\(\int \frac {(625+1500 x+1350 x^2+540 x^3+81 x^4) \log (2)+(625+1500 x+1350 x^2+540 x^3+81 x^4) \log ^2(2)+e^{2 x} (4 x^2+4 x^3+(4 x^3+x^4) \log (2)+x^4 \log ^2(2))+e^x (-10 x^2+22 x^3+18 x^4+(-100 x-170 x^2-96 x^3-18 x^4) \log (2)+(-50 x^2-60 x^3-18 x^4) \log ^2(2))+((50 x^2+60 x^3+18 x^4) \log (2)+(50 x^2+60 x^3+18 x^4) \log ^2(2)+e^x (-4 x^3+2 x^4+(-4 x^3-2 x^4) \log (2)-2 x^4 \log ^2(2))) \log (x)+(x^4 \log (2)+x^4 \log ^2(2)) \log ^2(x)}{(625+1500 x+1350 x^2+540 x^3+81 x^4) \log ^2(2)+e^{2 x} (4 x^2+4 x^3 \log (2)+x^4 \log ^2(2))+e^x ((-100 x-120 x^2-36 x^3) \log (2)+(-50 x^2-60 x^3-18 x^4) \log ^2(2))+((50 x^2+60 x^3+18 x^4) \log ^2(2)+e^x (-4 x^3 \log (2)-2 x^4 \log ^2(2))) \log (x)+x^4 \log ^2(2) \log ^2(x)} \, dx\) [4908]

Optimal result

Integrand size = 408, antiderivative size = 36 \[ \int \frac {\left (625+1500 x+1350 x^2+540 x^3+81 x^4\right ) \log (2)+\left (625+1500 x+1350 x^2+540 x^3+81 x^4\right ) \log ^2(2)+e^{2 x} \left (4 x^2+4 x^3+\left (4 x^3+x^4\right ) \log (2)+x^4 \log ^2(2)\right )+e^x \left (-10 x^2+22 x^3+18 x^4+\left (-100 x-170 x^2-96 x^3-18 x^4\right ) \log (2)+\left (-50 x^2-60 x^3-18 x^4\right ) \log ^2(2)\right )+\left (\left (50 x^2+60 x^3+18 x^4\right ) \log (2)+\left (50 x^2+60 x^3+18 x^4\right ) \log ^2(2)+e^x \left (-4 x^3+2 x^4+\left (-4 x^3-2 x^4\right ) \log (2)-2 x^4 \log ^2(2)\right )\right ) \log (x)+\left (x^4 \log (2)+x^4 \log ^2(2)\right ) \log ^2(x)}{\left (625+1500 x+1350 x^2+540 x^3+81 x^4\right ) \log ^2(2)+e^{2 x} \left (4 x^2+4 x^3 \log (2)+x^4 \log ^2(2)\right )+e^x \left (\left (-100 x-120 x^2-36 x^3\right ) \log (2)+\left (-50 x^2-60 x^3-18 x^4\right ) \log ^2(2)\right )+\left (\left (50 x^2+60 x^3+18 x^4\right ) \log ^2(2)+e^x \left (-4 x^3 \log (2)-2 x^4 \log ^2(2)\right )\right ) \log (x)+x^4 \log ^2(2) \log ^2(x)} \, dx=x+\frac {x}{\log (2)-\frac {2 e^x}{x \left (-e^x+\left (3+\frac {5}{x}\right )^2+\log (x)\right )}} \]

[Out]

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

Rubi [F]

\[ \int \frac {\left (625+1500 x+1350 x^2+540 x^3+81 x^4\right ) \log (2)+\left (625+1500 x+1350 x^2+540 x^3+81 x^4\right ) \log ^2(2)+e^{2 x} \left (4 x^2+4 x^3+\left (4 x^3+x^4\right ) \log (2)+x^4 \log ^2(2)\right )+e^x \left (-10 x^2+22 x^3+18 x^4+\left (-100 x-170 x^2-96 x^3-18 x^4\right ) \log (2)+\left (-50 x^2-60 x^3-18 x^4\right ) \log ^2(2)\right )+\left (\left (50 x^2+60 x^3+18 x^4\right ) \log (2)+\left (50 x^2+60 x^3+18 x^4\right ) \log ^2(2)+e^x \left (-4 x^3+2 x^4+\left (-4 x^3-2 x^4\right ) \log (2)-2 x^4 \log ^2(2)\right )\right ) \log (x)+\left (x^4 \log (2)+x^4 \log ^2(2)\right ) \log ^2(x)}{\left (625+1500 x+1350 x^2+540 x^3+81 x^4\right ) \log ^2(2)+e^{2 x} \left (4 x^2+4 x^3 \log (2)+x^4 \log ^2(2)\right )+e^x \left (\left (-100 x-120 x^2-36 x^3\right ) \log (2)+\left (-50 x^2-60 x^3-18 x^4\right ) \log ^2(2)\right )+\left (\left (50 x^2+60 x^3+18 x^4\right ) \log ^2(2)+e^x \left (-4 x^3 \log (2)-2 x^4 \log ^2(2)\right )\right ) \log (x)+x^4 \log ^2(2) \log ^2(x)} \, dx=\int \frac {\left (625+1500 x+1350 x^2+540 x^3+81 x^4\right ) \log (2)+\left (625+1500 x+1350 x^2+540 x^3+81 x^4\right ) \log ^2(2)+e^{2 x} \left (4 x^2+4 x^3+\left (4 x^3+x^4\right ) \log (2)+x^4 \log ^2(2)\right )+e^x \left (-10 x^2+22 x^3+18 x^4+\left (-100 x-170 x^2-96 x^3-18 x^4\right ) \log (2)+\left (-50 x^2-60 x^3-18 x^4\right ) \log ^2(2)\right )+\left (\left (50 x^2+60 x^3+18 x^4\right ) \log (2)+\left (50 x^2+60 x^3+18 x^4\right ) \log ^2(2)+e^x \left (-4 x^3+2 x^4+\left (-4 x^3-2 x^4\right ) \log (2)-2 x^4 \log ^2(2)\right )\right ) \log (x)+\left (x^4 \log (2)+x^4 \log ^2(2)\right ) \log ^2(x)}{\left (625+1500 x+1350 x^2+540 x^3+81 x^4\right ) \log ^2(2)+e^{2 x} \left (4 x^2+4 x^3 \log (2)+x^4 \log ^2(2)\right )+e^x \left (\left (-100 x-120 x^2-36 x^3\right ) \log (2)+\left (-50 x^2-60 x^3-18 x^4\right ) \log ^2(2)\right )+\left (\left (50 x^2+60 x^3+18 x^4\right ) \log ^2(2)+e^x \left (-4 x^3 \log (2)-2 x^4 \log ^2(2)\right )\right ) \log (x)+x^4 \log ^2(2) \log ^2(x)} \, dx \]

[In]

Int[((625 + 1500*x + 1350*x^2 + 540*x^3 + 81*x^4)*Log[2] + (625 + 1500*x + 1350*x^2 + 540*x^3 + 81*x^4)*Log[2]
^2 + E^(2*x)*(4*x^2 + 4*x^3 + (4*x^3 + x^4)*Log[2] + x^4*Log[2]^2) + E^x*(-10*x^2 + 22*x^3 + 18*x^4 + (-100*x
- 170*x^2 - 96*x^3 - 18*x^4)*Log[2] + (-50*x^2 - 60*x^3 - 18*x^4)*Log[2]^2) + ((50*x^2 + 60*x^3 + 18*x^4)*Log[
2] + (50*x^2 + 60*x^3 + 18*x^4)*Log[2]^2 + E^x*(-4*x^3 + 2*x^4 + (-4*x^3 - 2*x^4)*Log[2] - 2*x^4*Log[2]^2))*Lo
g[x] + (x^4*Log[2] + x^4*Log[2]^2)*Log[x]^2)/((625 + 1500*x + 1350*x^2 + 540*x^3 + 81*x^4)*Log[2]^2 + E^(2*x)*
(4*x^2 + 4*x^3*Log[2] + x^4*Log[2]^2) + E^x*((-100*x - 120*x^2 - 36*x^3)*Log[2] + (-50*x^2 - 60*x^3 - 18*x^4)*
Log[2]^2) + ((50*x^2 + 60*x^3 + 18*x^4)*Log[2]^2 + E^x*(-4*x^3*Log[2] - 2*x^4*Log[2]^2))*Log[x] + x^4*Log[2]^2
*Log[x]^2),x]

[Out]

