5*E^x + 3*x)*(-3 + Sqrt[9 - 4*Log[3]] + 2*x*Log[3])), x])/Log[3]

+ (60*(1 - 3/Sqrt[9 - 4*Log[3]])*(9 - Log[9])*Log[1 - 3*x + x^2*Log[3]]*Defer[Int][1/((5*E^x + 3*x)*(-3 + Sqr

t[9 - 4*Log[3]] + 2*x*Log[3])), x])/Log[3]^2 - (20*(1 - 3/Sqrt[9 - 4*Log[3]])*(9 - Log[3])*(3 + Log[9])*Log[1

- 3*x + x^2*Log[3]]*Defer[Int][1/((5*E^x + 3*x)*(-3 + Sqrt[9 - 4*Log[3]] + 2*x*Log[3])), x])/Log[3]^2 - (24*Sq

rt[9 - 4*Log[3]]*(9 - Log[3])*Log[27]*Defer[Int][1/((5*E^x + 3*x)^2*(3 + Sqrt[9 - 4*Log[3]] - x*Log[9])), x])/

Log[3]^4 + (72*((3 - Log[3])*Log[27] + 9*(9 - Log[81]))*Defer[Int][1/((5*E^x + 3*x)^2*(3 + Sqrt[9 - 4*Log[3]]

- x*Log[9])), x])/(Sqrt[9 - 4*Log[3]]*Log[3]^3) - (216*(3 + (Log[3]*(9 - Log[2187]))/Log[27])*Defer[Int][1/((5

*E^x + 3*x)^2*(3 + Sqrt[9 - 4*Log[3]] - x*Log[9])), x])/(Sqrt[9 - 4*Log[3]]*Log[3]^2) - (120*(3 - Log[3])*Log[

1 - 3*x + x^2*Log[3]]*Defer[Int][1/((5*E^x + 3*x)^2*(3 + Sqrt[9 - 4*Log[3]] - x*Log[9])), x])/(Sqrt[9 - 4*Log[

3]]*Log[3]) - (72*Sqrt[9 - Log[81]]*Log[243]*Log[1 - 3*x + x^2*Log[3]]*Defer[Int][1/((5*E^x + 3*x)^2*(3 + Sqrt

[9 - 4*Log[3]] - x*Log[9])), x])/Log[3]^3 + (24*(135 - 15*Log[81] + (3 - Log[3])*Log[243])*Log[1 - 3*x + x^2*L

og[3]]*Defer[Int][1/((5*E^x + 3*x)^2*(3 + Sqrt[9 - 4*Log[3]] - x*Log[9])), x])/(Sqrt[9 - 4*Log[3]]*Log[3]^2) +

(48*Defer[Int][1/((5*E^x + 3*x)*(3 + Sqrt[9 - 4*Log[3]] - x*Log[9])), x])/Sqrt[9 - 4*Log[3]] + (240*(3 - Log[

3])*Defer[Int][1/((5*E^x + 3*x)*(3 + Sqrt[9 - 4*Log[3]] - x*Log[9])), x])/(Sqrt[9 - 4*Log[3]]*Log[3]) - (72*(9

- Log[3])*(1 + Log[3])*Defer[Int][1/((5*E^x + 3*x)*(3 + Sqrt[9 - 4*Log[3]] - x*Log[9])), x])/(Sqrt[9 - 4*Log[

3]]*Log[3]^2) + (24*(9 - Log[9])*Log[27]*Defer[Int][1/((5*E^x + 3*x)*(3 + Sqrt[9 - 4*Log[3]] - x*Log[9])), x])

/(Sqrt[9 - 4*Log[3]]*Log[3]^3) + (280*Log[1 - 3*x + x^2*Log[3]]*Defer[Int][1/((5*E^x + 3*x)*(3 + Sqrt[9 - 4*Lo

g[3]] - x*Log[9])), x])/Sqrt[9 - 4*Log[3]] + (40*(9 - Log[3])*Log[1 - 3*x + x^2*Log[3]]*Defer[Int][1/((5*E^x +

3*x)*(3 + Sqrt[9 - 4*Log[3]] - x*Log[9])), x])/(Sqrt[9 - 4*Log[3]]*Log[3]) - (120*(3 + Log[9])*Log[1 - 3*x +

x^2*Log[3]]*Defer[Int][1/((5*E^x + 3*x)*(3 + Sqrt[9 - 4*Log[3]] - x*Log[9])), x])/(Sqrt[9 - 4*Log[3]]*Log[3])

- (24*Sqrt[9 - 4*Log[3]]*(9 - Log[3])*Log[27]*Defer[Int][1/((5*E^x + 3*x)^2*(-3 + Sqrt[9 - 4*Log[3]] + x*Log[9

])), x])/Log[3]^4 + (72*((3 - Log[3])*Log[27] + 9*(9 - Log[81]))*Defer[Int][1/((5*E^x + 3*x)^2*(-3 + Sqrt[9 -

4*Log[3]] + x*Log[9])), x])/(Sqrt[9 - 4*Log[3]]*Log[3]^3) - (216*(3 + (Log[3]*(9 - Log[2187]))/Log[27])*Defer[

Int][1/((5*E^x + 3*x)^2*(-3 + Sqrt[9 - 4*Log[3]] + x*Log[9])), x])/(Sqrt[9 - 4*Log[3]]*Log[3]^2) - (120*(3 - L

og[3])*Log[1 - 3*x + x^2*Log[3]]*Defer[Int][1/((5*E^x + 3*x)^2*(-3 + Sqrt[9 - 4*Log[3]] + x*Log[9])), x])/(Sqr

t[9 - 4*Log[3]]*Log[3]) - (72*Sqrt[9 - Log[81]]*Log[243]*Log[1 - 3*x + x^2*Log[3]]*Defer[Int][1/((5*E^x + 3*x)

^2*(-3 + Sqrt[9 - 4*Log[3]] + x*Log[9])), x])/Log[3]^3 + (24*(135 - 15*Log[81] + (3 - Log[3])*Log[243])*Log[1

- 3*x + x^2*Log[3]]*Defer[Int][1/((5*E^x + 3*x)^2*(-3 + Sqrt[9 - 4*Log[3]] + x*Log[9])), x])/(Sqrt[9 - 4*Log[3

]]*Log[3]^2) + (48*Defer[Int][1/((5*E^x + 3*x)*(-3 + Sqrt[9 - 4*Log[3]] + x*Log[9])), x])/Sqrt[9 - 4*Log[3]] +

(240*(3 - Log[3])*Defer[Int][1/((5*E^x + 3*x)*(-3 + Sqrt[9 - 4*Log[3]] + x*Log[9])), x])/(Sqrt[9 - 4*Log[3]]*

Log[3]) - (72*(9 - Log[3])*(1 + Log[3])*Defer[Int][1/((5*E^x + 3*x)*(-3 + Sqrt[9 - 4*Log[3]] + x*Log[9])), x])

/(Sqrt[9 - 4*Log[3]]*Log[3]^2) + (24*(9 - Log[9])*Log[27]*Defer[Int][1/((5*E^x + 3*x)*(-3 + Sqrt[9 - 4*Log[3]]

+ x*Log[9])), x])/(Sqrt[9 - 4*Log[3]]*Log[3]^3) + (280*Log[1 - 3*x + x^2*Log[3]]*Defer[Int][1/((5*E^x + 3*x)*

(-3 + Sqrt[9 - 4*Log[3]] + x*Log[9])), x])/Sqrt[9 - 4*Log[3]] + (40*(9 - Log[3])*Log[1 - 3*x + x^2*Log[3]]*Def

er[Int][1/((5*E^x + 3*x)*(-3 + Sqrt[9 - 4*Log[3]] + x*Log[9])), x])/(Sqrt[9 - 4*Log[3]]*Log[3]) - (120*(3 + Lo

g[9])*Log[1 - 3*x + x^2*Log[3]]*Defer[Int][1/((5*E^x + 3*x)*(-3 + Sqrt[9 - 4*Log[3]] + x*Log[9])), x])/(Sqrt[9

- 4*Log[3]]*Log[3]) + 24*Defer[Int][(x*Log[27] + E^x*Log[243])^(-1), x] + 140*Log[1 - 3*x + x^2*Log[3]]*Defer

[Int][(x*Log[27] + E^x*Log[243])^(-1), x] + 40*(3 - Log[3])*Defer[Int][x/(x*Log[27] + E^x*Log[243]), x] - 20*(

