∫ 800x log(2)+2ex2 log2(2)+e5+ex−x (16exx3 log(2)+(−16x2−16x3) log(2))________________ 40000+64e10+2ex−2xx2+(400ex+800x2) log(2)+(e2x2+4ex3+4x4) log2(2)+e5+ex−x(−3200x+(−16ex2−32x3) log(2)) dx

Optimal. Leaf size=35 \[ \frac {x}{\frac {e}{2}+x+\frac {4 \left (-e^{5+e^x-x}+\frac {25}{x}\right )}{\log (2)}} \]

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Rubi [F] time = 154.70, 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 {800 x \log (2)+2 e x^2 \log ^2(2)+e^{5+e^x-x} \left (16 e^x x^3 \log (2)+\left (-16 x^2-16 x^3\right ) \log (2)\right )}{40000+64 e^{10+2 e^x-2 x} x^2+\left (400 e x+800 x^2\right ) \log (2)+\left (e^2 x^2+4 e x^3+4 x^4\right ) \log ^2(2)+e^{5+e^x-x} \left (-3200 x+\left (-16 e x^2-32 x^3\right ) \log (2)\right )} \, dx \end {gather*}

Int[(800*x*Log[2] + 2*E*x^2*Log[2]^2 + E^(5 + E^x - x)*(16*E^x*x^3*Log[2] + (-16*x^2 - 16*x^3)*Log[2]))/(40000

+ 64*E^(10 + 2*E^x - 2*x)*x^2 + (400*E*x + 800*x^2)*Log[2] + (E^2*x^2 + 4*E*x^3 + 4*x^4)*Log[2]^2 + E^(5 + E^

(16*Log[2]^2*(E^2*Log[2]^2 - 200*Log[4])*Defer[Int][E^(6 + E^x + x)/(-200*E^x + 8*E^(5 + E^x)*x - E^(1 + x)*x*

Log[2] - E^x*x^2*Log[4])^2, x])/Log[4]^3 - (16*(2 + E)*Log[2]^4*(1 + (200*Log[4])/(E*Log[2]*(E*Log[2] + Log[4]

)))*Defer[Int][E^(7 + E^x + x)/(-200*E^x + 8*E^(5 + E^x)*x - E^(1 + x)*x*Log[2] - E^x*x^2*Log[4])^2, x])/Log[4

]^3 + (128*Log[2]^3*Defer[Int][E^(12 + 2*E^x + x)/(-200*E^x + 8*E^(5 + E^x)*x - E^(1 + x)*x*Log[2] - E^x*x^2*L

og[4])^2, x])/Log[4]^3 - (16*Log[2]^3*Defer[Int][(E^(7 + E^x + x)*x)/(-200*E^x + 8*E^(5 + E^x)*x - E^(1 + x)*x

*Log[2] - E^x*x^2*Log[4])^2, x])/Log[4]^2 + (128*Log[2]*Defer[Int][(E^(10 + 2*E^x + x)*x^2)/(-200*E^x + 8*E^(5

+ E^x)*x - E^(1 + x)*x*Log[2] - E^x*x^2*Log[4])^2, x])/Log[4] + (16*Log[2]^2*Defer[Int][E^(6 + E^x + x)/(-200

*E^x + 8*E^(5 + E^x)*x - E^(1 + x)*x*Log[2] - E^x*x^2*Log[4]), x])/Log[4]^2 + (3200*Log[2]*Defer[Int][E^(5 + E

^x + x)/(200*E^x - 8*E^(5 + E^x)*x + E^(1 + x)*x*Log[2] + E^x*x^2*Log[4])^2, x])/Log[4] + (3200*(1 + E)*Log[2]

*Defer[Int][E^(6 + E^x + x)/(200*E^x - 8*E^(5 + E^x)*x + E^(1 + x)*x*Log[2] + E^x*x^2*Log[4])^2, x])/(E*Log[4]

) - (25600*Log[2]*Defer[Int][E^(10 + 2*E^x + x)/(200*E^x - 8*E^(5 + E^x)*x + E^(1 + x)*x*Log[2] + E^x*x^2*Log[

4])^2, x])/Log[4]^2 - (3200*Log[2]*Defer[Int][(E^(5 + E^x + x)*x)/(200*E^x - 8*E^(5 + E^x)*x + E^(1 + x)*x*Log

[2] + E^x*x^2*Log[4])^2, x])/Log[4] + (16*(2 + E)*Log[2]^3*(1 + (200*Log[4])/(E*Log[2]*(E*Log[2] + Log[4])))*D

efer[Int][(E^(6 + E^x + x)*x)/(200*E^x - 8*E^(5 + E^x)*x + E^(1 + x)*x*Log[2] + E^x*x^2*Log[4])^2, x])/Log[4]^