(x*(1 + Log[2]))/Log[2] + 4/(Log[2]^2*(2 + x*Log[2])) + (12960*Defer[Int][(2*E^x*x - 25*Log[2] - 30*x*Log[2] -
9*x^2*Log[2] + E^x*x^2*Log[2] - x^2*Log[2]*Log[x])^(-2), x])/Log[2]^4 - (576*(59 + 90/Log[32])*Defer[Int][(2*
E^x*x - 25*Log[2] - 30*x*Log[2] - 9*x^2*Log[2] + E^x*x^2*Log[2] - x^2*Log[2]*Log[x])^(-2), x])/Log[2]^3 + (360
*(73 - 36*Log[2] + (3*(20 + Log[8]*Log[16] + Log[2048]))/Log[2])*Defer[Int][(2*E^x*x - 25*Log[2] - 30*x*Log[2]
- 9*x^2*Log[2] + E^x*x^2*Log[2] - x^2*Log[2]*Log[x])^(-2), x])/Log[2]^2 - (100*(58*Log[2] - 180*Log[2]^2 + 3*
(56 + 5*Log[8]*Log[16] + 4*Log[2048] + Log[4096]))*Defer[Int][(2*E^x*x - 25*Log[2] - 30*x*Log[2] - 9*x^2*Log[2
] + E^x*x^2*Log[2] - x^2*Log[2]*Log[x])^(-2), x])/Log[2]^2 + (150*(6 + 5*(4 - 4*Log[2]^2 + Log[2]*(4 + Log[16]
))*(1 + (8 - 12*Log[2]^2 + Log[8]*Log[16] + Log[2048])/(12 - 12*Log[2]^2 + Log[8]*Log[16] + Log[4096])))*Defer
[Int][(2*E^x*x - 25*Log[2] - 30*x*Log[2] - 9*x^2*Log[2] + E^x*x^2*Log[2] - x^2*Log[2]*Log[x])^(-2), x])/Log[2]
- (5184*Defer[Int][x/(2*E^x*x - 25*Log[2] - 30*x*Log[2] - 9*x^2*Log[2] + E^x*x^2*Log[2] - x^2*Log[2]*Log[x])^
2, x])/Log[2]^3 + (216*(59 + 90/Log[32])*Defer[Int][x/(2*E^x*x - 25*Log[2] - 30*x*Log[2] - 9*x^2*Log[2] + E^x*
x^2*Log[2] - x^2*Log[2]*Log[x])^2, x])/Log[2]^2 - (120*(73 - 36*Log[2] + (3*(20 + Log[8]*Log[16] + Log[2048]))
/Log[2])*Defer[Int][x/(2*E^x*x - 25*Log[2] - 30*x*Log[2] - 9*x^2*Log[2] + E^x*x^2*Log[2] - x^2*Log[2]*Log[x])^
2, x])/Log[2] + (25*(58*Log[2] - 180*Log[2]^2 + 3*(56 + 5*Log[8]*Log[16] + 4*Log[2048] + Log[4096]))*Defer[Int
][x/(2*E^x*x - 25*Log[2] - 30*x*Log[2] - 9*x^2*Log[2] + E^x*x^2*Log[2] - x^2*Log[2]*Log[x])^2, x])/Log[2] + (1
944*Defer[Int][x^2/(2*E^x*x - 25*Log[2] - 30*x*Log[2] - 9*x^2*Log[2] + E^x*x^2*Log[2] - x^2*Log[2]*Log[x])^2,
x])/Log[2]^2 - (72*(59 + 90/Log[32])*Defer[Int][x^2/(2*E^x*x - 25*Log[2] - 30*x*Log[2] - 9*x^2*Log[2] + E^x*x^
2*Log[2] - x^2*Log[2]*Log[x])^2, x])/Log[2] + 30*(73 - 36*Log[2] + (3*(20 + Log[8]*Log[16] + Log[2048]))/Log[2
])*Defer[Int][x^2/(2*E^x*x - 25*Log[2] - 30*x*Log[2] - 9*x^2*Log[2] + E^x*x^2*Log[2] - x^2*Log[2]*Log[x])^2, x
] - (648*Defer[Int][x^3/(2*E^x*x - 25*Log[2] - 30*x*Log[2] - 9*x^2*Log[2] + E^x*x^2*Log[2] - x^2*Log[2]*Log[x]
)^2, x])/Log[2] + 18*(59 + 90/Log[32])*Defer[Int][x^3/(2*E^x*x - 25*Log[2] - 30*x*Log[2] - 9*x^2*Log[2] + E^x*
x^2*Log[2] - x^2*Log[2]*Log[x])^2, x] + 162*Defer[Int][x^4/(2*E^x*x - 25*Log[2] - 30*x*Log[2] - 9*x^2*Log[2] +
E^x*x^2*Log[2] - x^2*Log[2]*Log[x])^2, x] + (10368*Defer[Int][1/((2 + x*Log[2])^2*(2*E^x*x - 25*Log[2] - 30*x
*Log[2] - 9*x^2*Log[2] + E^x*x^2*Log[2] - x^2*Log[2]*Log[x])^2), x])/Log[2]^4 + 2500*Log[2]*Defer[Int][1/((2 +
x*Log[2])^2*(2*E^x*x - 25*Log[2] - 30*x*Log[2] - 9*x^2*Log[2] + E^x*x^2*Log[2] - x^2*Log[2]*Log[x])^2), x] -
250*(44 - 20*Log[2]^2 + 5*Log[2]*(4 + Log[16]))*Defer[Int][1/((2 + x*Log[2])^2*(2*E^x*x - 25*Log[2] - 30*x*Log
[2] - 9*x^2*Log[2] + E^x*x^2*Log[2] - x^2*Log[2]*Log[x])^2), x] - (576*(59 + 90/Log[32])*Defer[Int][1/((2 + x*
Log[2])^2*(2*E^x*x - 25*Log[2] - 30*x*Log[2] - 9*x^2*Log[2] + E^x*x^2*Log[2] - x^2*Log[2]*Log[x])^2), x])/Log[
2]^3 + (480*(73 - 36*Log[2] + (3*(20 + Log[8]*Log[16] + Log[2048]))/Log[2])*Defer[Int][1/((2 + x*Log[2])^2*(2*
E^x*x - 25*Log[2] - 30*x*Log[2] - 9*x^2*Log[2] + E^x*x^2*Log[2] - x^2*Log[2]*Log[x])^2), x])/Log[2]^2 - (200*(
58*Log[2] - 180*Log[2]^2 + 3*(56 + 5*Log[8]*Log[16] + 4*Log[2048] + Log[4096]))*Defer[Int][1/((2 + x*Log[2])^2
*(2*E^x*x - 25*Log[2] - 30*x*Log[2] - 9*x^2*Log[2] + E^x*x^2*Log[2] - x^2*Log[2]*Log[x])^2), x])/Log[2]^2 + (6
00*(6 + 5*(4 - 4*Log[2]^2 + Log[2]*(4 + Log[16]))*(1 + (8 - 12*Log[2]^2 + Log[8]*Log[16] + Log[2048])/(12 - 12
*Log[2]^2 + Log[8]*Log[16] + Log[4096])))*Defer[Int][1/((2 + x*Log[2])^2*(2*E^x*x - 25*Log[2] - 30*x*Log[2] -
9*x^2*Log[2] + E^x*x^2*Log[2] - x^2*Log[2]*Log[x])^2), x])/Log[2] - (31104*Defer[Int][1/((2 + x*Log[2])*(2*E^x
*x - 25*Log[2] - 30*x*Log[2] - 9*x^2*Log[2] + E^x*x^2*Log[2] - x^2*Log[2]*Log[x])^2), x])/Log[2]^4 + (1440*(59
+ 90/Log[32])*Defer[Int][1/((2 + x*Log[2])*(2*E^x*x - 25*Log[2] - 30*x*Log[2] - 9*x^2*Log[2] + E^x*x^2*Log[2]
- x^2*Log[2]*Log[x])^2), x])/Log[2]^3 - (960*(73 - 36*Log[2] + (3*(20 + Log[8]*Log[16] + Log[2048]))/Log[2])*
Defer[Int][1/((2 + x*Log[2])*(2*E^x*x - 25*Log[2] - 30*x*Log[2] - 9*x^2*Log[2] + E^x*x^2*Log[2] - x^2*Log[2]*L
og[x])^2), x])/Log[2]^2 + (300*(58*Log[2] - 180*Log[2]^2 + 3*(56 + 5*Log[8]*Log[16] + 4*Log[2048] + Log[4096])
)*Defer[Int][1/((2 + x*Log[2])*(2*E^x*x - 25*Log[2] - 30*x*Log[2] - 9*x^2*Log[2] + E^x*x^2*Log[2] - x^2*Log[2]
*Log[x])^2), x])/Log[2]^2 - (600*(6 + 5*(4 - 4*Log[2]^2 + Log[2]*(4 + Log[16]))*(1 + (8 - 12*Log[2]^2 + Log[8]
*Log[16] + Log[2048])/(12 - 12*Log[2]^2 + Log[8]*Log[16] + Log[4096])))*Defer[Int][1/((2 + x*Log[2])*(2*E^x*x
- 25*Log[2] - 30*x*Log[2] - 9*x^2*Log[2] + E^x*x^2*Log[2] - x^2*Log[2]*Log[x])^2), x])/Log[2] + 125*Log[2]*(44
- 20*Log[2]^2 + 5*Log[2]*(4 + Log[16]))*Defer[Int][1/((x*Log[2]^2 + Log[4])*(2*E^x*x - 25*Log[2] - 30*x*Log[2
] - 9*x^2*Log[2] + E^x*x^2*Log[2] - x^2*Log[2]*Log[x])^2), x] + (216*Defer[Int][(2*E^x*x - 25*Log[2] - 30*x*Lo