3 + Log[9])*Log[1 - 3*x + x^2*Log[3]]*Defer[Int][x/(x*Log[27] + E^x*Log[243]), x] - 36*(1 + Log[3])*Defer[Int]

[x^2/(x*Log[27] + E^x*Log[243]), x] + 20*Log[3]*Log[1 - 3*x + x^2*Log[3]]*Defer[Int][x^2/(x*Log[27] + E^x*Log[

243]), x] + 4*Log[27]*Defer[Int][x^3/(x*Log[27] + E^x*Log[243]), x] + (60*(1 + 3/Sqrt[9 - 4*Log[3]])*(3 - Log[

3])*Log[9]*Defer[Int][Defer[Int][(5*E^x + 3*x)^(-2), x]/(-3 - Sqrt[9 - 4*Log[3]] + 2*x*Log[3]), x])/Log[3]^2 +

(36*(1 + 3/Sqrt[9 - 4*Log[3]])*Log[9]*(9 - Log[81])*Log[243]*Defer[Int][Defer[Int][(5*E^x + 3*x)^(-2), x]/(-3

- Sqrt[9 - 4*Log[3]] + 2*x*Log[3]), x])/Log[3]^4 - (12*(135 - 15*Log[81] + (3 - Log[3])*Log[243])*(Log[9] + L

og[729]/Sqrt[9 - Log[81]])*Defer[Int][Defer[Int][(5*E^x + 3*x)^(-2), x]/(-3 - Sqrt[9 - 4*Log[3]] + 2*x*Log[3])

, x])/Log[3]^3 + (60*(1 - 3/Sqrt[9 - 4*Log[3]])*(3 - Log[3])*Log[9]*Defer[Int][Defer[Int][(5*E^x + 3*x)^(-2),

x]/(-3 + Sqrt[9 - 4*Log[3]] + 2*x*Log[3]), x])/Log[3]^2 + (36*(1 - 3/Sqrt[9 - 4*Log[3]])*Log[9]*(9 - Log[81])*

Log[243]*Defer[Int][Defer[Int][(5*E^x + 3*x)^(-2), x]/(-3 + Sqrt[9 - 4*Log[3]] + 2*x*Log[3]), x])/Log[3]^4 - (

12*(1 - 3/Sqrt[9 - 4*Log[3]])*Log[9]*(135 - 15*Log[81] + (3 - Log[3])*Log[243])*Defer[Int][Defer[Int][(5*E^x +

3*x)^(-2), x]/(-3 + Sqrt[9 - 4*Log[3]] + 2*x*Log[3]), x])/Log[3]^3 + (360*(3 - Log[3])*Defer[Int][Defer[Int][

(5*E^x + 3*x)^(-2), x]/(3 + Sqrt[9 - 4*Log[3]] - x*Log[9]), x])/(Sqrt[9 - 4*Log[3]]*Log[3]) + (216*Sqrt[9 - Lo

g[81]]*Log[243]*Defer[Int][Defer[Int][(5*E^x + 3*x)^(-2), x]/(3 + Sqrt[9 - 4*Log[3]] - x*Log[9]), x])/Log[3]^3

- (72*(135 - 15*Log[81] + (3 - Log[3])*Log[243])*Defer[Int][Defer[Int][(5*E^x + 3*x)^(-2), x]/(3 + Sqrt[9 - 4

*Log[3]] - x*Log[9]), x])/(Sqrt[9 - 4*Log[3]]*Log[3]^2) + (360*(3 - Log[3])*Defer[Int][Defer[Int][(5*E^x + 3*x

)^(-2), x]/(-3 + Sqrt[9 - 4*Log[3]] + x*Log[9]), x])/(Sqrt[9 - 4*Log[3]]*Log[3]) + (216*Sqrt[9 - Log[81]]*Log[

243]*Defer[Int][Defer[Int][(5*E^x + 3*x)^(-2), x]/(-3 + Sqrt[9 - 4*Log[3]] + x*Log[9]), x])/Log[3]^3 - (72*(13

5 - 15*Log[81] + (3 - Log[3])*Log[243])*Defer[Int][Defer[Int][(5*E^x + 3*x)^(-2), x]/(-3 + Sqrt[9 - 4*Log[3]]

+ x*Log[9]), x])/(Sqrt[9 - 4*Log[3]]*Log[3]^2) - (180*(1 + 3/Sqrt[9 - 4*Log[3]])*(3 - Log[3])*Log[9]*Defer[Int

][Defer[Int][x/(5*E^x + 3*x)^2, x]/(-3 - Sqrt[9 - 4*Log[3]] + 2*x*Log[3]), x])/Log[3]^2 + (60*(1 + 3/Sqrt[9 -

4*Log[3]])*Log[9]*Defer[Int][Defer[Int][x/(5*E^x + 3*x)^2, x]/(-3 - Sqrt[9 - 4*Log[3]] + 2*x*Log[3]), x])/Log[

3] + (12*(1 + 3/Sqrt[9 - 4*Log[3]])*Log[9]*(9 - Log[81])*Log[243]*Defer[Int][Defer[Int][x/(5*E^x + 3*x)^2, x]/

(-3 - Sqrt[9 - 4*Log[3]] + 2*x*Log[3]), x])/Log[3]^3 - (180*(1 - 3/Sqrt[9 - 4*Log[3]])*(3 - Log[3])*Log[9]*Def

er[Int][Defer[Int][x/(5*E^x + 3*x)^2, x]/(-3 + Sqrt[9 - 4*Log[3]] + 2*x*Log[3]), x])/Log[3]^2 + (60*(1 - 3/Sqr

t[9 - 4*Log[3]])*Log[9]*Defer[Int][Defer[Int][x/(5*E^x + 3*x)^2, x]/(-3 + Sqrt[9 - 4*Log[3]] + 2*x*Log[3]), x]

)/Log[3] + (12*(1 - 3/Sqrt[9 - 4*Log[3]])*Log[9]*(9 - Log[81])*Log[243]*Defer[Int][Defer[Int][x/(5*E^x + 3*x)^

2, x]/(-3 + Sqrt[9 - 4*Log[3]] + 2*x*Log[3]), x])/Log[3]^3 + (360*Defer[Int][Defer[Int][x/(5*E^x + 3*x)^2, x]/

(3 + Sqrt[9 - 4*Log[3]] - x*Log[9]), x])/Sqrt[9 - 4*Log[3]] - (1080*(3 - Log[3])*Defer[Int][Defer[Int][x/(5*E^

x + 3*x)^2, x]/(3 + Sqrt[9 - 4*Log[3]] - x*Log[9]), x])/(Sqrt[9 - 4*Log[3]]*Log[3]) + (72*Sqrt[9 - Log[81]]*Lo

g[243]*Defer[Int][Defer[Int][x/(5*E^x + 3*x)^2, x]/(3 + Sqrt[9 - 4*Log[3]] - x*Log[9]), x])/Log[3]^2 + (360*De

fer[Int][Defer[Int][x/(5*E^x + 3*x)^2, x]/(-3 + Sqrt[9 - 4*Log[3]] + x*Log[9]), x])/Sqrt[9 - 4*Log[3]] - (1080

*(3 - Log[3])*Defer[Int][Defer[Int][x/(5*E^x + 3*x)^2, x]/(-3 + Sqrt[9 - 4*Log[3]] + x*Log[9]), x])/(Sqrt[9 -

4*Log[3]]*Log[3]) + (72*Sqrt[9 - Log[81]]*Log[243]*Defer[Int][Defer[Int][x/(5*E^x + 3*x)^2, x]/(-3 + Sqrt[9 -

4*Log[3]] + x*Log[9]), x])/Log[3]^2 - (180*(1 + 3/Sqrt[9 - 4*Log[3]])*Log[9]*Defer[Int][Defer[Int][x^2/(5*E^x

+ 3*x)^2, x]/(-3 - Sqrt[9 - 4*Log[3]] + 2*x*Log[3]), x])/Log[3] + (12*(1 + 3/Sqrt[9 - 4*Log[3]])*(3 - Log[3])*

Log[9]*Log[243]*Defer[Int][Defer[Int][x^2/(5*E^x + 3*x)^2, x]/(-3 - Sqrt[9 - 4*Log[3]] + 2*x*Log[3]), x])/Log[