2 - (128*Log[2]^2*Defer[Int][(E^(11 + 2*E^x + x)*x)/(200*E^x - 8*E^(5 + E^x)*x + E^(1 + x)*x*Log[2] + E^x*x^2*

Log[4])^2, x])/Log[4]^2 - (16*(2 + E)*Log[2]^2*Defer[Int][(E^(5 + E^x + x)*x^2)/(200*E^x - 8*E^(5 + E^x)*x + E

^(1 + x)*x*Log[2] + E^x*x^2*Log[4])^2, x])/Log[4] + (16*Log[2]^2*Defer[Int][(E^(6 + E^x + x)*x^2)/(200*E^x - 8

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

3)/(200*E^x - 8*E^(5 + E^x)*x + E^(1 + x)*x*Log[2] + E^x*x^2*Log[4])^2, x] + (2*Log[2]^2*Defer[Int][E^(1 + x)/

(200*E^x - 8*E^(5 + E^x)*x + E^(1 + x)*x*Log[2] + E^x*x^2*Log[4]), x])/Log[4] + (16*Log[2]*Defer[Int][(E^(5 +

E^x + x)*x)/(200*E^x - 8*E^(5 + E^x)*x + E^(1 + x)*x*Log[2] + E^x*x^2*Log[4]), x])/Log[4] + (3200*Log[2]*(200

- E*Log[2])*(1 + (I*E*Log[2])/Sqrt[-(E^2*Log[2]^2) + 800*Log[4]])*Defer[Int][E^(6 + E^x + x)/((-200*E^x + 8*E^

(5 + E^x)*x - E^(1 + x)*x*Log[2] - E^x*x^2*Log[4])^2*(E*Log[2] + 2*x*Log[4] - I*Sqrt[-(E^2*Log[2]^2) + 800*Log

[4]])), x])/(E*Log[4]) - (16*Log[2]^3*(E^2*Log[2]^2 - 400*Log[4])*(1 + (I*E*Log[2])/Sqrt[-(E^2*Log[2]^2) + 800

*Log[4]])*Defer[Int][E^(7 + E^x + x)/((-200*E^x + 8*E^(5 + E^x)*x - E^(1 + x)*x*Log[2] - E^x*x^2*Log[4])^2*(E*

Log[2] + 2*x*Log[4] - I*Sqrt[-(E^2*Log[2]^2) + 800*Log[4]])), x])/Log[4]^3 - (3200*(1 + E)*Log[2]^2*(1 + (I*E*

Log[2])/Sqrt[-(E^2*Log[2]^2) + 800*Log[4]])*Defer[Int][E^(7 + E^x + x)/((-200*E^x + 8*E^(5 + E^x)*x - E^(1 + x

)*x*Log[2] - E^x*x^2*Log[4])^2*(E*Log[2] + 2*x*Log[4] - I*Sqrt[-(E^2*Log[2]^2) + 800*Log[4]])), x])/(E*Log[4])

+ (25600*Log[2]^2*(1 + (I*E*Log[2])/Sqrt[-(E^2*Log[2]^2) + 800*Log[4]])*Defer[Int][E^(11 + 2*E^x + x)/((-200*

E^x + 8*E^(5 + E^x)*x - E^(1 + x)*x*Log[2] - E^x*x^2*Log[4])^2*(E*Log[2] + 2*x*Log[4] - I*Sqrt[-(E^2*Log[2]^2)

+ 800*Log[4]])), x])/Log[4]^2 + (2*Log[2]^3*(1 + (I*E*Log[2])/Sqrt[-(E^2*Log[2]^2) + 800*Log[4]])*Defer[Int][

E^(2 + x)/((-200*E^x + 8*E^(5 + E^x)*x - E^(1 + x)*x*Log[2] - E^x*x^2*Log[4])*(E*Log[2] + 2*x*Log[4] - I*Sqrt[

-(E^2*Log[2]^2) + 800*Log[4]])), x])/Log[4] + (16*(2 + E)*Log[2]^3*(E^2*Log[2]^2 - 200*Log[4])*(1 + (200*Log[4

])/(E*Log[2]*(E*Log[2] + Log[4])))*(1 + (I*E*Log[2])/Sqrt[-(E^2*Log[2]^2) + 800*Log[4]])*Defer[Int][E^(6 + E^x

+ x)/((200*E^x - 8*E^(5 + E^x)*x + E^(1 + x)*x*Log[2] + E^x*x^2*Log[4])^2*(E*Log[2] + 2*x*Log[4] - I*Sqrt[-(E

^2*Log[2]^2) + 800*Log[4]])), x])/Log[4]^3 - (128*Log[2]^2*(E^2*Log[2]^2 - 200*Log[4])*(1 + (I*E*Log[2])/Sqrt[