g[2] - 9*x^2*Log[2] + E^x*x^2*Log[2] - x^2*Log[2]*Log[x])^(-1), x])/Log[2]^3 - (8*(18 + 29*Log[2])*Defer[Int][
(2*E^x*x - 25*Log[2] - 30*x*Log[2] - 9*x^2*Log[2] + E^x*x^2*Log[2] - x^2*Log[2]*Log[x])^(-1), x])/Log[2]^3 + (
22*(2 + Log[32])*Defer[Int][(2*E^x*x - 25*Log[2] - 30*x*Log[2] - 9*x^2*Log[2] + E^x*x^2*Log[2] - x^2*Log[2]*Lo
g[x])^(-1), x])/Log[2]^2 - (72*Defer[Int][x/(2*E^x*x - 25*Log[2] - 30*x*Log[2] - 9*x^2*Log[2] + E^x*x^2*Log[2]
- x^2*Log[2]*Log[x]), x])/Log[2]^2 + (2*(18 + 29*Log[2])*Defer[Int][x/(2*E^x*x - 25*Log[2] - 30*x*Log[2] - 9*
x^2*Log[2] + E^x*x^2*Log[2] - x^2*Log[2]*Log[x]), x])/Log[2]^2 + (18*Defer[Int][x^2/(2*E^x*x - 25*Log[2] - 30*
x*Log[2] - 9*x^2*Log[2] + E^x*x^2*Log[2] - x^2*Log[2]*Log[x]), x])/Log[2] + (288*Defer[Int][1/((2 + x*Log[2])^
2*(2*E^x*x - 25*Log[2] - 30*x*Log[2] - 9*x^2*Log[2] + E^x*x^2*Log[2] - x^2*Log[2]*Log[x])), x])/Log[2]^3 + (88
*(2 + Log[32])*Defer[Int][1/((2 + x*Log[2])^2*(2*E^x*x - 25*Log[2] - 30*x*Log[2] - 9*x^2*Log[2] + E^x*x^2*Log[
2] - x^2*Log[2]*Log[x])), x])/Log[2]^2 + (40*(1 + 10*Log[2]^2 - (1 + Log[4])*Log[32])*Defer[Int][1/((2 + x*Log
[2])^2*(2*E^x*x - 25*Log[2] - 30*x*Log[2] - 9*x^2*Log[2] + E^x*x^2*Log[2] - x^2*Log[2]*Log[x])), x])/Log[2] -
(576*Defer[Int][1/((2 + x*Log[2])*(2*E^x*x - 25*Log[2] - 30*x*Log[2] - 9*x^2*Log[2] + E^x*x^2*Log[2] - x^2*Log
[2]*Log[x])), x])/Log[2]^3 + (24*(18 + 29*Log[2])*Defer[Int][1/((2 + x*Log[2])*(2*E^x*x - 25*Log[2] - 30*x*Log
[2] - 9*x^2*Log[2] + E^x*x^2*Log[2] - x^2*Log[2]*Log[x])), x])/Log[2]^3 - (88*(2 + Log[32])*Defer[Int][1/((2 +
x*Log[2])*(2*E^x*x - 25*Log[2] - 30*x*Log[2] - 9*x^2*Log[2] + E^x*x^2*Log[2] - x^2*Log[2]*Log[x])), x])/Log[2
]^2 - (20*(1 + 10*Log[2]^2 - (1 + Log[4])*Log[32])*Defer[Int][1/((2 + x*Log[2])*(2*E^x*x - 25*Log[2] - 30*x*Lo
g[2] - 9*x^2*Log[2] + E^x*x^2*Log[2] - x^2*Log[2]*Log[x])), x])/Log[2] - (16*(18 + 29*Log[2])*Defer[Int][1/((x
*Log[2]^2 + Log[4])^2*(2*E^x*x - 25*Log[2] - 30*x*Log[2] - 9*x^2*Log[2] + E^x*x^2*Log[2] - x^2*Log[2]*Log[x]))
, x])/Log[2] + (2880*Defer[Int][Log[x]/(-2*E^x*x + 25*Log[2] + 30*x*Log[2] + 9*x^2*Log[2] - E^x*x^2*Log[2] + x
^2*Log[2]*Log[x])^2, x])/Log[2]^4 - (20*(16 - 20*Log[2]^2 - 5*Log[4]^2 + 10*Log[2]*(2 + Log[16]))*Defer[Int][L
og[x]/(-2*E^x*x + 25*Log[2] + 30*x*Log[2] + 9*x^2*Log[2] - E^x*x^2*Log[2] + x^2*Log[2]*Log[x])^2, x])/Log[2]^2
- (32*(72 + 30*Log[4] - 9*Log[4]^2 + Log[2]*(58 + 9*Log[16]))*Defer[Int][Log[x]/(-2*E^x*x + 25*Log[2] + 30*x*
Log[2] + 9*x^2*Log[2] - E^x*x^2*Log[2] + x^2*Log[2]*Log[x])^2, x])/Log[2]^4 - (12*(36 - 25*Log[4] - 30*(4 - Lo
g[4]^2 + Log[2]*Log[16])*(1 + (8 - 12*Log[2]^2 + Log[8]*Log[16] + Log[2048])/(12 - 3*Log[4]^2 + Log[8]*Log[16]
)))*Defer[Int][Log[x]/(-2*E^x*x + 25*Log[2] + 30*x*Log[2] + 9*x^2*Log[2] - E^x*x^2*Log[2] + x^2*Log[2]*Log[x])
^2, x])/Log[2]^3 - (1152*Defer[Int][(x*Log[x])/(-2*E^x*x + 25*Log[2] + 30*x*Log[2] + 9*x^2*Log[2] - E^x*x^2*Lo
g[2] + x^2*Log[2]*Log[x])^2, x])/Log[2]^3 + (5*(16 - 20*Log[2]^2 - 5*Log[4]^2 + 10*Log[2]*(2 + Log[16]))*Defer
[Int][(x*Log[x])/(-2*E^x*x + 25*Log[2] + 30*x*Log[2] + 9*x^2*Log[2] - E^x*x^2*Log[2] + x^2*Log[2]*Log[x])^2, x
])/Log[2] + (12*(72 + 30*Log[4] - 9*Log[4]^2 + Log[2]*(58 + 9*Log[16]))*Defer[Int][(x*Log[x])/(-2*E^x*x + 25*L
og[2] + 30*x*Log[2] + 9*x^2*Log[2] - E^x*x^2*Log[2] + x^2*Log[2]*Log[x])^2, x])/Log[2]^3 + (4*(36 - 25*Log[4]
- 30*(4 - Log[4]^2 + Log[2]*Log[16])*(1 + (8 - 12*Log[2]^2 + Log[8]*Log[16] + Log[2048])/(12 - 3*Log[4]^2 + Lo
g[8]*Log[16])))*Defer[Int][(x*Log[x])/(-2*E^x*x + 25*Log[2] + 30*x*Log[2] + 9*x^2*Log[2] - E^x*x^2*Log[2] + x^
2*Log[2]*Log[x])^2, x])/Log[2]^2 + (432*Defer[Int][(x^2*Log[x])/(-2*E^x*x + 25*Log[2] + 30*x*Log[2] + 9*x^2*Lo
g[2] - E^x*x^2*Log[2] + x^2*Log[2]*Log[x])^2, x])/Log[2]^2 - (4*(72 + 30*Log[4] - 9*Log[4]^2 + Log[2]*(58 + 9*
Log[16]))*Defer[Int][(x^2*Log[x])/(-2*E^x*x + 25*Log[2] + 30*x*Log[2] + 9*x^2*Log[2] - E^x*x^2*Log[2] + x^2*Lo
g[2]*Log[x])^2, x])/Log[2]^2 - ((36 - 25*Log[4] - 30*(4 - Log[4]^2 + Log[2]*Log[16])*(1 + (8 - 12*Log[2]^2 + L
og[8]*Log[16] + Log[2048])/(12 - 3*Log[4]^2 + Log[8]*Log[16])))*Defer[Int][(x^2*Log[x])/(-2*E^x*x + 25*Log[2]
+ 30*x*Log[2] + 9*x^2*Log[2] - E^x*x^2*Log[2] + x^2*Log[2]*Log[x])^2, x])/Log[2] - (144*Defer[Int][(x^3*Log[x]
)/(-2*E^x*x + 25*Log[2] + 30*x*Log[2] + 9*x^2*Log[2] - E^x*x^2*Log[2] + x^2*Log[2]*Log[x])^2, x])/Log[2] + ((7
2 + 30*Log[4] - 9*Log[4]^2 + Log[2]*(58 + 9*Log[16]))*Defer[Int][(x^3*Log[x])/(-2*E^x*x + 25*Log[2] + 30*x*Log
[2] + 9*x^2*Log[2] - E^x*x^2*Log[2] + x^2*Log[2]*Log[x])^2, x])/Log[2] + 36*Defer[Int][(x^4*Log[x])/(-2*E^x*x
+ 25*Log[2] + 30*x*Log[2] + 9*x^2*Log[2] - E^x*x^2*Log[2] + x^2*Log[2]*Log[x])^2, x] + (2304*Defer[Int][Log[x]
/((2 + x*Log[2])^2*(-2*E^x*x + 25*Log[2] + 30*x*Log[2] + 9*x^2*Log[2] - E^x*x^2*Log[2] + x^2*Log[2]*Log[x])^2)
, x])/Log[2]^4 - (40*(16 - 20*Log[2]^2 - 5*Log[4]^2 + 10*Log[2]*(2 + Log[16]))*Defer[Int][Log[x]/((2 + x*Log[2
])^2*(-2*E^x*x + 25*Log[2] + 30*x*Log[2] + 9*x^2*Log[2] - E^x*x^2*Log[2] + x^2*Log[2]*Log[x])^2), x])/Log[2]^2
- (32*(72 + 30*Log[4] - 9*Log[4]^2 + Log[2]*(58 + 9*Log[16]))*Defer[Int][Log[x]/((2 + x*Log[2])^2*(-2*E^x*x +
25*Log[2] + 30*x*Log[2] + 9*x^2*Log[2] - E^x*x^2*Log[2] + x^2*Log[2]*Log[x])^2), x])/Log[2]^4 - (16*(36 - 25*