3]^2 - (180*(1 - 3/Sqrt[9 - 4*Log[3]])*Log[9]*Defer[Int][Defer[Int][x^2/(5*E^x + 3*x)^2, x]/(-3 + Sqrt[9 - 4*L

og[3]] + 2*x*Log[3]), x])/Log[3] + (12*(1 - 3/Sqrt[9 - 4*Log[3]])*(3 - Log[3])*Log[9]*Log[243]*Defer[Int][Defe

r[Int][x^2/(5*E^x + 3*x)^2, x]/(-3 + Sqrt[9 - 4*Log[3]] + 2*x*Log[3]), x])/Log[3]^2 - (1080*Defer[Int][Defer[I

nt][x^2/(5*E^x + 3*x)^2, x]/(3 + Sqrt[9 - 4*Log[3]] - x*Log[9]), x])/Sqrt[9 - 4*Log[3]] + (72*(3 - Log[3])*Log

[243]*Defer[Int][Defer[Int][x^2/(5*E^x + 3*x)^2, x]/(3 + Sqrt[9 - 4*Log[3]] - x*Log[9]), x])/(Sqrt[9 - 4*Log[3

]]*Log[3]) - (1080*Defer[Int][Defer[Int][x^2/(5*E^x + 3*x)^2, x]/(-3 + Sqrt[9 - 4*Log[3]] + x*Log[9]), x])/Sqr

t[9 - 4*Log[3]] + (72*(3 - Log[3])*Log[243]*Defer[Int][Defer[Int][x^2/(5*E^x + 3*x)^2, x]/(-3 + Sqrt[9 - 4*Log

[3]] + x*Log[9]), x])/(Sqrt[9 - 4*Log[3]]*Log[3]) + (12*(1 + 3/Sqrt[9 - 4*Log[3]])*Log[9]*Log[243]*Defer[Int][

Defer[Int][x^3/(5*E^x + 3*x)^2, x]/(-3 - Sqrt[9 - 4*Log[3]] + 2*x*Log[3]), x])/Log[3] + (12*(1 - 3/Sqrt[9 - 4*

Log[3]])*Log[9]*Log[243]*Defer[Int][Defer[Int][x^3/(5*E^x + 3*x)^2, x]/(-3 + Sqrt[9 - 4*Log[3]] + 2*x*Log[3]),

x])/Log[3] + (72*Log[243]*Defer[Int][Defer[Int][x^3/(5*E^x + 3*x)^2, x]/(3 + Sqrt[9 - 4*Log[3]] - x*Log[9]),

x])/Sqrt[9 - 4*Log[3]] + (72*Log[243]*Defer[Int][Defer[Int][x^3/(5*E^x + 3*x)^2, x]/(-3 + Sqrt[9 - 4*Log[3]] +

x*Log[9]), x])/Sqrt[9 - 4*Log[3]] - (20*(1 + 3/Sqrt[9 - 4*Log[3]])*(9 - Log[3])*Log[9]*Defer[Int][Defer[Int][

(5*E^x + 3*x)^(-1), x]/(-3 - Sqrt[9 - 4*Log[3]] + 2*x*Log[3]), x])/Log[3]^2 + (60*(3 + Log[9])*(Log[9] + Log[7

29]/Sqrt[9 - Log[81]])*Defer[Int][Defer[Int][(5*E^x + 3*x)^(-1), x]/(-3 - Sqrt[9 - 4*Log[3]] + 2*x*Log[3]), x]

)/Log[3]^2 - (20*(1 - 3/Sqrt[9 - 4*Log[3]])*(9 - Log[3])*Log[9]*Defer[Int][Defer[Int][(5*E^x + 3*x)^(-1), x]/(

-3 + Sqrt[9 - 4*Log[3]] + 2*x*Log[3]), x])/Log[3]^2 + (60*(1 - 3/Sqrt[9 - 4*Log[3]])*Log[9]*(3 + Log[9])*Defer

[Int][Defer[Int][(5*E^x + 3*x)^(-1), x]/(-3 + Sqrt[9 - 4*Log[3]] + 2*x*Log[3]), x])/Log[3]^2 - (120*(9 - Log[3

])*Defer[Int][Defer[Int][(5*E^x + 3*x)^(-1), x]/(3 + Sqrt[9 - 4*Log[3]] - x*Log[9]), x])/(Sqrt[9 - 4*Log[3]]*L

og[3]) + (360*(3 + Log[9])*Defer[Int][Defer[Int][(5*E^x + 3*x)^(-1), x]/(3 + Sqrt[9 - 4*Log[3]] - x*Log[9]), x

])/(Sqrt[9 - 4*Log[3]]*Log[3]) - (120*(9 - Log[3])*Defer[Int][Defer[Int][(5*E^x + 3*x)^(-1), x]/(-3 + Sqrt[9 -

4*Log[3]] + x*Log[9]), x])/(Sqrt[9 - 4*Log[3]]*Log[3]) + (360*(3 + Log[9])*Defer[Int][Defer[Int][(5*E^x + 3*x

)^(-1), x]/(-3 + Sqrt[9 - 4*Log[3]] + x*Log[9]), x])/(Sqrt[9 - 4*Log[3]]*Log[3]) - (60*(1 + 3/Sqrt[9 - 4*Log[3

]])*Log[9]*Defer[Int][Defer[Int][x/(5*E^x + 3*x), x]/(-3 - Sqrt[9 - 4*Log[3]] + 2*x*Log[3]), x])/Log[3] - (60*

(1 - 3/Sqrt[9 - 4*Log[3]])*Log[9]*Defer[Int][Defer[Int][x/(5*E^x + 3*x), x]/(-3 + Sqrt[9 - 4*Log[3]] + 2*x*Log

[3]), x])/Log[3] - (360*Defer[Int][Defer[Int][x/(5*E^x + 3*x), x]/(3 + Sqrt[9 - 4*Log[3]] - x*Log[9]), x])/Sqr

t[9 - 4*Log[3]] - (360*Defer[Int][Defer[Int][x/(5*E^x + 3*x), x]/(-3 + Sqrt[9 - 4*Log[3]] + x*Log[9]), x])/Sqr

t[9 - 4*Log[3]] + (120*(3 + Sqrt[9 - 4*Log[3]])*(3 - Log[3])*Log[9]*Defer[Int][Defer[Int][1/((5*E^x + 3*x)^2*(

3 + Sqrt[9 - 4*Log[3]] - x*Log[9])), x]/(-3 - Sqrt[9 - 4*Log[3]] + 2*x*Log[3]), x])/(Log[3]*(9 - Log[81])) + (

72*(3 + Sqrt[9 - 4*Log[3]])*Log[9]*Log[243]*Defer[Int][Defer[Int][1/((5*E^x + 3*x)^2*(3 + Sqrt[9 - 4*Log[3]] -

x*Log[9])), x]/(-3 - Sqrt[9 - 4*Log[3]] + 2*x*Log[3]), x])/Log[3]^3 - (24*(3 + Sqrt[9 - 4*Log[3]])*Log[9]*(13

5 - 15*Log[81] + (3 - Log[3])*Log[243])*Defer[Int][Defer[Int][1/((5*E^x + 3*x)^2*(3 + Sqrt[9 - 4*Log[3]] - x*L

og[9])), x]/(-3 - Sqrt[9 - 4*Log[3]] + 2*x*Log[3]), x])/(Log[3]^2*(9 - Log[81])) - (120*(3 - Sqrt[9 - 4*Log[3]

])*(3 - Log[3])*Log[9]*Defer[Int][Defer[Int][1/((5*E^x + 3*x)^2*(3 + Sqrt[9 - 4*Log[3]] - x*Log[9])), x]/(-3 +

Sqrt[9 - 4*Log[3]] + 2*x*Log[3]), x])/(Log[3]*(9 - Log[81])) - (72*(3 - Sqrt[9 - 4*Log[3]])*Log[9]*Log[243]*D

efer[Int][Defer[Int][1/((5*E^x + 3*x)^2*(3 + Sqrt[9 - 4*Log[3]] - x*Log[9])), x]/(-3 + Sqrt[9 - 4*Log[3]] + 2*

x*Log[3]), x])/Log[3]^3 + (24*(3 - Sqrt[9 - 4*Log[3]])*Log[9]*(135 - 15*Log[81] + (3 - Log[3])*Log[243])*Defer

[Int][Defer[Int][1/((5*E^x + 3*x)^2*(3 + Sqrt[9 - 4*Log[3]] - x*Log[9])), x]/(-3 + Sqrt[9 - 4*Log[3]] + 2*x*Lo

g[3]), x])/(Log[3]^2*(9 - Log[81])) + (720*(3 - Log[3])*Defer[Int][Defer[Int][1/((5*E^x + 3*x)^2*(3 + Sqrt[9 -