-(E^2*Log[2]^2) + 800*Log[4]])*Defer[Int][E^(11 + 2*E^x + x)/((200*E^x - 8*E^(5 + E^x)*x + E^(1 + x)*x*Log[2]

+ E^x*x^2*Log[4])^2*(E*Log[2] + 2*x*Log[4] - I*Sqrt[-(E^2*Log[2]^2) + 800*Log[4]])), x])/Log[4]^3 + 800*Log[2]

*(1 + (I*E*Log[2])/Sqrt[-(E^2*Log[2]^2) + 800*Log[4]])*Defer[Int][E^x/((200*E^x - 8*E^(5 + E^x)*x + E^(1 + x)*

x*Log[2] + E^x*x^2*Log[4])*(E*Log[2] + 2*x*Log[4] - I*Sqrt[-(E^2*Log[2]^2) + 800*Log[4]])), x] + (16*Log[2]*(E

^2*Log[2]^2 - 200*Log[4])*(1 + (I*E*Log[2])/Sqrt[-(E^2*Log[2]^2) + 800*Log[4]])*Defer[Int][E^(5 + E^x + x)/((2

00*E^x - 8*E^(5 + E^x)*x + E^(1 + x)*x*Log[2] + E^x*x^2*Log[4])*(E*Log[2] + 2*x*Log[4] - I*Sqrt[-(E^2*Log[2]^2

) + 800*Log[4]])), x])/Log[4]^2 + (3200*Log[2]*(200 - E*Log[2])*(1 - (I*E*Log[2])/Sqrt[-(E^2*Log[2]^2) + 800*L

og[4]])*Defer[Int][E^(6 + E^x + x)/((-200*E^x + 8*E^(5 + E^x)*x - E^(1 + x)*x*Log[2] - E^x*x^2*Log[4])^2*(E*Lo

g[2] + 2*x*Log[4] + I*Sqrt[-(E^2*Log[2]^2) + 800*Log[4]])), x])/(E*Log[4]) - (16*Log[2]^3*(E^2*Log[2]^2 - 400*

Log[4])*(1 - (I*E*Log[2])/Sqrt[-(E^2*Log[2]^2) + 800*Log[4]])*Defer[Int][E^(7 + E^x + x)/((-200*E^x + 8*E^(5 +

E^x)*x - E^(1 + x)*x*Log[2] - E^x*x^2*Log[4])^2*(E*Log[2] + 2*x*Log[4] + I*Sqrt[-(E^2*Log[2]^2) + 800*Log[4]]

)), x])/Log[4]^3 - (3200*(1 + E)*Log[2]^2*(1 - (I*E*Log[2])/Sqrt[-(E^2*Log[2]^2) + 800*Log[4]])*Defer[Int][E^(

7 + E^x + x)/((-200*E^x + 8*E^(5 + E^x)*x - E^(1 + x)*x*Log[2] - E^x*x^2*Log[4])^2*(E*Log[2] + 2*x*Log[4] + I*

Sqrt[-(E^2*Log[2]^2) + 800*Log[4]])), x])/(E*Log[4]) + (25600*Log[2]^2*(1 - (I*E*Log[2])/Sqrt[-(E^2*Log[2]^2)

+ 800*Log[4]])*Defer[Int][E^(11 + 2*E^x + x)/((-200*E^x + 8*E^(5 + E^x)*x - E^(1 + x)*x*Log[2] - E^x*x^2*Log[4

])^2*(E*Log[2] + 2*x*Log[4] + I*Sqrt[-(E^2*Log[2]^2) + 800*Log[4]])), x])/Log[4]^2 + (2*Log[2]^3*(1 - (I*E*Log

[2])/Sqrt[-(E^2*Log[2]^2) + 800*Log[4]])*Defer[Int][E^(2 + x)/((-200*E^x + 8*E^(5 + E^x)*x - E^(1 + x)*x*Log[2

] - E^x*x^2*Log[4])*(E*Log[2] + 2*x*Log[4] + I*Sqrt[-(E^2*Log[2]^2) + 800*Log[4]])), x])/Log[4] + (16*(2 + E)*

Log[2]^3*(E^2*Log[2]^2 - 200*Log[4])*(1 + (200*Log[4])/(E*Log[2]*(E*Log[2] + Log[4])))*(1 - (I*E*Log[2])/Sqrt[

-(E^2*Log[2]^2) + 800*Log[4]])*Defer[Int][E^(6 + E^x + x)/((200*E^x - 8*E^(5 + E^x)*x + E^(1 + x)*x*Log[2] + E