Log[4] - 30*(4 - Log[4]^2 + Log[2]*Log[16])*(1 + (8 - 12*Log[2]^2 + Log[8]*Log[16] + Log[2048])/(12 - 3*Log[4]
^2 + Log[8]*Log[16])))*Defer[Int][Log[x]/((2 + x*Log[2])^2*(-2*E^x*x + 25*Log[2] + 30*x*Log[2] + 9*x^2*Log[2]
- E^x*x^2*Log[2] + x^2*Log[2]*Log[x])^2), x])/Log[2]^3 - (6912*Defer[Int][Log[x]/((2 + x*Log[2])*(-2*E^x*x + 2
5*Log[2] + 30*x*Log[2] + 9*x^2*Log[2] - E^x*x^2*Log[2] + x^2*Log[2]*Log[x])^2), x])/Log[2]^4 + (60*(16 - 20*Lo
g[2]^2 - 5*Log[4]^2 + 10*Log[2]*(2 + Log[16]))*Defer[Int][Log[x]/((2 + x*Log[2])*(-2*E^x*x + 25*Log[2] + 30*x*
Log[2] + 9*x^2*Log[2] - E^x*x^2*Log[2] + x^2*Log[2]*Log[x])^2), x])/Log[2]^2 + (80*(72 + 30*Log[4] - 9*Log[4]^
2 + Log[2]*(58 + 9*Log[16]))*Defer[Int][Log[x]/((2 + x*Log[2])*(-2*E^x*x + 25*Log[2] + 30*x*Log[2] + 9*x^2*Log
[2] - E^x*x^2*Log[2] + x^2*Log[2]*Log[x])^2), x])/Log[2]^4 + (32*(36 - 25*Log[4] - 30*(4 - Log[4]^2 + Log[2]*L
og[16])*(1 + (8 - 12*Log[2]^2 + Log[8]*Log[16] + Log[2048])/(12 - 3*Log[4]^2 + Log[8]*Log[16])))*Defer[Int][Lo
g[x]/((2 + x*Log[2])*(-2*E^x*x + 25*Log[2] + 30*x*Log[2] + 9*x^2*Log[2] - E^x*x^2*Log[2] + x^2*Log[2]*Log[x])^
2), x])/Log[2]^3 - (48*Defer[Int][Log[x]^2/(-2*E^x*x + 25*Log[2] + 30*x*Log[2] + 9*x^2*Log[2] - E^x*x^2*Log[2]
+ x^2*Log[2]*Log[x])^2, x])/Log[2]^3 + (80*Log[4]*Defer[Int][Log[x]^2/(-2*E^x*x + 25*Log[2] + 30*x*Log[2] + 9
*x^2*Log[2] - E^x*x^2*Log[2] + x^2*Log[2]*Log[x])^2, x])/Log[2]^5 - (32*(4 - Log[4]^2 + Log[2]*Log[16])*Defer[
Int][Log[x]^2/(-2*E^x*x + 25*Log[2] + 30*x*Log[2] + 9*x^2*Log[2] - E^x*x^2*Log[2] + x^2*Log[2]*Log[x])^2, x])/
Log[2]^4 + (16*Defer[Int][(x*Log[x]^2)/(-2*E^x*x + 25*Log[2] + 30*x*Log[2] + 9*x^2*Log[2] - E^x*x^2*Log[2] + x
^2*Log[2]*Log[x])^2, x])/Log[2]^2 - (32*Log[4]*Defer[Int][(x*Log[x]^2)/(-2*E^x*x + 25*Log[2] + 30*x*Log[2] + 9
*x^2*Log[2] - E^x*x^2*Log[2] + x^2*Log[2]*Log[x])^2, x])/Log[2]^4 + (12*(4 - Log[4]^2 + Log[2]*Log[16])*Defer[
Int][(x*Log[x]^2)/(-2*E^x*x + 25*Log[2] + 30*x*Log[2] + 9*x^2*Log[2] - E^x*x^2*Log[2] + x^2*Log[2]*Log[x])^2,
x])/Log[2]^3 - (4*Defer[Int][(x^2*Log[x]^2)/(-2*E^x*x + 25*Log[2] + 30*x*Log[2] + 9*x^2*Log[2] - E^x*x^2*Log[2
] + x^2*Log[2]*Log[x])^2, x])/Log[2] + (12*Log[4]*Defer[Int][(x^2*Log[x]^2)/(-2*E^x*x + 25*Log[2] + 30*x*Log[2
] + 9*x^2*Log[2] - E^x*x^2*Log[2] + x^2*Log[2]*Log[x])^2, x])/Log[2]^3 - (4*(4 - Log[4]^2 + Log[2]*Log[16])*De
fer[Int][(x^2*Log[x]^2)/(-2*E^x*x + 25*Log[2] + 30*x*Log[2] + 9*x^2*Log[2] - E^x*x^2*Log[2] + x^2*Log[2]*Log[x
])^2, x])/Log[2]^2 - (4*Log[4]*Defer[Int][(x^3*Log[x]^2)/(-2*E^x*x + 25*Log[2] + 30*x*Log[2] + 9*x^2*Log[2] -
E^x*x^2*Log[2] + x^2*Log[2]*Log[x])^2, x])/Log[2]^2 + ((4 - Log[4]^2 + Log[2]*Log[16])*Defer[Int][(x^3*Log[x]^
2)/(-2*E^x*x + 25*Log[2] + 30*x*Log[2] + 9*x^2*Log[2] - E^x*x^2*Log[2] + x^2*Log[2]*Log[x])^2, x])/Log[2] + (L
og[4]*Defer[Int][(x^4*Log[x]^2)/(-2*E^x*x + 25*Log[2] + 30*x*Log[2] + 9*x^2*Log[2] - E^x*x^2*Log[2] + x^2*Log[
2]*Log[x])^2, x])/Log[2] - (64*Defer[Int][Log[x]^2/((2 + x*Log[2])^2*(-2*E^x*x + 25*Log[2] + 30*x*Log[2] + 9*x
^2*Log[2] - E^x*x^2*Log[2] + x^2*Log[2]*Log[x])^2), x])/Log[2]^3 + (64*Log[4]*Defer[Int][Log[x]^2/((2 + x*Log[
2])^2*(-2*E^x*x + 25*Log[2] + 30*x*Log[2] + 9*x^2*Log[2] - E^x*x^2*Log[2] + x^2*Log[2]*Log[x])^2), x])/Log[2]^
5 - (32*(4 - Log[4]^2 + Log[2]*Log[16])*Defer[Int][Log[x]^2/((2 + x*Log[2])^2*(-2*E^x*x + 25*Log[2] + 30*x*Log
[2] + 9*x^2*Log[2] - E^x*x^2*Log[2] + x^2*Log[2]*Log[x])^2), x])/Log[2]^4 + (128*Defer[Int][Log[x]^2/((2 + x*L
og[2])*(-2*E^x*x + 25*Log[2] + 30*x*Log[2] + 9*x^2*Log[2] - E^x*x^2*Log[2] + x^2*Log[2]*Log[x])^2), x])/Log[2]
^3 - (192*Log[4]*Defer[Int][Log[x]^2/((2 + x*Log[2])*(-2*E^x*x + 25*Log[2] + 30*x*Log[2] + 9*x^2*Log[2] - E^x*
x^2*Log[2] + x^2*Log[2]*Log[x])^2), x])/Log[2]^5 + (80*(4 - Log[4]^2 + Log[2]*Log[16])*Defer[Int][Log[x]^2/((2
+ x*Log[2])*(-2*E^x*x + 25*Log[2] + 30*x*Log[2] + 9*x^2*Log[2] - E^x*x^2*Log[2] + x^2*Log[2]*Log[x])^2), x])/
Log[2]^4 - (8*Defer[Int][Log[x]/(-2*E^x*x + 25*Log[2] + 30*x*Log[2] + 9*x^2*Log[2] - E^x*x^2*Log[2] + x^2*Log[
2]*Log[x]), x])/Log[2]^3 + (8*Defer[Int][Log[x]/(-2*E^x*x + 25*Log[2] + 30*x*Log[2] + 9*x^2*Log[2] - E^x*x^2*L
og[2] + x^2*Log[2]*Log[x]), x])/Log[2]^2 + (4*Defer[Int][(x*Log[x])/(-2*E^x*x + 25*Log[2] + 30*x*Log[2] + 9*x^
2*Log[2] - E^x*x^2*Log[2] + x^2*Log[2]*Log[x]), x])/Log[2]^2 - (2*Defer[Int][(x^2*Log[x])/(-2*E^x*x + 25*Log[2
] + 30*x*Log[2] + 9*x^2*Log[2] - E^x*x^2*Log[2] + x^2*Log[2]*Log[x]), x])/Log[2] - (32*Defer[Int][Log[x]/((2 +
x*Log[2])^2*(-2*E^x*x + 25*Log[2] + 30*x*Log[2] + 9*x^2*Log[2] - E^x*x^2*Log[2] + x^2*Log[2]*Log[x])), x])/Lo
g[2]^3 + (32*Defer[Int][Log[x]/((2 + x*Log[2])^2*(-2*E^x*x + 25*Log[2] + 30*x*Log[2] + 9*x^2*Log[2] - E^x*x^2*
Log[2] + x^2*Log[2]*Log[x])), x])/Log[2]^2 + (16*Defer[Int][Log[x]/((2 + x*Log[2])*(-2*E^x*x + 25*Log[2] + 30*
x*Log[2] + 9*x^2*Log[2] - E^x*x^2*Log[2] + x^2*Log[2]*Log[x])), x])/Log[2]^3 - (32*Defer[Int][Log[x]/((2 + x*L
og[2])*(-2*E^x*x + 25*Log[2] + 30*x*Log[2] + 9*x^2*Log[2] - E^x*x^2*Log[2] + x^2*Log[2]*Log[x])), x])/Log[2]^2
+ (32*Defer[Int][Log[x]/((x*Log[2]^2 + Log[4])^2*(-2*E^x*x + 25*Log[2] + 30*x*Log[2] + 9*x^2*Log[2] - E^x*x^2
*Log[2] + x^2*Log[2]*Log[x])), x])/Log[2]