4*Log[3]] - x*Log[9])), x]/(3 + Sqrt[9 - 4*Log[3]] - x*Log[9]), x])/(9 - Log[81]) + (432*Log[243]*Defer[Int][

Defer[Int][1/((5*E^x + 3*x)^2*(3 + Sqrt[9 - 4*Log[3]] - x*Log[9])), x]/(3 + Sqrt[9 - 4*Log[3]] - x*Log[9]), x]

)/Log[3]^2 - (144*(135 - 15*Log[81] + (3 - Log[3])*Log[243])*Defer[Int][Defer[Int][1/((5*E^x + 3*x)^2*(3 + Sqr

t[9 - 4*Log[3]] - x*Log[9])), x]/(3 + Sqrt[9 - 4*Log[3]] - x*Log[9]), x])/(Log[3]*(9 - Log[81])) + (720*(3 - L

og[3])*Defer[Int][Defer[Int][1/((5*E^x + 3*x)^2*(3 + Sqrt[9 - 4*Log[3]] - x*Log[9])), x]/(-3 + Sqrt[9 - 4*Log[

3]] + x*Log[9]), x])/(9 - Log[81]) + (432*Log[243]*Defer[Int][Defer[Int][1/((5*E^x + 3*x)^2*(3 + Sqrt[9 - 4*Lo

g[3]] - x*Log[9])), x]/(-3 + Sqrt[9 - 4*Log[3]] + x*Log[9]), x])/Log[3]^2 - (144*(135 - 15*Log[81] + (3 - Log[

3])*Log[243])*Defer[Int][Defer[Int][1/((5*E^x + 3*x)^2*(3 + Sqrt[9 - 4*Log[3]] - x*Log[9])), x]/(-3 + Sqrt[9 -

4*Log[3]] + x*Log[9]), x])/(Log[3]*(9 - Log[81])) - (280*(3 + Sqrt[9 - 4*Log[3]])*Log[9]*Defer[Int][Defer[Int

][1/((5*E^x + 3*x)*(3 + Sqrt[9 - 4*Log[3]] - x*Log[9])), x]/(-3 - Sqrt[9 - 4*Log[3]] + 2*x*Log[3]), x])/(9 - L

og[81]) - (40*(3 + Sqrt[9 - 4*Log[3]])*(9 - Log[3])*Log[9]*Defer[Int][Defer[Int][1/((5*E^x + 3*x)*(3 + Sqrt[9

- 4*Log[3]] - x*Log[9])), x]/(-3 - Sqrt[9 - 4*Log[3]] + 2*x*Log[3]), x])/(Log[3]*(9 - Log[81])) + (120*(3 + Sq

rt[9 - 4*Log[3]])*Log[9]*(3 + Log[9])*Defer[Int][Defer[Int][1/((5*E^x + 3*x)*(3 + Sqrt[9 - 4*Log[3]] - x*Log[9

])), x]/(-3 - Sqrt[9 - 4*Log[3]] + 2*x*Log[3]), x])/(Log[3]*(9 - Log[81])) + (280*(3 - Sqrt[9 - 4*Log[3]])*Log

[9]*Defer[Int][Defer[Int][1/((5*E^x + 3*x)*(3 + Sqrt[9 - 4*Log[3]] - x*Log[9])), x]/(-3 + Sqrt[9 - 4*Log[3]] +

2*x*Log[3]), x])/(9 - Log[81]) + (40*(3 - Sqrt[9 - 4*Log[3]])*(9 - Log[3])*Log[9]*Defer[Int][Defer[Int][1/((5

*E^x + 3*x)*(3 + Sqrt[9 - 4*Log[3]] - x*Log[9])), x]/(-3 + Sqrt[9 - 4*Log[3]] + 2*x*Log[3]), x])/(Log[3]*(9 -

Log[81])) - (120*(3 - Sqrt[9 - 4*Log[3]])*Log[9]*(3 + Log[9])*Defer[Int][Defer[Int][1/((5*E^x + 3*x)*(3 + Sqrt

[9 - 4*Log[3]] - x*Log[9])), x]/(-3 + Sqrt[9 - 4*Log[3]] + 2*x*Log[3]), x])/(Log[3]*(9 - Log[81])) - (1680*Log

[3]*Defer[Int][Defer[Int][1/((5*E^x + 3*x)*(3 + Sqrt[9 - 4*Log[3]] - x*Log[9])), x]/(3 + Sqrt[9 - 4*Log[3]] -

x*Log[9]), x])/(9 - 4*Log[3]) + (720*(3 + Log[9])*Defer[Int][Defer[Int][1/((5*E^x + 3*x)*(3 + Sqrt[9 - 4*Log[3

]] - x*Log[9])), x]/(3 + Sqrt[9 - 4*Log[3]] - x*Log[9]), x])/(9 - 4*Log[3]) - (240*(9 - Log[3])*Defer[Int][Def

er[Int][1/((5*E^x + 3*x)*(3 + Sqrt[9 - 4*Log[3]] - x*Log[9])), x]/(3 + Sqrt[9 - 4*Log[3]] - x*Log[9]), x])/(9

- Log[81]) - (1680*Log[3]*Defer[Int][Defer[Int][1/((5*E^x + 3*x)*(3 + Sqrt[9 - 4*Log[3]] - x*Log[9])), x]/(-3

+ Sqrt[9 - 4*Log[3]] + x*Log[9]), x])/(9 - 4*Log[3]) + (720*(3 + Log[9])*Defer[Int][Defer[Int][1/((5*E^x + 3*x

)*(3 + Sqrt[9 - 4*Log[3]] - x*Log[9])), x]/(-3 + Sqrt[9 - 4*Log[3]] + x*Log[9]), x])/(9 - 4*Log[3]) - (240*(9

- Log[3])*Defer[Int][Defer[Int][1/((5*E^x + 3*x)*(3 + Sqrt[9 - 4*Log[3]] - x*Log[9])), x]/(-3 + Sqrt[9 - 4*Log

[3]] + x*Log[9]), x])/(9 - Log[81]) + (12*(3 + Sqrt[9 - 4*Log[3]])^2*(9 - Log[3])*Log[9]*Log[243]*Defer[Int][D

efer[Int][1/((5*E^x + 3*x)^2*(-3 - Sqrt[9 - 4*Log[3]] + x*Log[9])), x]/(-3 - Sqrt[9 - 4*Log[3]] + 2*x*Log[3]),

x])/Log[3]^4 - (36*(3 + Sqrt[9 - 4*Log[3]])^2*Log[9]*(135 - 15*Log[81] + (3 - Log[3])*Log[243])*Defer[Int][De

fer[Int][1/((5*E^x + 3*x)^2*(-3 - Sqrt[9 - 4*Log[3]] + x*Log[9])), x]/(-3 - Sqrt[9 - 4*Log[3]] + 2*x*Log[3]),

x])/(Log[3]^3*(9 - Log[81])) + (180*(1 + 3/Sqrt[9 - 4*Log[3]])^2*Log[9]*(3 + (Log[3]*(9 - Log[2187]))/Log[27])

*Defer[Int][Defer[Int][1/((5*E^x + 3*x)^2*(-3 - Sqrt[9 - 4*Log[3]] + x*Log[9])), x]/(-3 - Sqrt[9 - 4*Log[3]] +

2*x*Log[3]), x])/Log[3]^2 - (48*(9 - Log[3])*Log[9]*Log[243]*Defer[Int][Defer[Int][1/((5*E^x + 3*x)^2*(-3 - S

qrt[9 - 4*Log[3]] + x*Log[9])), x]/(-3 + Sqrt[9 - 4*Log[3]] + 2*x*Log[3]), x])/Log[3]^3 + (144*Log[9]*(135 - 1

5*Log[81] + (3 - Log[3])*Log[243])*Defer[Int][Defer[Int][1/((5*E^x + 3*x)^2*(-3 - Sqrt[9 - 4*Log[3]] + x*Log[9

])), x]/(-3 + Sqrt[9 - 4*Log[3]] + 2*x*Log[3]), x])/(Log[3]^2*(9 - Log[81])) - (180*Log[9]*Log[81]*(3 + (Log[3

]*(9 - Log[2187]))/Log[27])*Defer[Int][Defer[Int][1/((5*E^x + 3*x)^2*(-3 - Sqrt[9 - 4*Log[3]] + x*Log[9])), x]