^x*x^2*Log[4])^2*(E*Log[2] + 2*x*Log[4] + I*Sqrt[-(E^2*Log[2]^2) + 800*Log[4]])), x])/Log[4]^3 - (128*Log[2]^2

*(E^2*Log[2]^2 - 200*Log[4])*(1 - (I*E*Log[2])/Sqrt[-(E^2*Log[2]^2) + 800*Log[4]])*Defer[Int][E^(11 + 2*E^x +

x)/((200*E^x - 8*E^(5 + E^x)*x + E^(1 + x)*x*Log[2] + E^x*x^2*Log[4])^2*(E*Log[2] + 2*x*Log[4] + I*Sqrt[-(E^2*

Log[2]^2) + 800*Log[4]])), x])/Log[4]^3 + 800*Log[2]*(1 - (I*E*Log[2])/Sqrt[-(E^2*Log[2]^2) + 800*Log[4]])*Def

er[Int][E^x/((200*E^x - 8*E^(5 + E^x)*x + E^(1 + x)*x*Log[2] + E^x*x^2*Log[4])*(E*Log[2] + 2*x*Log[4] + I*Sqrt

[-(E^2*Log[2]^2) + 800*Log[4]])), x] + (16*Log[2]*(E^2*Log[2]^2 - 200*Log[4])*(1 - (I*E*Log[2])/Sqrt[-(E^2*Log

[2]^2) + 800*Log[4]])*Defer[Int][E^(5 + E^x + x)/((200*E^x - 8*E^(5 + E^x)*x + E^(1 + x)*x*Log[2] + E^x*x^2*Lo

g[4])*(E*Log[2] + 2*x*Log[4] + I*Sqrt[-(E^2*Log[2]^2) + 800*Log[4]])), x])/Log[4]^2 - ((1280000*I)*Log[2]*Defe

r[Int][E^(5 + E^x + x)/((-200*E^x + 8*E^(5 + E^x)*x - E^(1 + x)*x*Log[2] - E^x*x^2*Log[4])^2*(-(E*Log[2]) + I*

Sqrt[-(E^2*Log[2]^2) + 800*Log[4]] - x*Log[16])), x])/Sqrt[-(E^2*Log[2]^2) + 800*Log[4]] - ((1280000*I)*(1 + E

)*Log[2]*Defer[Int][E^(6 + E^x + x)/((-200*E^x + 8*E^(5 + E^x)*x - E^(1 + x)*x*Log[2] - E^x*x^2*Log[4])^2*(-(E

*Log[2]) + I*Sqrt[-(E^2*Log[2]^2) + 800*Log[4]] - x*Log[16])), x])/(E*Sqrt[-(E^2*Log[2]^2) + 800*Log[4]]) - ((

6400*I)*Log[2]^2*(E^2*Log[2]^2 - 200*Log[4])*Defer[Int][E^(6 + E^x + x)/((-200*E^x + 8*E^(5 + E^x)*x - E^(1 +

x)*x*Log[2] - E^x*x^2*Log[4])^2*(-(E*Log[2]) + I*Sqrt[-(E^2*Log[2]^2) + 800*Log[4]] - x*Log[16])), x])/(Log[4]

^2*Sqrt[-(E^2*Log[2]^2) + 800*Log[4]]) + ((6400*I)*(2 + E)*Log[2]^4*(1 + (200*Log[4])/(E*Log[2]*(E*Log[2] + Lo

g[4])))*Defer[Int][E^(7 + E^x + x)/((-200*E^x + 8*E^(5 + E^x)*x - E^(1 + x)*x*Log[2] - E^x*x^2*Log[4])^2*(-(E*

Log[2]) + I*Sqrt[-(E^2*Log[2]^2) + 800*Log[4]] - x*Log[16])), x])/(Log[4]^2*Sqrt[-(E^2*Log[2]^2) + 800*Log[4]]

) + ((10240000*I)*Log[2]*Defer[Int][E^(10 + 2*E^x + x)/((-200*E^x + 8*E^(5 + E^x)*x - E^(1 + x)*x*Log[2] - E^x

*x^2*Log[4])^2*(-(E*Log[2]) + I*Sqrt[-(E^2*Log[2]^2) + 800*Log[4]] - x*Log[16])), x])/(Log[4]*Sqrt[-(E^2*Log[2

]^2) + 800*Log[4]]) - ((51200*I)*Log[2]^3*Defer[Int][E^(12 + 2*E^x + x)/((-200*E^x + 8*E^(5 + E^x)*x - E^(1 +

x)*x*Log[2] - E^x*x^2*Log[4])^2*(-(E*Log[2]) + I*Sqrt[-(E^2*Log[2]^2) + 800*Log[4]] - x*Log[16])), x])/(Log[4]