Rubi steps Aborted

Mathematica [F]

\[ \int \frac {\left (625+1500 x+1350 x^2+540 x^3+81 x^4\right ) \log (2)+\left (625+1500 x+1350 x^2+540 x^3+81 x^4\right ) \log ^2(2)+e^{2 x} \left (4 x^2+4 x^3+\left (4 x^3+x^4\right ) \log (2)+x^4 \log ^2(2)\right )+e^x \left (-10 x^2+22 x^3+18 x^4+\left (-100 x-170 x^2-96 x^3-18 x^4\right ) \log (2)+\left (-50 x^2-60 x^3-18 x^4\right ) \log ^2(2)\right )+\left (\left (50 x^2+60 x^3+18 x^4\right ) \log (2)+\left (50 x^2+60 x^3+18 x^4\right ) \log ^2(2)+e^x \left (-4 x^3+2 x^4+\left (-4 x^3-2 x^4\right ) \log (2)-2 x^4 \log ^2(2)\right )\right ) \log (x)+\left (x^4 \log (2)+x^4 \log ^2(2)\right ) \log ^2(x)}{\left (625+1500 x+1350 x^2+540 x^3+81 x^4\right ) \log ^2(2)+e^{2 x} \left (4 x^2+4 x^3 \log (2)+x^4 \log ^2(2)\right )+e^x \left (\left (-100 x-120 x^2-36 x^3\right ) \log (2)+\left (-50 x^2-60 x^3-18 x^4\right ) \log ^2(2)\right )+\left (\left (50 x^2+60 x^3+18 x^4\right ) \log ^2(2)+e^x \left (-4 x^3 \log (2)-2 x^4 \log ^2(2)\right )\right ) \log (x)+x^4 \log ^2(2) \log ^2(x)} \, dx=\int \frac {\left (625+1500 x+1350 x^2+540 x^3+81 x^4\right ) \log (2)+\left (625+1500 x+1350 x^2+540 x^3+81 x^4\right ) \log ^2(2)+e^{2 x} \left (4 x^2+4 x^3+\left (4 x^3+x^4\right ) \log (2)+x^4 \log ^2(2)\right )+e^x \left (-10 x^2+22 x^3+18 x^4+\left (-100 x-170 x^2-96 x^3-18 x^4\right ) \log (2)+\left (-50 x^2-60 x^3-18 x^4\right ) \log ^2(2)\right )+\left (\left (50 x^2+60 x^3+18 x^4\right ) \log (2)+\left (50 x^2+60 x^3+18 x^4\right ) \log ^2(2)+e^x \left (-4 x^3+2 x^4+\left (-4 x^3-2 x^4\right ) \log (2)-2 x^4 \log ^2(2)\right )\right ) \log (x)+\left (x^4 \log (2)+x^4 \log ^2(2)\right ) \log ^2(x)}{\left (625+1500 x+1350 x^2+540 x^3+81 x^4\right ) \log ^2(2)+e^{2 x} \left (4 x^2+4 x^3 \log (2)+x^4 \log ^2(2)\right )+e^x \left (\left (-100 x-120 x^2-36 x^3\right ) \log (2)+\left (-50 x^2-60 x^3-18 x^4\right ) \log ^2(2)\right )+\left (\left (50 x^2+60 x^3+18 x^4\right ) \log ^2(2)+e^x \left (-4 x^3 \log (2)-2 x^4 \log ^2(2)\right )\right ) \log (x)+x^4 \log ^2(2) \log ^2(x)} \, dx \]

[In]

Integrate[((625 + 1500*x + 1350*x^2 + 540*x^3 + 81*x^4)*Log[2] + (625 + 1500*x + 1350*x^2 + 540*x^3 + 81*x^4)*
Log[2]^2 + E^(2*x)*(4*x^2 + 4*x^3 + (4*x^3 + x^4)*Log[2] + x^4*Log[2]^2) + E^x*(-10*x^2 + 22*x^3 + 18*x^4 + (-
100*x - 170*x^2 - 96*x^3 - 18*x^4)*Log[2] + (-50*x^2 - 60*x^3 - 18*x^4)*Log[2]^2) + ((50*x^2 + 60*x^3 + 18*x^4
)*Log[2] + (50*x^2 + 60*x^3 + 18*x^4)*Log[2]^2 + E^x*(-4*x^3 + 2*x^4 + (-4*x^3 - 2*x^4)*Log[2] - 2*x^4*Log[2]^
2))*Log[x] + (x^4*Log[2] + x^4*Log[2]^2)*Log[x]^2)/((625 + 1500*x + 1350*x^2 + 540*x^3 + 81*x^4)*Log[2]^2 + E^
(2*x)*(4*x^2 + 4*x^3*Log[2] + x^4*Log[2]^2) + E^x*((-100*x - 120*x^2 - 36*x^3)*Log[2] + (-50*x^2 - 60*x^3 - 18
*x^4)*Log[2]^2) + ((50*x^2 + 60*x^3 + 18*x^4)*Log[2]^2 + E^x*(-4*x^3*Log[2] - 2*x^4*Log[2]^2))*Log[x] + x^4*Lo
g[2]^2*Log[x]^2),x]

[Out]