/(-3 + Sqrt[9 - 4*Log[3]] + 2*x*Log[3]), x])/(Log[3]^2*(9 - Log[81])) + (72*(3 + Sqrt[9 - 4*Log[3]])*(9 - Log[

3])*Log[243]*Defer[Int][Defer[Int][1/((5*E^x + 3*x)^2*(-3 - Sqrt[9 - 4*Log[3]] + x*Log[9])), x]/(3 + Sqrt[9 -

4*Log[3]] - x*Log[9]), x])/Log[3]^3 - (216*(3 + Sqrt[9 - 4*Log[3]])*(135 - 15*Log[81] + (3 - Log[3])*Log[243])

*Defer[Int][Defer[Int][1/((5*E^x + 3*x)^2*(-3 - Sqrt[9 - 4*Log[3]] + x*Log[9])), x]/(3 + Sqrt[9 - 4*Log[3]] -

x*Log[9]), x])/(Log[3]^2*(9 - Log[81])) + (1080*(3 + Sqrt[9 - 4*Log[3]])*(3 + (Log[3]*(9 - Log[2187]))/Log[27]

)*Defer[Int][Defer[Int][1/((5*E^x + 3*x)^2*(-3 - Sqrt[9 - 4*Log[3]] + x*Log[9])), x]/(3 + Sqrt[9 - 4*Log[3]] -

x*Log[9]), x])/(Log[3]*(9 - Log[81])) + (72*(3 + Sqrt[9 - 4*Log[3]])*(9 - Log[3])*Log[243]*Defer[Int][Defer[I

nt][1/((5*E^x + 3*x)^2*(-3 - Sqrt[9 - 4*Log[3]] + x*Log[9])), x]/(-3 + Sqrt[9 - 4*Log[3]] + x*Log[9]), x])/Log

[3]^3 - (216*(3 + Sqrt[9 - 4*Log[3]])*(135 - 15*Log[81] + (3 - Log[3])*Log[243])*Defer[Int][Defer[Int][1/((5*E

^x + 3*x)^2*(-3 - Sqrt[9 - 4*Log[3]] + x*Log[9])), x]/(-3 + Sqrt[9 - 4*Log[3]] + x*Log[9]), x])/(Log[3]^2*(9 -

Log[81])) + (1080*(3 + Sqrt[9 - 4*Log[3]])*(3 + (Log[3]*(9 - Log[2187]))/Log[27])*Defer[Int][Defer[Int][1/((5

*E^x + 3*x)^2*(-3 - Sqrt[9 - 4*Log[3]] + x*Log[9])), x]/(-3 + Sqrt[9 - 4*Log[3]] + x*Log[9]), x])/(Log[3]*(9 -

Log[81])) + 40*(1 + 3/Sqrt[9 - 4*Log[3]])^2*Log[9]*Defer[Int][Defer[Int][1/((5*E^x + 3*x)*(-3 - Sqrt[9 - 4*Lo

g[3]] + x*Log[9])), x]/(-3 - Sqrt[9 - 4*Log[3]] + 2*x*Log[3]), x] - (420*(3 + Sqrt[9 - 4*Log[3]])^2*Log[9]*Def

er[Int][Defer[Int][1/((5*E^x + 3*x)*(-3 - Sqrt[9 - 4*Log[3]] + x*Log[9])), x]/(-3 - Sqrt[9 - 4*Log[3]] + 2*x*L

og[3]), x])/((9 - 4*Log[3])*Log[3]) - (60*(3 + Sqrt[9 - 4*Log[3]])^2*(9 - Log[9])*Log[9]*Defer[Int][Defer[Int]

[1/((5*E^x + 3*x)*(-3 - Sqrt[9 - 4*Log[3]] + x*Log[9])), x]/(-3 - Sqrt[9 - 4*Log[3]] + 2*x*Log[3]), x])/(Log[3

]^2*(9 - Log[81])) + (20*(3 + Sqrt[9 - 4*Log[3]])^2*(9 - Log[3])*Log[9]*(3 + Log[9])*Defer[Int][Defer[Int][1/(

(5*E^x + 3*x)*(-3 - Sqrt[9 - 4*Log[3]] + x*Log[9])), x]/(-3 - Sqrt[9 - 4*Log[3]] + 2*x*Log[3]), x])/(Log[3]^2*

(9 - Log[81])) + (1680*Log[9]*Defer[Int][Defer[Int][1/((5*E^x + 3*x)*(-3 - Sqrt[9 - 4*Log[3]] + x*Log[9])), x]

/(-3 + Sqrt[9 - 4*Log[3]] + 2*x*Log[3]), x])/(9 - 4*Log[3]) + (240*(9 - Log[9])*Log[9]*Defer[Int][Defer[Int][1

/((5*E^x + 3*x)*(-3 - Sqrt[9 - 4*Log[3]] + x*Log[9])), x]/(-3 + Sqrt[9 - 4*Log[3]] + 2*x*Log[3]), x])/(Log[3]*

(9 - Log[81])) - (80*(9 - Log[3])*Log[9]*(3 + Log[9])*Defer[Int][Defer[Int][1/((5*E^x + 3*x)*(-3 - Sqrt[9 - 4*

Log[3]] + x*Log[9])), x]/(-3 + Sqrt[9 - 4*Log[3]] + 2*x*Log[3]), x])/(Log[3]*(9 - Log[81])) - (40*Log[9]*Log[8

1]*Defer[Int][Defer[Int][1/((5*E^x + 3*x)*(-3 - Sqrt[9 - 4*Log[3]] + x*Log[9])), x]/(-3 + Sqrt[9 - 4*Log[3]] +

2*x*Log[3]), x])/(9 - Log[81]) - (2520*(3 + Sqrt[9 - 4*Log[3]])*Defer[Int][Defer[Int][1/((5*E^x + 3*x)*(-3 -

Sqrt[9 - 4*Log[3]] + x*Log[9])), x]/(3 + Sqrt[9 - 4*Log[3]] - x*Log[9]), x])/(9 - Log[81]) + (240*(3 + Sqrt[9

- 4*Log[3]])*Log[3]*Defer[Int][Defer[Int][1/((5*E^x + 3*x)*(-3 - Sqrt[9 - 4*Log[3]] + x*Log[9])), x]/(3 + Sqrt

[9 - 4*Log[3]] - x*Log[9]), x])/(9 - Log[81]) - (360*(3 + Sqrt[9 - 4*Log[3]])*(9 - Log[9])*Defer[Int][Defer[In

t][1/((5*E^x + 3*x)*(-3 - Sqrt[9 - 4*Log[3]] + x*Log[9])), x]/(3 + Sqrt[9 - 4*Log[3]] - x*Log[9]), x])/(Log[3]

*(9 - Log[81])) + (120*(3 + Sqrt[9 - 4*Log[3]])*(9 - Log[3])*(3 + Log[9])*Defer[Int][Defer[Int][1/((5*E^x + 3*

x)*(-3 - Sqrt[9 - 4*Log[3]] + x*Log[9])), x]/(3 + Sqrt[9 - 4*Log[3]] - x*Log[9]), x])/(Log[3]*(9 - Log[81])) -

(2520*(3 + Sqrt[9 - 4*Log[3]])*Defer[Int][Defer[Int][1/((5*E^x + 3*x)*(-3 - Sqrt[9 - 4*Log[3]] + x*Log[9])),

x]/(-3 + Sqrt[9 - 4*Log[3]] + x*Log[9]), x])/(9 - Log[81]) + (240*(3 + Sqrt[9 - 4*Log[3]])*Log[3]*Defer[Int][D

efer[Int][1/((5*E^x + 3*x)*(-3 - Sqrt[9 - 4*Log[3]] + x*Log[9])), x]/(-3 + Sqrt[9 - 4*Log[3]] + x*Log[9]), x])

/(9 - Log[81]) - (360*(3 + Sqrt[9 - 4*Log[3]])*(9 - Log[9])*Defer[Int][Defer[Int][1/((5*E^x + 3*x)*(-3 - Sqrt[

9 - 4*Log[3]] + x*Log[9])), x]/(-3 + Sqrt[9 - 4*Log[3]] + x*Log[9]), x])/(Log[3]*(9 - Log[81])) + (120*(3 + Sq

rt[9 - 4*Log[3]])*(9 - Log[3])*(3 + Log[9])*Defer[Int][Defer[Int][1/((5*E^x + 3*x)*(-3 - Sqrt[9 - 4*Log[3]] +

x*Log[9])), x]/(-3 + Sqrt[9 - 4*Log[3]] + x*Log[9]), x])/(Log[3]*(9 - Log[81])) + (120*(3 + Sqrt[9 - 4*Log[3]]