^2*Sqrt[-(E^2*Log[2]^2) + 800*Log[4]]) + ((800*I)*Log[2]^2*Defer[Int][E^(1 + x)/((-200*E^x + 8*E^(5 + E^x)*x -

E^(1 + x)*x*Log[2] - E^x*x^2*Log[4])*(-(E*Log[2]) + I*Sqrt[-(E^2*Log[2]^2) + 800*Log[4]] - x*Log[16])), x])/S

qrt[-(E^2*Log[2]^2) + 800*Log[4]] - ((6400*I)*Log[2]^2*Defer[Int][E^(6 + E^x + x)/((-200*E^x + 8*E^(5 + E^x)*x

- E^(1 + x)*x*Log[2] - E^x*x^2*Log[4])*(-(E*Log[2]) + I*Sqrt[-(E^2*Log[2]^2) + 800*Log[4]] - x*Log[16])), x])

/(Log[4]*Sqrt[-(E^2*Log[2]^2) + 800*Log[4]]) - ((1280000*I)*Log[2]*Defer[Int][E^(5 + E^x + x)/((-200*E^x + 8*E

^(5 + E^x)*x - E^(1 + x)*x*Log[2] - E^x*x^2*Log[4])^2*(E*Log[2] + I*Sqrt[-(E^2*Log[2]^2) + 800*Log[4]] + x*Log

[16])), x])/Sqrt[-(E^2*Log[2]^2) + 800*Log[4]] - ((1280000*I)*(1 + E)*Log[2]*Defer[Int][E^(6 + E^x + x)/((-200

*E^x + 8*E^(5 + E^x)*x - E^(1 + x)*x*Log[2] - E^x*x^2*Log[4])^2*(E*Log[2] + I*Sqrt[-(E^2*Log[2]^2) + 800*Log[4

]] + x*Log[16])), x])/(E*Sqrt[-(E^2*Log[2]^2) + 800*Log[4]]) - ((6400*I)*Log[2]^2*(E^2*Log[2]^2 - 200*Log[4])*

Defer[Int][E^(6 + E^x + x)/((-200*E^x + 8*E^(5 + E^x)*x - E^(1 + x)*x*Log[2] - E^x*x^2*Log[4])^2*(E*Log[2] + I

*Sqrt[-(E^2*Log[2]^2) + 800*Log[4]] + x*Log[16])), x])/(Log[4]^2*Sqrt[-(E^2*Log[2]^2) + 800*Log[4]]) + ((6400*

I)*(2 + E)*Log[2]^4*(1 + (200*Log[4])/(E*Log[2]*(E*Log[2] + Log[4])))*Defer[Int][E^(7 + E^x + x)/((-200*E^x +

8*E^(5 + E^x)*x - E^(1 + x)*x*Log[2] - E^x*x^2*Log[4])^2*(E*Log[2] + I*Sqrt[-(E^2*Log[2]^2) + 800*Log[4]] + x*

Log[16])), x])/(Log[4]^2*Sqrt[-(E^2*Log[2]^2) + 800*Log[4]]) + ((10240000*I)*Log[2]*Defer[Int][E^(10 + 2*E^x +

x)/((-200*E^x + 8*E^(5 + E^x)*x - E^(1 + x)*x*Log[2] - E^x*x^2*Log[4])^2*(E*Log[2] + I*Sqrt[-(E^2*Log[2]^2) +

800*Log[4]] + x*Log[16])), x])/(Log[4]*Sqrt[-(E^2*Log[2]^2) + 800*Log[4]]) - ((51200*I)*Log[2]^3*Defer[Int][E

^(12 + 2*E^x + x)/((-200*E^x + 8*E^(5 + E^x)*x - E^(1 + x)*x*Log[2] - E^x*x^2*Log[4])^2*(E*Log[2] + I*Sqrt[-(E

^2*Log[2]^2) + 800*Log[4]] + x*Log[16])), x])/(Log[4]^2*Sqrt[-(E^2*Log[2]^2) + 800*Log[4]]) + ((800*I)*Log[2]^

2*Defer[Int][E^(1 + x)/((-200*E^x + 8*E^(5 + E^x)*x - E^(1 + x)*x*Log[2] - E^x*x^2*Log[4])*(E*Log[2] + I*Sqrt[

-(E^2*Log[2]^2) + 800*Log[4]] + x*Log[16])), x])/Sqrt[-(E^2*Log[2]^2) + 800*Log[4]] - ((6400*I)*Log[2]^2*Defer

[Int][E^(6 + E^x + x)/((-200*E^x + 8*E^(5 + E^x)*x - E^(1 + x)*x*Log[2] - E^x*x^2*Log[4])*(E*Log[2] + I*Sqrt[-

(E^2*Log[2]^2) + 800*Log[4]] + x*Log[16])), x])/(Log[4]*Sqrt[-(E^2*Log[2]^2) + 800*Log[4]])