Integrate[((625 + 1500*x + 1350*x^2 + 540*x^3 + 81*x^4)*Log[2] + (625 + 1500*x + 1350*x^2 + 540*x^3 + 81*x^4)*
Log[2]^2 + E^(2*x)*(4*x^2 + 4*x^3 + (4*x^3 + x^4)*Log[2] + x^4*Log[2]^2) + E^x*(-10*x^2 + 22*x^3 + 18*x^4 + (-
100*x - 170*x^2 - 96*x^3 - 18*x^4)*Log[2] + (-50*x^2 - 60*x^3 - 18*x^4)*Log[2]^2) + ((50*x^2 + 60*x^3 + 18*x^4
)*Log[2] + (50*x^2 + 60*x^3 + 18*x^4)*Log[2]^2 + E^x*(-4*x^3 + 2*x^4 + (-4*x^3 - 2*x^4)*Log[2] - 2*x^4*Log[2]^
2))*Log[x] + (x^4*Log[2] + x^4*Log[2]^2)*Log[x]^2)/((625 + 1500*x + 1350*x^2 + 540*x^3 + 81*x^4)*Log[2]^2 + E^
(2*x)*(4*x^2 + 4*x^3*Log[2] + x^4*Log[2]^2) + E^x*((-100*x - 120*x^2 - 36*x^3)*Log[2] + (-50*x^2 - 60*x^3 - 18
*x^4)*Log[2]^2) + ((50*x^2 + 60*x^3 + 18*x^4)*Log[2]^2 + E^x*(-4*x^3*Log[2] - 2*x^4*Log[2]^2))*Log[x] + x^4*Lo
g[2]^2*Log[x]^2), x]

Maple [A] (verified)

Time = 1.04 (sec) , antiderivative size = 61, normalized size of antiderivative = 1.69

method	result	size
risch	\(x +\frac {x}{\ln \left (2\right )}-\frac {2 x^{2} {\mathrm e}^{x}}{\ln \left (2\right ) \left (x^{2} \ln \left (2\right ) {\mathrm e}^{x}-x^{2} \ln \left (2\right ) \ln \left (x \right )-9 x^{2} \ln \left (2\right )-30 x \ln \left (2\right )+2 \,{\mathrm e}^{x} x -25 \ln \left (2\right )\right )}\)	\(61\)
parallelrisch	\(\frac {2 x^{3} \ln \left (2\right ) \ln \left (x \right )+50 x +50 x \ln \left (2\right )+60 x^{2} \ln \left (2\right )+18 x^{3} \ln \left (2\right )-4 \,{\mathrm e}^{x} x^{2}-2 \,{\mathrm e}^{x} x^{3}-2 x^{3} \ln \left (2\right ) {\mathrm e}^{x}+18 x^{3}+60 x^{2}+2 x^{3} \ln \left (x \right )}{2 x^{2} \ln \left (2\right ) \ln \left (x \right )-2 x^{2} \ln \left (2\right ) {\mathrm e}^{x}+18 x^{2} \ln \left (2\right )+60 x \ln \left (2\right )-4 \,{\mathrm e}^{x} x +50 \ln \left (2\right )}\)	\(116\)

[In]

int(((x^4*ln(2)^2+x^4*ln(2))*ln(x)^2+((-2*x^4*ln(2)^2+(-2*x^4-4*x^3)*ln(2)+2*x^4-4*x^3)*exp(x)+(18*x^4+60*x^3+
50*x^2)*ln(2)^2+(18*x^4+60*x^3+50*x^2)*ln(2))*ln(x)+(x^4*ln(2)^2+(x^4+4*x^3)*ln(2)+4*x^3+4*x^2)*exp(x)^2+((-18
*x^4-60*x^3-50*x^2)*ln(2)^2+(-18*x^4-96*x^3-170*x^2-100*x)*ln(2)+18*x^4+22*x^3-10*x^2)*exp(x)+(81*x^4+540*x^3+
1350*x^2+1500*x+625)*ln(2)^2+(81*x^4+540*x^3+1350*x^2+1500*x+625)*ln(2))/(x^4*ln(2)^2*ln(x)^2+((-2*x^4*ln(2)^2
-4*x^3*ln(2))*exp(x)+(18*x^4+60*x^3+50*x^2)*ln(2)^2)*ln(x)+(x^4*ln(2)^2+4*x^3*ln(2)+4*x^2)*exp(x)^2+((-18*x^4-
60*x^3-50*x^2)*ln(2)^2+(-36*x^3-120*x^2-100*x)*ln(2))*exp(x)+(81*x^4+540*x^3+1350*x^2+1500*x+625)*ln(2)^2),x,m
ethod=_RETURNVERBOSE)

[Out]

x+x/ln(2)-2/ln(2)*x^2*exp(x)/(x^2*ln(2)*exp(x)-x^2*ln(2)*ln(x)-9*x^2*ln(2)-30*x*ln(2)+2*exp(x)*x-25*ln(2))

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 102 vs. \(2 (37) = 74\).

Time = 0.26 (sec) , antiderivative size = 102, normalized size of antiderivative = 2.83 \[ \int \frac {\left (625+1500 x+1350 x^2+540 x^3+81 x^4\right ) \log (2)+\left (625+1500 x+1350 x^2+540 x^3+81 x^4\right ) \log ^2(2)+e^{2 x} \left (4 x^2+4 x^3+\left (4 x^3+x^4\right ) \log (2)+x^4 \log ^2(2)\right )+e^x \left (-10 x^2+22 x^3+18 x^4+\left (-100 x-170 x^2-96 x^3-18 x^4\right ) \log (2)+\left (-50 x^2-60 x^3-18 x^4\right ) \log ^2(2)\right )+\left (\left (50 x^2+60 x^3+18 x^4\right ) \log (2)+\left (50 x^2+60 x^3+18 x^4\right ) \log ^2(2)+e^x \left (-4 x^3+2 x^4+\left (-4 x^3-2 x^4\right ) \log (2)-2 x^4 \log ^2(2)\right )\right ) \log (x)+\left (x^4 \log (2)+x^4 \log ^2(2)\right ) \log ^2(x)}{\left (625+1500 x+1350 x^2+540 x^3+81 x^4\right ) \log ^2(2)+e^{2 x} \left (4 x^2+4 x^3 \log (2)+x^4 \log ^2(2)\right )+e^x \left (\left (-100 x-120 x^2-36 x^3\right ) \log (2)+\left (-50 x^2-60 x^3-18 x^4\right ) \log ^2(2)\right )+\left (\left (50 x^2+60 x^3+18 x^4\right ) \log ^2(2)+e^x \left (-4 x^3 \log (2)-2 x^4 \log ^2(2)\right )\right ) \log (x)+x^4 \log ^2(2) \log ^2(x)} \, dx=\frac {9 \, x^{3} + 30 \, x^{2} - {\left (x^{3} \log \left (2\right ) + x^{3} + 2 \, x^{2}\right )} e^{x} + {\left (9 \, x^{3} + 30 \, x^{2} + 25 \, x\right )} \log \left (2\right ) + {\left (x^{3} \log \left (2\right ) + x^{3}\right )} \log \left (x\right ) + 25 \, x}{x^{2} \log \left (2\right ) \log \left (x\right ) - {\left (x^{2} \log \left (2\right ) + 2 \, x\right )} e^{x} + {\left (9 \, x^{2} + 30 \, x + 25\right )} \log \left (2\right )} \]

[In]

integrate(((x^4*log(2)^2+x^4*log(2))*log(x)^2+((-2*x^4*log(2)^2+(-2*x^4-4*x^3)*log(2)+2*x^4-4*x^3)*exp(x)+(18*
x^4+60*x^3+50*x^2)*log(2)^2+(18*x^4+60*x^3+50*x^2)*log(2))*log(x)+(x^4*log(2)^2+(x^4+4*x^3)*log(2)+4*x^3+4*x^2
)*exp(x)^2+((-18*x^4-60*x^3-50*x^2)*log(2)^2+(-18*x^4-96*x^3-170*x^2-100*x)*log(2)+18*x^4+22*x^3-10*x^2)*exp(x
)+(81*x^4+540*x^3+1350*x^2+1500*x+625)*log(2)^2+(81*x^4+540*x^3+1350*x^2+1500*x+625)*log(2))/(x^4*log(2)^2*log
(x)^2+((-2*x^4*log(2)^2-4*x^3*log(2))*exp(x)+(18*x^4+60*x^3+50*x^2)*log(2)^2)*log(x)+(x^4*log(2)^2+4*x^3*log(2
)+4*x^2)*exp(x)^2+((-18*x^4-60*x^3-50*x^2)*log(2)^2+(-36*x^3-120*x^2-100*x)*log(2))*exp(x)+(81*x^4+540*x^3+135
0*x^2+1500*x+625)*log(2)^2),x, algorithm="fricas")

[Out]

(9*x^3 + 30*x^2 - (x^3*log(2) + x^3 + 2*x^2)*e^x + (9*x^3 + 30*x^2 + 25*x)*log(2) + (x^3*log(2) + x^3)*log(x)
+ 25*x)/(x^2*log(2)*log(x) - (x^2*log(2) + 2*x)*e^x + (9*x^2 + 30*x + 25)*log(2))

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 143 vs. \(2 (26) = 52\).