)*(3 - Log[3])*Log[9]*Defer[Int][Defer[Int][1/((5*E^x + 3*x)^2*(-3 + Sqrt[9 - 4*Log[3]] + x*Log[9])), x]/(-3 -

Sqrt[9 - 4*Log[3]] + 2*x*Log[3]), x])/(Log[3]*(9 - Log[81])) - (24*(9 - 3*Sqrt[9 - 4*Log[3]] - Log[9])*Log[9]

*Log[243]*Defer[Int][Defer[Int][1/((5*E^x + 3*x)^2*(-3 + Sqrt[9 - 4*Log[3]] + x*Log[9])), x]/(-3 - Sqrt[9 - 4*

Log[3]] + 2*x*Log[3]), x])/Log[3]^3 + (12*(3 + Sqrt[9 - 4*Log[3]])*(9 - 3*Sqrt[9 - 4*Log[3]] - Log[9])*Log[9]*

(135 - 15*Log[81] + (3 - Log[3])*Log[243])*Defer[Int][Defer[Int][1/((5*E^x + 3*x)^2*(-3 + Sqrt[9 - 4*Log[3]] +

x*Log[9])), x]/(-3 - Sqrt[9 - 4*Log[3]] + 2*x*Log[3]), x])/(Log[3]^3*(9 - Log[81])) - (180*Log[9]*Log[81]*(3

+ (Log[3]*(9 - Log[2187]))/Log[27])*Defer[Int][Defer[Int][1/((5*E^x + 3*x)^2*(-3 + Sqrt[9 - 4*Log[3]] + x*Log[

9])), x]/(-3 - Sqrt[9 - 4*Log[3]] + 2*x*Log[3]), x])/(Log[3]^2*(9 - Log[81])) - (120*(3 - Sqrt[9 - 4*Log[3]])*

(3 - Log[3])*Log[9]*Defer[Int][Defer[Int][1/((5*E^x + 3*x)^2*(-3 + Sqrt[9 - 4*Log[3]] + x*Log[9])), x]/(-3 + S

qrt[9 - 4*Log[3]] + 2*x*Log[3]), x])/(Log[3]*(9 - Log[81])) + (12*(3 - Sqrt[9 - 4*Log[3]])*(9*(3 - Log[3]) - S

qrt[9 - 4*Log[3]]*(9 - Log[3]))*Log[9]*Log[243]*Defer[Int][Defer[Int][1/((5*E^x + 3*x)^2*(-3 + Sqrt[9 - 4*Log[

3]] + x*Log[9])), x]/(-3 + Sqrt[9 - 4*Log[3]] + 2*x*Log[3]), x])/Log[3]^4 - (12*(3 - Sqrt[9 - 4*Log[3]])*(9 -

3*Sqrt[9 - 4*Log[3]] - Log[9])*Log[9]*(135 - 15*Log[81] + (3 - Log[3])*Log[243])*Defer[Int][Defer[Int][1/((5*E

^x + 3*x)^2*(-3 + Sqrt[9 - 4*Log[3]] + x*Log[9])), x]/(-3 + Sqrt[9 - 4*Log[3]] + 2*x*Log[3]), x])/(Log[3]^3*(9

- Log[81])) + (180*(1 - 3/Sqrt[9 - 4*Log[3]])^2*Log[9]*(3 + (Log[3]*(9 - Log[2187]))/Log[27])*Defer[Int][Defe

r[Int][1/((5*E^x + 3*x)^2*(-3 + Sqrt[9 - 4*Log[3]] + x*Log[9])), x]/(-3 + Sqrt[9 - 4*Log[3]] + 2*x*Log[3]), x]

)/Log[3]^2 + (720*(3 - Log[3])*Defer[Int][Defer[Int][1/((5*E^x + 3*x)^2*(-3 + Sqrt[9 - 4*Log[3]] + x*Log[9])),

x]/(3 + Sqrt[9 - 4*Log[3]] - x*Log[9]), x])/(9 - Log[81]) - (72*(9*(3 - Log[3]) - Sqrt[9 - 4*Log[3]]*(9 - Log

[3]))*Log[243]*Defer[Int][Defer[Int][1/((5*E^x + 3*x)^2*(-3 + Sqrt[9 - 4*Log[3]] + x*Log[9])), x]/(3 + Sqrt[9

- 4*Log[3]] - x*Log[9]), x])/Log[3]^3 + (72*(9 - 3*Sqrt[9 - 4*Log[3]] - Log[9])*(135 - 15*Log[81] + (3 - Log[3

])*Log[243])*Defer[Int][Defer[Int][1/((5*E^x + 3*x)^2*(-3 + Sqrt[9 - 4*Log[3]] + x*Log[9])), x]/(3 + Sqrt[9 -

4*Log[3]] - x*Log[9]), x])/(Log[3]^2*(9 - Log[81])) - (1080*(3 - Sqrt[9 - 4*Log[3]])*(3 + (Log[3]*(9 - Log[218

7]))/Log[27])*Defer[Int][Defer[Int][1/((5*E^x + 3*x)^2*(-3 + Sqrt[9 - 4*Log[3]] + x*Log[9])), x]/(3 + Sqrt[9 -

4*Log[3]] - x*Log[9]), x])/(Log[3]*(9 - Log[81])) + (720*(3 - Log[3])*Defer[Int][Defer[Int][1/((5*E^x + 3*x)^

2*(-3 + Sqrt[9 - 4*Log[3]] + x*Log[9])), x]/(-3 + Sqrt[9 - 4*Log[3]] + x*Log[9]), x])/(9 - Log[81]) - (72*(9*(

3 - Log[3]) - Sqrt[9 - 4*Log[3]]*(9 - Log[3]))*Log[243]*Defer[Int][Defer[Int][1/((5*E^x + 3*x)^2*(-3 + Sqrt[9

- 4*Log[3]] + x*Log[9])), x]/(-3 + Sqrt[9 - 4*Log[3]] + x*Log[9]), x])/Log[3]^3 + (72*(9 - 3*Sqrt[9 - 4*Log[3]

] - Log[9])*(135 - 15*Log[81] + (3 - Log[3])*Log[243])*Defer[Int][Defer[Int][1/((5*E^x + 3*x)^2*(-3 + Sqrt[9 -

4*Log[3]] + x*Log[9])), x]/(-3 + Sqrt[9 - 4*Log[3]] + x*Log[9]), x])/(Log[3]^2*(9 - Log[81])) - (1080*(3 - Sq

rt[9 - 4*Log[3]])*(3 + (Log[3]*(9 - Log[2187]))/Log[27])*Defer[Int][Defer[Int][1/((5*E^x + 3*x)^2*(-3 + Sqrt[9

- 4*Log[3]] + x*Log[9])), x]/(-3 + Sqrt[9 - 4*Log[3]] + x*Log[9]), x])/(Log[3]*(9 - Log[81])) + (20*(3 + Sqrt

[9 - 4*Log[3]])*(81 - 18*Log[3] + 2*Log[3]^2 - 3*Sqrt[9 - 4*Log[3]]*(9 - Log[9]) - 9*Log[9])*Log[9]*Defer[Int]

[Defer[Int][1/((5*E^x + 3*x)*(-3 + Sqrt[9 - 4*Log[3]] + x*Log[9])), x]/(-3 - Sqrt[9 - 4*Log[3]] + 2*x*Log[3]),

x])/(Log[3]^2*(9 - Log[81])) + (140*(3 + Sqrt[9 - 4*Log[3]])*(9 - 3*Sqrt[9 - 4*Log[3]] - Log[9])*Log[9]*Defer

[Int][Defer[Int][1/((5*E^x + 3*x)*(-3 + Sqrt[9 - 4*Log[3]] + x*Log[9])), x]/(-3 - Sqrt[9 - 4*Log[3]] + 2*x*Log

[3]), x])/(Log[3]*(9 - Log[81])) - (40*(9 - 3*Sqrt[9 - 4*Log[3]] - Log[9])*Log[9]*(3 + Log[9])*Defer[Int][Defe

r[Int][1/((5*E^x + 3*x)*(-3 + Sqrt[9 - 4*Log[3]] + x*Log[9])), x]/(-3 - Sqrt[9 - 4*Log[3]] + 2*x*Log[3]), x])/