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Mathematica [A] time = 0.12, size = 44, normalized size = 1.26 \begin {gather*} \frac {2 e^x x^2 \log (2)}{-8 e^{5+e^x} x+e^{1+x} x \log (2)+e^x \left (200+x^2 \log (4)\right )} \end {gather*}

Integrate[(800*x*Log[2] + 2*E*x^2*Log[2]^2 + E^(5 + E^x - x)*(16*E^x*x^3*Log[2] + (-16*x^2 - 16*x^3)*Log[2]))/

(40000 + 64*E^(10 + 2*E^x - 2*x)*x^2 + (400*E*x + 800*x^2)*Log[2] + (E^2*x^2 + 4*E*x^3 + 4*x^4)*Log[2]^2 + E^(

(2*E^x*x^2*Log[2])/(-8*E^(5 + E^x)*x + E^(1 + x)*x*Log[2] + E^x*(200 + x^2*Log[4]))

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fricas [A] time = 0.60, size = 36, normalized size = 1.03 \begin {gather*} -\frac {2 \, x^{2} \log \relax (2)}{8 \, x e^{\left (-x + e^{x} + 5\right )} - {\left (2 \, x^{2} + x e\right )} \log \relax (2) - 200} \end {gather*}

integrate(((16*x^3*log(2)*exp(x)+(-16*x^3-16*x^2)*log(2))*exp(exp(x)+5-x)+2*x^2*exp(1)*log(2)^2+800*x*log(2))/

(64*x^2*exp(exp(x)+5-x)^2+((-16*x^2*exp(1)-32*x^3)*log(2)-3200*x)*exp(exp(x)+5-x)+(x^2*exp(1)^2+4*x^3*exp(1)+4

*x^4)*log(2)^2+(400*x*exp(1)+800*x^2)*log(2)+40000),x, algorithm="fricas")

-2*x^2*log(2)/(8*x*e^(-x + e^x + 5) - (2*x^2 + x*e)*log(2) - 200)

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giac [B] time = 0.69, size = 1093, normalized size = 31.23 result too large to display

integrate(((16*x^3*log(2)*exp(x)+(-16*x^3-16*x^2)*log(2))*exp(exp(x)+5-x)+2*x^2*exp(1)*log(2)^2+800*x*log(2))/

(64*x^2*exp(exp(x)+5-x)^2+((-16*x^2*exp(1)-32*x^3)*log(2)-3200*x)*exp(exp(x)+5-x)+(x^2*exp(1)^2+4*x^3*exp(1)+4

*x^4)*log(2)^2+(400*x*exp(1)+800*x^2)*log(2)+40000),x, algorithm="giac")

2*(4*x^7*e^(3/2*x)*log(2)^3 - 4*x^7*e^(1/2*x)*log(2)^3 - 4*x^6*e^(1/2*x)*log(2)^3 + 4*x^6*e^(3/2*x + 1)*log(2)

^3 - 4*x^6*e^(1/2*x + 1)*log(2)^3 - 16*x^6*e^(1/2*x + e^x + 5)*log(2)^2 + 16*x^6*e^(-1/2*x + e^x + 5)*log(2)^2

+ x^5*e^(3/2*x + 2)*log(2)^3 - x^5*e^(1/2*x + 2)*log(2)^3 - 2*x^5*e^(1/2*x + 1)*log(2)^3 + 800*x^5*e^(3/2*x)*

log(2)^2 - 800*x^5*e^(1/2*x)*log(2)^2 - 8*x^5*e^(1/2*x + e^x + 6)*log(2)^2 + 8*x^5*e^(-1/2*x + e^x + 6)*log(2)

^2 + 16*x^5*e^(-1/2*x + e^x + 5)*log(2)^2 + 400*x^4*e^(3/2*x + 1)*log(2)^2 - 400*x^4*e^(1/2*x + 1)*log(2)^2 -

1600*x^4*e^(1/2*x + e^x + 5)*log(2) + 1600*x^4*e^(-1/2*x + e^x + 5)*log(2) + 200*x^3*e^(1/2*x + 1)*log(2)^2 +

40000*x^3*e^(3/2*x)*log(2) - 40000*x^3*e^(1/2*x)*log(2) - 1600*x^3*e^(-1/2*x + e^x + 5)*log(2) + 40000*x^2*e^(

1/2*x)*log(2))/(8*x^7*e^(3/2*x)*log(2)^3 - 8*x^7*e^(1/2*x)*log(2)^3 - 8*x^6*e^(1/2*x)*log(2)^3 + 12*x^6*e^(3/2