Time = 0.41 (sec) , antiderivative size = 143, normalized size of antiderivative = 3.97 \[ \int \frac {\left (625+1500 x+1350 x^2+540 x^3+81 x^4\right ) \log (2)+\left (625+1500 x+1350 x^2+540 x^3+81 x^4\right ) \log ^2(2)+e^{2 x} \left (4 x^2+4 x^3+\left (4 x^3+x^4\right ) \log (2)+x^4 \log ^2(2)\right )+e^x \left (-10 x^2+22 x^3+18 x^4+\left (-100 x-170 x^2-96 x^3-18 x^4\right ) \log (2)+\left (-50 x^2-60 x^3-18 x^4\right ) \log ^2(2)\right )+\left (\left (50 x^2+60 x^3+18 x^4\right ) \log (2)+\left (50 x^2+60 x^3+18 x^4\right ) \log ^2(2)+e^x \left (-4 x^3+2 x^4+\left (-4 x^3-2 x^4\right ) \log (2)-2 x^4 \log ^2(2)\right )\right ) \log (x)+\left (x^4 \log (2)+x^4 \log ^2(2)\right ) \log ^2(x)}{\left (625+1500 x+1350 x^2+540 x^3+81 x^4\right ) \log ^2(2)+e^{2 x} \left (4 x^2+4 x^3 \log (2)+x^4 \log ^2(2)\right )+e^x \left (\left (-100 x-120 x^2-36 x^3\right ) \log (2)+\left (-50 x^2-60 x^3-18 x^4\right ) \log ^2(2)\right )+\left (\left (50 x^2+60 x^3+18 x^4\right ) \log ^2(2)+e^x \left (-4 x^3 \log (2)-2 x^4 \log ^2(2)\right )\right ) \log (x)+x^4 \log ^2(2) \log ^2(x)} \, dx=x \left (1 + \frac {1}{\log {\left (2 \right )}}\right ) + \frac {- 2 x^{3} \log {\left (x \right )} - 18 x^{3} - 60 x^{2} - 50 x}{- x^{3} \log {\left (2 \right )}^{2} \log {\left (x \right )} - 9 x^{3} \log {\left (2 \right )}^{2} - 2 x^{2} \log {\left (2 \right )} \log {\left (x \right )} - 30 x^{2} \log {\left (2 \right )}^{2} - 18 x^{2} \log {\left (2 \right )} - 60 x \log {\left (2 \right )} - 25 x \log {\left (2 \right )}^{2} + \left (x^{3} \log {\left (2 \right )}^{2} + 4 x^{2} \log {\left (2 \right )} + 4 x\right ) e^{x} - 50 \log {\left (2 \right )}} + \frac {4}{x \log {\left (2 \right )}^{3} + 2 \log {\left (2 \right )}^{2}} \]

[In]

integrate(((x**4*ln(2)**2+x**4*ln(2))*ln(x)**2+((-2*x**4*ln(2)**2+(-2*x**4-4*x**3)*ln(2)+2*x**4-4*x**3)*exp(x)
+(18*x**4+60*x**3+50*x**2)*ln(2)**2+(18*x**4+60*x**3+50*x**2)*ln(2))*ln(x)+(x**4*ln(2)**2+(x**4+4*x**3)*ln(2)+
4*x**3+4*x**2)*exp(x)**2+((-18*x**4-60*x**3-50*x**2)*ln(2)**2+(-18*x**4-96*x**3-170*x**2-100*x)*ln(2)+18*x**4+
22*x**3-10*x**2)*exp(x)+(81*x**4+540*x**3+1350*x**2+1500*x+625)*ln(2)**2+(81*x**4+540*x**3+1350*x**2+1500*x+62
5)*ln(2))/(x**4*ln(2)**2*ln(x)**2+((-2*x**4*ln(2)**2-4*x**3*ln(2))*exp(x)+(18*x**4+60*x**3+50*x**2)*ln(2)**2)*
ln(x)+(x**4*ln(2)**2+4*x**3*ln(2)+4*x**2)*exp(x)**2+((-18*x**4-60*x**3-50*x**2)*ln(2)**2+(-36*x**3-120*x**2-10
0*x)*ln(2))*exp(x)+(81*x**4+540*x**3+1350*x**2+1500*x+625)*ln(2)**2),x)

[Out]

x*(1 + 1/log(2)) + (-2*x**3*log(x) - 18*x**3 - 60*x**2 - 50*x)/(-x**3*log(2)**2*log(x) - 9*x**3*log(2)**2 - 2*
x**2*log(2)*log(x) - 30*x**2*log(2)**2 - 18*x**2*log(2) - 60*x*log(2) - 25*x*log(2)**2 + (x**3*log(2)**2 + 4*x
**2*log(2) + 4*x)*exp(x) - 50*log(2)) + 4/(x*log(2)**3 + 2*log(2)**2)

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 174 vs. \(2 (37) = 74\).

Time = 0.41 (sec) , antiderivative size = 174, normalized size of antiderivative = 4.83 \[ \int \frac {\left (625+1500 x+1350 x^2+540 x^3+81 x^4\right ) \log (2)+\left (625+1500 x+1350 x^2+540 x^3+81 x^4\right ) \log ^2(2)+e^{2 x} \left (4 x^2+4 x^3+\left (4 x^3+x^4\right ) \log (2)+x^4 \log ^2(2)\right )+e^x \left (-10 x^2+22 x^3+18 x^4+\left (-100 x-170 x^2-96 x^3-18 x^4\right ) \log (2)+\left (-50 x^2-60 x^3-18 x^4\right ) \log ^2(2)\right )+\left (\left (50 x^2+60 x^3+18 x^4\right ) \log (2)+\left (50 x^2+60 x^3+18 x^4\right ) \log ^2(2)+e^x \left (-4 x^3+2 x^4+\left (-4 x^3-2 x^4\right ) \log (2)-2 x^4 \log ^2(2)\right )\right ) \log (x)+\left (x^4 \log (2)+x^4 \log ^2(2)\right ) \log ^2(x)}{\left (625+1500 x+1350 x^2+540 x^3+81 x^4\right ) \log ^2(2)+e^{2 x} \left (4 x^2+4 x^3 \log (2)+x^4 \log ^2(2)\right )+e^x \left (\left (-100 x-120 x^2-36 x^3\right ) \log (2)+\left (-50 x^2-60 x^3-18 x^4\right ) \log ^2(2)\right )+\left (\left (50 x^2+60 x^3+18 x^4\right ) \log ^2(2)+e^x \left (-4 x^3 \log (2)-2 x^4 \log ^2(2)\right )\right ) \log (x)+x^4 \log ^2(2) \log ^2(x)} \, dx=\frac {9 \, {\left (\log \left (2\right )^{3} + \log \left (2\right )^{2}\right )} x^{3} + 6 \, {\left (5 \, \log \left (2\right )^{3} + 5 \, \log \left (2\right )^{2} + 3 \, \log \left (2\right )\right )} x^{2} + 5 \, {\left (5 \, \log \left (2\right )^{3} + 5 \, \log \left (2\right )^{2} + 12 \, \log \left (2\right )\right )} x - {\left ({\left (\log \left (2\right )^{3} + \log \left (2\right )^{2}\right )} x^{3} + 2 \, {\left (\log \left (2\right )^{2} + \log \left (2\right )\right )} x^{2} + 4 \, x\right )} e^{x} + {\left ({\left (\log \left (2\right )^{3} + \log \left (2\right )^{2}\right )} x^{3} + 2 \, x^{2} \log \left (2\right )\right )} \log \left (x\right ) + 50 \, \log \left (2\right )}{x^{2} \log \left (2\right )^{3} \log \left (x\right ) + 9 \, x^{2} \log \left (2\right )^{3} + 30 \, x \log \left (2\right )^{3} + 25 \, \log \left (2\right )^{3} - {\left (x^{2} \log \left (2\right )^{3} + 2 \, x \log \left (2\right )^{2}\right )} e^{x}} \]

[In]

integrate(((x^4*log(2)^2+x^4*log(2))*log(x)^2+((-2*x^4*log(2)^2+(-2*x^4-4*x^3)*log(2)+2*x^4-4*x^3)*exp(x)+(18*
x^4+60*x^3+50*x^2)*log(2)^2+(18*x^4+60*x^3+50*x^2)*log(2))*log(x)+(x^4*log(2)^2+(x^4+4*x^3)*log(2)+4*x^3+4*x^2
)*exp(x)^2+((-18*x^4-60*x^3-50*x^2)*log(2)^2+(-18*x^4-96*x^3-170*x^2-100*x)*log(2)+18*x^4+22*x^3-10*x^2)*exp(x
)+(81*x^4+540*x^3+1350*x^2+1500*x+625)*log(2)^2+(81*x^4+540*x^3+1350*x^2+1500*x+625)*log(2))/(x^4*log(2)^2*log
(x)^2+((-2*x^4*log(2)^2-4*x^3*log(2))*exp(x)+(18*x^4+60*x^3+50*x^2)*log(2)^2)*log(x)+(x^4*log(2)^2+4*x^3*log(2
)+4*x^2)*exp(x)^2+((-18*x^4-60*x^3-50*x^2)*log(2)^2+(-36*x^3-120*x^2-100*x)*log(2))*exp(x)+(81*x^4+540*x^3+135
0*x^2+1500*x+625)*log(2)^2),x, algorithm="maxima")

[Out]

(9*(log(2)^3 + log(2)^2)*x^3 + 6*(5*log(2)^3 + 5*log(2)^2 + 3*log(2))*x^2 + 5*(5*log(2)^3 + 5*log(2)^2 + 12*lo
g(2))*x - ((log(2)^3 + log(2)^2)*x^3 + 2*(log(2)^2 + log(2))*x^2 + 4*x)*e^x + ((log(2)^3 + log(2)^2)*x^3 + 2*x
^2*log(2))*log(x) + 50*log(2))/(x^2*log(2)^3*log(x) + 9*x^2*log(2)^3 + 30*x*log(2)^3 + 25*log(2)^3 - (x^2*log(
2)^3 + 2*x*log(2)^2)*e^x)

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 198 vs. \(2 (37) = 74\).