(Log[3]*(9 - Log[81])) - (40*Log[9]*Log[81]*Defer[Int][Defer[Int][1/((5*E^x + 3*x)*(-3 + Sqrt[9 - 4*Log[3]] +

x*Log[9])), x]/(-3 - Sqrt[9 - 4*Log[3]] + 2*x*Log[3]), x])/(9 - Log[81]) + 40*(1 - 3/Sqrt[9 - 4*Log[3]])^2*Log

[9]*Defer[Int][Defer[Int][1/((5*E^x + 3*x)*(-3 + Sqrt[9 - 4*Log[3]] + x*Log[9])), x]/(-3 + Sqrt[9 - 4*Log[3]]

+ 2*x*Log[3]), x] - (20*(3 - Sqrt[9 - 4*Log[3]])*(81 - 18*Log[3] + 2*Log[3]^2 - 3*Sqrt[9 - 4*Log[3]]*(9 - Log[

9]) - 9*Log[9])*Log[9]*Defer[Int][Defer[Int][1/((5*E^x + 3*x)*(-3 + Sqrt[9 - 4*Log[3]] + x*Log[9])), x]/(-3 +

Sqrt[9 - 4*Log[3]] + 2*x*Log[3]), x])/(Log[3]^2*(9 - Log[81])) - (140*(3 - Sqrt[9 - 4*Log[3]])*(9 - 3*Sqrt[9 -

4*Log[3]] - Log[9])*Log[9]*Defer[Int][Defer[Int][1/((5*E^x + 3*x)*(-3 + Sqrt[9 - 4*Log[3]] + x*Log[9])), x]/(

-3 + Sqrt[9 - 4*Log[3]] + 2*x*Log[3]), x])/(Log[3]*(9 - Log[81])) + (20*(3 - Sqrt[9 - 4*Log[3]])*(9*(3 - Log[3

]) - Sqrt[9 - 4*Log[3]]*(9 - Log[3]))*Log[9]*(3 + Log[9])*Defer[Int][Defer[Int][1/((5*E^x + 3*x)*(-3 + Sqrt[9

- 4*Log[3]] + x*Log[9])), x]/(-3 + Sqrt[9 - 4*Log[3]] + 2*x*Log[3]), x])/(Log[3]^2*(9 - Log[81])) - (240*(3 -

Sqrt[9 - 4*Log[3]])*Log[3]*Defer[Int][Defer[Int][1/((5*E^x + 3*x)*(-3 + Sqrt[9 - 4*Log[3]] + x*Log[9])), x]/(3

+ Sqrt[9 - 4*Log[3]] - x*Log[9]), x])/(9 - Log[81]) + (120*(81 - 18*Log[3] + 2*Log[3]^2 - 3*Sqrt[9 - 4*Log[3]

]*(9 - Log[9]) - 9*Log[9])*Defer[Int][Defer[Int][1/((5*E^x + 3*x)*(-3 + Sqrt[9 - 4*Log[3]] + x*Log[9])), x]/(3

+ Sqrt[9 - 4*Log[3]] - x*Log[9]), x])/(Log[3]*(9 - Log[81])) + (840*(9 - 3*Sqrt[9 - 4*Log[3]] - Log[9])*Defer

[Int][Defer[Int][1/((5*E^x + 3*x)*(-3 + Sqrt[9 - 4*Log[3]] + x*Log[9])), x]/(3 + Sqrt[9 - 4*Log[3]] - x*Log[9]

), x])/(9 - Log[81]) - (120*(9*(3 - Log[3]) - Sqrt[9 - 4*Log[3]]*(9 - Log[3]))*(3 + Log[9])*Defer[Int][Defer[I

nt][1/((5*E^x + 3*x)*(-3 + Sqrt[9 - 4*Log[3]] + x*Log[9])), x]/(3 + Sqrt[9 - 4*Log[3]] - x*Log[9]), x])/(Log[3

]*(9 - Log[81])) - (240*(3 - Sqrt[9 - 4*Log[3]])*Log[3]*Defer[Int][Defer[Int][1/((5*E^x + 3*x)*(-3 + Sqrt[9 -

4*Log[3]] + x*Log[9])), x]/(-3 + Sqrt[9 - 4*Log[3]] + x*Log[9]), x])/(9 - Log[81]) + (120*(81 - 18*Log[3] + 2*

Log[3]^2 - 3*Sqrt[9 - 4*Log[3]]*(9 - Log[9]) - 9*Log[9])*Defer[Int][Defer[Int][1/((5*E^x + 3*x)*(-3 + Sqrt[9 -

4*Log[3]] + x*Log[9])), x]/(-3 + Sqrt[9 - 4*Log[3]] + x*Log[9]), x])/(Log[3]*(9 - Log[81])) + (840*(9 - 3*Sqr

t[9 - 4*Log[3]] - Log[9])*Defer[Int][Defer[Int][1/((5*E^x + 3*x)*(-3 + Sqrt[9 - 4*Log[3]] + x*Log[9])), x]/(-3

+ Sqrt[9 - 4*Log[3]] + x*Log[9]), x])/(9 - Log[81]) - (120*(9*(3 - Log[3]) - Sqrt[9 - 4*Log[3]]*(9 - Log[3]))

*(3 + Log[9])*Defer[Int][Defer[Int][1/((5*E^x + 3*x)*(-3 + Sqrt[9 - 4*Log[3]] + x*Log[9])), x]/(-3 + Sqrt[9 -

4*Log[3]] + x*Log[9]), x])/(Log[3]*(9 - Log[81])) - 140*(1 + 3/Sqrt[9 - 4*Log[3]])*Log[9]*Defer[Int][Defer[Int

][(x*Log[27] + E^x*Log[243])^(-1), x]/(-3 - Sqrt[9 - 4*Log[3]] + 2*x*Log[3]), x] - 140*(1 - 3/Sqrt[9 - 4*Log[3

]])*Log[9]*Defer[Int][Defer[Int][(x*Log[27] + E^x*Log[243])^(-1), x]/(-3 + Sqrt[9 - 4*Log[3]] + 2*x*Log[3]), x

] - (840*Log[3]*Defer[Int][Defer[Int][(x*Log[27] + E^x*Log[243])^(-1), x]/(3 + Sqrt[9 - 4*Log[3]] - x*Log[9]),

x])/Sqrt[9 - 4*Log[3]] - (840*Log[3]*Defer[Int][Defer[Int][(x*Log[27] + E^x*Log[243])^(-1), x]/(-3 + Sqrt[9 -

4*Log[3]] + x*Log[9]), x])/Sqrt[9 - 4*Log[3]] + 20*(1 + 3/Sqrt[9 - 4*Log[3]])*Log[9]*(3 + Log[9])*Defer[Int][

Defer[Int][x/(x*Log[27] + E^x*Log[243]), x]/(-3 - Sqrt[9 - 4*Log[3]] + 2*x*Log[3]), x] + 20*(1 - 3/Sqrt[9 - 4*

Log[3]])*Log[9]*(3 + Log[9])*Defer[Int][Defer[Int][x/(x*Log[27] + E^x*Log[243]), x]/(-3 + Sqrt[9 - 4*Log[3]] +

2*x*Log[3]), x] + (120*Log[3]*(3 + Log[9])*Defer[Int][Defer[Int][x/(x*Log[27] + E^x*Log[243]), x]/(3 + Sqrt[9

- 4*Log[3]] - x*Log[9]), x])/Sqrt[9 - 4*Log[3]] + (120*Log[3]*(3 + Log[9])*Defer[Int][Defer[Int][x/(x*Log[27]

+ E^x*Log[243]), x]/(-3 + Sqrt[9 - 4*Log[3]] + x*Log[9]), x])/Sqrt[9 - 4*Log[3]] - 20*(1 + 3/Sqrt[9 - 4*Log[3

]])*Log[3]*Log[9]*Defer[Int][Defer[Int][x^2/(x*Log[27] + E^x*Log[243]), x]/(-3 - Sqrt[9 - 4*Log[3]] + 2*x*Log[

3]), x] - 20*(1 - 3/Sqrt[9 - 4*Log[3]])*Log[3]*Log[9]*Defer[Int][Defer[Int][x^2/(x*Log[27] + E^x*Log[243]), x]

/(-3 + Sqrt[9 - 4*Log[3]] + 2*x*Log[3]), x] - (120*Log[3]^2*Defer[Int][Defer[Int][x^2/(x*Log[27] + E^x*Log[243

]), x]/(3 + Sqrt[9 - 4*Log[3]] - x*Log[9]), x])/Sqrt[9 - 4*Log[3]] - (120*Log[3]^2*Defer[Int][Defer[Int][x^2/(

x*Log[27] + E^x*Log[243]), x]/(-3 + Sqrt[9 - 4*Log[3]] + x*Log[9]), x])/Sqrt[9 - 4*Log[3]]

Rubi steps

Aborted

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Mathematica [A] time = 0.20, size = 58, normalized size = 1.76 \begin {gather*} \frac {4 x^2 \left (5-15 x+x^2 \log (243)\right ) \left (e^x-\log \left (1-3 x+x^2 \log (3)\right )\right )}{\left (5 e^x+3 x\right ) \left (1-3 x+x^2 \log (3)\right )} \end {gather*}

Antiderivative was successfully veriﬁed.