*x + 1)*log(2)^3 - 12*x^6*e^(1/2*x + 1)*log(2)^3 - 64*x^6*e^(1/2*x + e^x + 5)*log(2)^2 + 64*x^6*e^(-1/2*x + e^

x + 5)*log(2)^2 + 6*x^5*e^(3/2*x + 2)*log(2)^3 - 6*x^5*e^(1/2*x + 2)*log(2)^3 - 8*x^5*e^(1/2*x + 1)*log(2)^3 +

2400*x^5*e^(3/2*x)*log(2)^2 - 2400*x^5*e^(1/2*x)*log(2)^2 - 64*x^5*e^(1/2*x + e^x + 6)*log(2)^2 + 64*x^5*e^(-

1/2*x + e^x + 6)*log(2)^2 + 64*x^5*e^(-1/2*x + e^x + 5)*log(2)^2 + x^4*e^(3/2*x + 3)*log(2)^3 - x^4*e^(1/2*x +

3)*log(2)^3 - 2*x^4*e^(1/2*x + 2)*log(2)^3 + 128*x^5*e^(-1/2*x + 2*e^x + 10)*log(2) - 128*x^5*e^(-3/2*x + 2*e

^x + 10)*log(2) - 800*x^4*e^(1/2*x)*log(2)^2 + 2400*x^4*e^(3/2*x + 1)*log(2)^2 - 16*x^4*e^(1/2*x + e^x + 7)*lo

g(2)^2 - 2400*x^4*e^(1/2*x + 1)*log(2)^2 + 16*x^4*e^(-1/2*x + e^x + 7)*log(2)^2 + 32*x^4*e^(-1/2*x + e^x + 6)*

log(2)^2 - 12800*x^4*e^(1/2*x + e^x + 5)*log(2) + 64*x^4*e^(-1/2*x + 2*e^x + 11)*log(2) + 12800*x^4*e^(-1/2*x

+ e^x + 5)*log(2) - 64*x^4*e^(-3/2*x + 2*e^x + 11)*log(2) - 128*x^4*e^(-3/2*x + 2*e^x + 10)*log(2) + 600*x^3*e

^(3/2*x + 2)*log(2)^2 - 600*x^3*e^(1/2*x + 2)*log(2)^2 + 240000*x^3*e^(3/2*x)*log(2) - 240000*x^3*e^(1/2*x)*lo

g(2) - 6400*x^3*e^(1/2*x + e^x + 6)*log(2) + 6400*x^3*e^(-1/2*x + e^x + 6)*log(2) + 200*x^2*e^(1/2*x + 2)*log(

2)^2 + 12800*x^3*e^(-1/2*x + 2*e^x + 10) - 12800*x^3*e^(-3/2*x + 2*e^x + 10) + 80000*x^2*e^(1/2*x)*log(2) + 12

0000*x^2*e^(3/2*x + 1)*log(2) - 120000*x^2*e^(1/2*x + 1)*log(2) - 3200*x^2*e^(-1/2*x + e^x + 6)*log(2) - 64000

0*x^2*e^(1/2*x + e^x + 5) + 640000*x^2*e^(-1/2*x + e^x + 5) + 12800*x^2*e^(-3/2*x + 2*e^x + 10) + 80000*x*e^(1

/2*x + 1)*log(2) + 8000000*x*e^(3/2*x) - 8000000*x*e^(1/2*x) - 640000*x*e^(-1/2*x + e^x + 5) + 8000000*e^(1/2*

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method	result	size

norman	\(\frac {2 x^{2} \ln \relax (2)}{x \,{\mathrm e} \ln \relax (2)+2 x^{2} \ln \relax (2)-8 \,{\mathrm e}^{{\mathrm e}^{x}+5-x} x +200}\)	\(36\)
risch	\(\frac {2 x^{2} \ln \relax (2)}{x \,{\mathrm e} \ln \relax (2)+2 x^{2} \ln \relax (2)-8 \,{\mathrm e}^{{\mathrm e}^{x}+5-x} x +200}\)	\(36\)

int(((16*x^3*ln(2)*exp(x)+(-16*x^3-16*x^2)*ln(2))*exp(exp(x)+5-x)+2*x^2*exp(1)*ln(2)^2+800*x*ln(2))/(64*x^2*ex

p(exp(x)+5-x)^2+((-16*x^2*exp(1)-32*x^3)*ln(2)-3200*x)*exp(exp(x)+5-x)+(x^2*exp(1)^2+4*x^3*exp(1)+4*x^4)*ln(2)

^2+(400*x*exp(1)+800*x^2)*ln(2)+40000),x,method=_RETURNVERBOSE)

2*x^2*ln(2)/(x*exp(1)*ln(2)+2*x^2*ln(2)-8*exp(exp(x)+5-x)*x+200)