[In]

Integrate[(180*x^3 - 120*x^4*Log[3] + E^(2*x)*(200*x - 600*x^2 + 200*x^3*Log[3]) + E^x*(360*x^2 - 120*x^3 - 18

0*x^4 + (-200*x^3 + 60*x^4 + 60*x^5)*Log[3]) + (-60*x^2 + 180*x^3 - 60*x^4*Log[3] + E^x*(-200*x + 700*x^2 - 30

0*x^3 + (-200*x^3 + 100*x^4)*Log[3]))*Log[1 - 3*x + x^2*Log[3]])/(9*x^2 - 27*x^3 + 9*x^4*Log[3] + E^(2*x)*(25

- 75*x + 25*x^2*Log[3]) + E^x*(30*x - 90*x^2 + 30*x^3*Log[3])),x]

[Out]

(4*x^2*(5 - 15*x + x^2*Log[243])*(E^x - Log[1 - 3*x + x^2*Log[3]]))/((5*E^x + 3*x)*(1 - 3*x + x^2*Log[3]))

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fricas [A] time = 0.48, size = 36, normalized size = 1.09 \begin {gather*} \frac {20 \, {\left (x^{2} e^{x} - x^{2} \log \left (x^{2} \log \relax (3) - 3 \, x + 1\right )\right )}}{3 \, x + 5 \, e^{x}} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((100*x^4-200*x^3)*log(3)-300*x^3+700*x^2-200*x)*exp(x)-60*x^4*log(3)+180*x^3-60*x^2)*log(x^2*log(

3)-3*x+1)+(200*x^3*log(3)-600*x^2+200*x)*exp(x)^2+((60*x^5+60*x^4-200*x^3)*log(3)-180*x^4-120*x^3+360*x^2)*exp

(x)-120*x^4*log(3)+180*x^3)/((25*x^2*log(3)-75*x+25)*exp(x)^2+(30*x^3*log(3)-90*x^2+30*x)*exp(x)+9*x^4*log(3)-

27*x^3+9*x^2),x, algorithm="fricas")

[Out]

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

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giac [A] time = 0.20, size = 36, normalized size = 1.09 \begin {gather*} \frac {20 \, {\left (x^{2} e^{x} - x^{2} \log \left (x^{2} \log \relax (3) - 3 \, x + 1\right )\right )}}{3 \, x + 5 \, e^{x}} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((100*x^4-200*x^3)*log(3)-300*x^3+700*x^2-200*x)*exp(x)-60*x^4*log(3)+180*x^3-60*x^2)*log(x^2*log(

3)-3*x+1)+(200*x^3*log(3)-600*x^2+200*x)*exp(x)^2+((60*x^5+60*x^4-200*x^3)*log(3)-180*x^4-120*x^3+360*x^2)*exp

(x)-120*x^4*log(3)+180*x^3)/((25*x^2*log(3)-75*x+25)*exp(x)^2+(30*x^3*log(3)-90*x^2+30*x)*exp(x)+9*x^4*log(3)-

27*x^3+9*x^2),x, algorithm="giac")

[Out]

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

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maple [A] time = 0.05, size = 46, normalized size = 1.39


method	result	size

risch	\(-\frac {20 x^{2} \ln \left (x^{2} \ln \relax (3)-3 x +1\right )}{3 x +5 \,{\mathrm e}^{x}}+\frac {20 x^{2} {\mathrm e}^{x}}{3 x +5 \,{\mathrm e}^{x}}\)	\(46\)

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int(((((100*x^4-200*x^3)*ln(3)-300*x^3+700*x^2-200*x)*exp(x)-60*x^4*ln(3)+180*x^3-60*x^2)*ln(x^2*ln(3)-3*x+1)+

(200*x^3*ln(3)-600*x^2+200*x)*exp(x)^2+((60*x^5+60*x^4-200*x^3)*ln(3)-180*x^4-120*x^3+360*x^2)*exp(x)-120*x^4*

ln(3)+180*x^3)/((25*x^2*ln(3)-75*x+25)*exp(x)^2+(30*x^3*ln(3)-90*x^2+30*x)*exp(x)+9*x^4*ln(3)-27*x^3+9*x^2),x,

method=_RETURNVERBOSE)

[Out]

-20*x^2/(3*x+5*exp(x))*ln(x^2*ln(3)-3*x+1)+20*x^2*exp(x)/(3*x+5*exp(x))

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maxima [A] time = 0.67, size = 36, normalized size = 1.09 \begin {gather*} \frac {20 \, {\left (x^{2} e^{x} - x^{2} \log \left (x^{2} \log \relax (3) - 3 \, x + 1\right )\right )}}{3 \, x + 5 \, e^{x}} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((100*x^4-200*x^3)*log(3)-300*x^3+700*x^2-200*x)*exp(x)-60*x^4*log(3)+180*x^3-60*x^2)*log(x^2*log(

3)-3*x+1)+(200*x^3*log(3)-600*x^2+200*x)*exp(x)^2+((60*x^5+60*x^4-200*x^3)*log(3)-180*x^4-120*x^3+360*x^2)*exp

(x)-120*x^4*log(3)+180*x^3)/((25*x^2*log(3)-75*x+25)*exp(x)^2+(30*x^3*log(3)-90*x^2+30*x)*exp(x)+9*x^4*log(3)-

27*x^3+9*x^2),x, algorithm="maxima")

[Out]

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

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mupad [B] time = 5.37, size = 32, normalized size = 0.97 \begin {gather*} -\frac {20\,x^2\,\left (\ln \left (\ln \relax (3)\,x^2-3\,x+1\right )-{\mathrm {e}}^x\right )}{3\,x+5\,{\mathrm {e}}^x} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

int((exp(x)*(log(3)*(60*x^4 - 200*x^3 + 60*x^5) + 360*x^2 - 120*x^3 - 180*x^4) - log(x^2*log(3) - 3*x + 1)*(ex

p(x)*(200*x + log(3)*(200*x^3 - 100*x^4) - 700*x^2 + 300*x^3) + 60*x^4*log(3) + 60*x^2 - 180*x^3) - 120*x^4*lo

g(3) + exp(2*x)*(200*x + 200*x^3*log(3) - 600*x^2) + 180*x^3)/(exp(x)*(30*x + 30*x^3*log(3) - 90*x^2) + exp(2*

x)*(25*x^2*log(3) - 75*x + 25) + 9*x^4*log(3) + 9*x^2 - 27*x^3),x)

[Out]

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

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sympy [A] time = 0.50, size = 37, normalized size = 1.12 \begin {gather*} 4 x^{2} + \frac {- 12 x^{3} - 20 x^{2} \log {\left (x^{2} \log {\relax (3 )} - 3 x + 1 \right )}}{3 x + 5 e^{x}} \end {gather*}

Veriﬁcation of antiderivative is not currently implemented for this CAS.

[In]

integrate(((((100*x**4-200*x**3)*ln(3)-300*x**3+700*x**2-200*x)*exp(x)-60*x**4*ln(3)+180*x**3-60*x**2)*ln(x**2

*ln(3)-3*x+1)+(200*x**3*ln(3)-600*x**2+200*x)*exp(x)**2+((60*x**5+60*x**4-200*x**3)*ln(3)-180*x**4-120*x**3+36

0*x**2)*exp(x)-120*x**4*ln(3)+180*x**3)/((25*x**2*ln(3)-75*x+25)*exp(x)**2+(30*x**3*ln(3)-90*x**2+30*x)*exp(x)

+9*x**4*ln(3)-27*x**3+9*x**2),x)

[Out]

4*x**2 + (-12*x**3 - 20*x**2*log(x**2*log(3) - 3*x + 1))/(3*x + 5*exp(x))

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