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maxima [A] time = 0.91, size = 38, normalized size = 1.09 \begin {gather*} \frac {2 \, x^{2} e^{x} \log \relax (2)}{{\left (2 \, x^{2} \log \relax (2) + x e \log \relax (2) + 200\right )} e^{x} - 8 \, x e^{\left (e^{x} + 5\right )}} \end {gather*}

integrate(((16*x^3*log(2)*exp(x)+(-16*x^3-16*x^2)*log(2))*exp(exp(x)+5-x)+2*x^2*exp(1)*log(2)^2+800*x*log(2))/

(64*x^2*exp(exp(x)+5-x)^2+((-16*x^2*exp(1)-32*x^3)*log(2)-3200*x)*exp(exp(x)+5-x)+(x^2*exp(1)^2+4*x^3*exp(1)+4

*x^4)*log(2)^2+(400*x*exp(1)+800*x^2)*log(2)+40000),x, algorithm="maxima")

2*x^2*e^x*log(2)/((2*x^2*log(2) + x*e*log(2) + 200)*e^x - 8*x*e^(e^x + 5))

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mupad [F] time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \int \frac {800\,x\,\ln \relax (2)-{\mathrm {e}}^{{\mathrm {e}}^x-x+5}\,\left (\ln \relax (2)\,\left (16\,x^3+16\,x^2\right )-16\,x^3\,{\mathrm {e}}^x\,\ln \relax (2)\right )+2\,x^2\,\mathrm {e}\,{\ln \relax (2)}^2}{64\,x^2\,{\mathrm {e}}^{2\,{\mathrm {e}}^x-2\,x+10}-{\mathrm {e}}^{{\mathrm {e}}^x-x+5}\,\left (3200\,x+\ln \relax (2)\,\left (32\,x^3+16\,\mathrm {e}\,x^2\right )\right )+\ln \relax (2)\,\left (800\,x^2+400\,\mathrm {e}\,x\right )+{\ln \relax (2)}^2\,\left (4\,x^4+4\,\mathrm {e}\,x^3+{\mathrm {e}}^2\,x^2\right )+40000} \,d x \end {gather*}

int((800*x*log(2) - exp(exp(x) - x + 5)*(log(2)*(16*x^2 + 16*x^3) - 16*x^3*exp(x)*log(2)) + 2*x^2*exp(1)*log(2

)^2)/(64*x^2*exp(2*exp(x) - 2*x + 10) - exp(exp(x) - x + 5)*(3200*x + log(2)*(16*x^2*exp(1) + 32*x^3)) + log(2

)*(400*x*exp(1) + 800*x^2) + log(2)^2*(x^2*exp(2) + 4*x^3*exp(1) + 4*x^4) + 40000),x)

int((800*x*log(2) - exp(exp(x) - x + 5)*(log(2)*(16*x^2 + 16*x^3) - 16*x^3*exp(x)*log(2)) + 2*x^2*exp(1)*log(2

)^2)/(64*x^2*exp(2*exp(x) - 2*x + 10) - exp(exp(x) - x + 5)*(3200*x + log(2)*(16*x^2*exp(1) + 32*x^3)) + log(2

)*(400*x*exp(1) + 800*x^2) + log(2)^2*(x^2*exp(2) + 4*x^3*exp(1) + 4*x^4) + 40000), x)

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sympy [A] time = 0.28, size = 39, normalized size = 1.11 \begin {gather*} - \frac {2 x^{2} \log {\relax (2 )}}{- 2 x^{2} \log {\relax (2 )} + 8 x e^{- x + e^{x} + 5} - e x \log {\relax (2 )} - 200} \end {gather*}

integrate(((16*x**3*ln(2)*exp(x)+(-16*x**3-16*x**2)*ln(2))*exp(exp(x)+5-x)+2*x**2*exp(1)*ln(2)**2+800*x*ln(2))

/(64*x**2*exp(exp(x)+5-x)**2+((-16*x**2*exp(1)-32*x**3)*ln(2)-3200*x)*exp(exp(x)+5-x)+(x**2*exp(1)**2+4*x**3*e

-2*x**2*log(2)/(-2*x**2*log(2) + 8*x*exp(-x + exp(x) + 5) - E*x*log(2) - 200)

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3.25.77 \(\int \frac {800 x \log (2)+2 e x^2 \log ^2(2)+e^{5+e^x-x} (16 e^x x^3 \log (2)+(-16 x^2-16 x^3) \log (2))}{40000+64 e^{10+2 e^x-2 x} x^2+(400 e x+800 x^2) \log (2)+(e^2 x^2+4 e x^3+4 x^4) \log ^2(2)+e^{5+e^x-x} (-3200 x+(-16 e x^2-32 x^3) \log (2))} \, dx\)