Time = 0.65 (sec) , antiderivative size = 198, normalized size of antiderivative = 5.50 \[ \int \frac {\left (625+1500 x+1350 x^2+540 x^3+81 x^4\right ) \log (2)+\left (625+1500 x+1350 x^2+540 x^3+81 x^4\right ) \log ^2(2)+e^{2 x} \left (4 x^2+4 x^3+\left (4 x^3+x^4\right ) \log (2)+x^4 \log ^2(2)\right )+e^x \left (-10 x^2+22 x^3+18 x^4+\left (-100 x-170 x^2-96 x^3-18 x^4\right ) \log (2)+\left (-50 x^2-60 x^3-18 x^4\right ) \log ^2(2)\right )+\left (\left (50 x^2+60 x^3+18 x^4\right ) \log (2)+\left (50 x^2+60 x^3+18 x^4\right ) \log ^2(2)+e^x \left (-4 x^3+2 x^4+\left (-4 x^3-2 x^4\right ) \log (2)-2 x^4 \log ^2(2)\right )\right ) \log (x)+\left (x^4 \log (2)+x^4 \log ^2(2)\right ) \log ^2(x)}{\left (625+1500 x+1350 x^2+540 x^3+81 x^4\right ) \log ^2(2)+e^{2 x} \left (4 x^2+4 x^3 \log (2)+x^4 \log ^2(2)\right )+e^x \left (\left (-100 x-120 x^2-36 x^3\right ) \log (2)+\left (-50 x^2-60 x^3-18 x^4\right ) \log ^2(2)\right )+\left (\left (50 x^2+60 x^3+18 x^4\right ) \log ^2(2)+e^x \left (-4 x^3 \log (2)-2 x^4 \log ^2(2)\right )\right ) \log (x)+x^4 \log ^2(2) \log ^2(x)} \, dx=\frac {x^{3} e^{x} \log \left (2\right )^{2} - x^{3} \log \left (2\right )^{2} \log \left (x\right ) + x^{3} e^{x} \log \left (2\right ) - 9 \, x^{3} \log \left (2\right )^{2} + x^{2} e^{x} \log \left (2\right )^{2} - x^{3} \log \left (2\right ) \log \left (x\right ) - x^{2} \log \left (2\right )^{2} \log \left (x\right ) - 9 \, x^{3} \log \left (2\right ) + 3 \, x^{2} e^{x} \log \left (2\right ) - 39 \, x^{2} \log \left (2\right )^{2} - x^{2} \log \left (2\right ) \log \left (x\right ) - 39 \, x^{2} \log \left (2\right ) + 2 \, x e^{x} \log \left (2\right ) - 55 \, x \log \left (2\right )^{2} + 2 \, x e^{x} - 55 \, x \log \left (2\right ) - 25 \, \log \left (2\right )^{2} - 25 \, \log \left (2\right )}{x^{2} e^{x} \log \left (2\right )^{2} - x^{2} \log \left (2\right )^{2} \log \left (x\right ) - 9 \, x^{2} \log \left (2\right )^{2} + 2 \, x e^{x} \log \left (2\right ) - 30 \, x \log \left (2\right )^{2} - 25 \, \log \left (2\right )^{2}} \]

[In]

integrate(((x^4*log(2)^2+x^4*log(2))*log(x)^2+((-2*x^4*log(2)^2+(-2*x^4-4*x^3)*log(2)+2*x^4-4*x^3)*exp(x)+(18*
x^4+60*x^3+50*x^2)*log(2)^2+(18*x^4+60*x^3+50*x^2)*log(2))*log(x)+(x^4*log(2)^2+(x^4+4*x^3)*log(2)+4*x^3+4*x^2
)*exp(x)^2+((-18*x^4-60*x^3-50*x^2)*log(2)^2+(-18*x^4-96*x^3-170*x^2-100*x)*log(2)+18*x^4+22*x^3-10*x^2)*exp(x
)+(81*x^4+540*x^3+1350*x^2+1500*x+625)*log(2)^2+(81*x^4+540*x^3+1350*x^2+1500*x+625)*log(2))/(x^4*log(2)^2*log
(x)^2+((-2*x^4*log(2)^2-4*x^3*log(2))*exp(x)+(18*x^4+60*x^3+50*x^2)*log(2)^2)*log(x)+(x^4*log(2)^2+4*x^3*log(2
)+4*x^2)*exp(x)^2+((-18*x^4-60*x^3-50*x^2)*log(2)^2+(-36*x^3-120*x^2-100*x)*log(2))*exp(x)+(81*x^4+540*x^3+135
0*x^2+1500*x+625)*log(2)^2),x, algorithm="giac")

[Out]

(x^3*e^x*log(2)^2 - x^3*log(2)^2*log(x) + x^3*e^x*log(2) - 9*x^3*log(2)^2 + x^2*e^x*log(2)^2 - x^3*log(2)*log(
x) - x^2*log(2)^2*log(x) - 9*x^3*log(2) + 3*x^2*e^x*log(2) - 39*x^2*log(2)^2 - x^2*log(2)*log(x) - 39*x^2*log(
2) + 2*x*e^x*log(2) - 55*x*log(2)^2 + 2*x*e^x - 55*x*log(2) - 25*log(2)^2 - 25*log(2))/(x^2*e^x*log(2)^2 - x^2
*log(2)^2*log(x) - 9*x^2*log(2)^2 + 2*x*e^x*log(2) - 30*x*log(2)^2 - 25*log(2)^2)

Mupad [F(-1)]

Timed out. \[ \int \frac {\left (625+1500 x+1350 x^2+540 x^3+81 x^4\right ) \log (2)+\left (625+1500 x+1350 x^2+540 x^3+81 x^4\right ) \log ^2(2)+e^{2 x} \left (4 x^2+4 x^3+\left (4 x^3+x^4\right ) \log (2)+x^4 \log ^2(2)\right )+e^x \left (-10 x^2+22 x^3+18 x^4+\left (-100 x-170 x^2-96 x^3-18 x^4\right ) \log (2)+\left (-50 x^2-60 x^3-18 x^4\right ) \log ^2(2)\right )+\left (\left (50 x^2+60 x^3+18 x^4\right ) \log (2)+\left (50 x^2+60 x^3+18 x^4\right ) \log ^2(2)+e^x \left (-4 x^3+2 x^4+\left (-4 x^3-2 x^4\right ) \log (2)-2 x^4 \log ^2(2)\right )\right ) \log (x)+\left (x^4 \log (2)+x^4 \log ^2(2)\right ) \log ^2(x)}{\left (625+1500 x+1350 x^2+540 x^3+81 x^4\right ) \log ^2(2)+e^{2 x} \left (4 x^2+4 x^3 \log (2)+x^4 \log ^2(2)\right )+e^x \left (\left (-100 x-120 x^2-36 x^3\right ) \log (2)+\left (-50 x^2-60 x^3-18 x^4\right ) \log ^2(2)\right )+\left (\left (50 x^2+60 x^3+18 x^4\right ) \log ^2(2)+e^x \left (-4 x^3 \log (2)-2 x^4 \log ^2(2)\right )\right ) \log (x)+x^4 \log ^2(2) \log ^2(x)} \, dx=\int \frac {\left (x^4\,{\ln \left (2\right )}^2+x^4\,\ln \left (2\right )\right )\,{\ln \left (x\right )}^2+\left ({\ln \left (2\right )}^2\,\left (18\,x^4+60\,x^3+50\,x^2\right )-{\mathrm {e}}^x\,\left (2\,x^4\,{\ln \left (2\right )}^2+\ln \left (2\right )\,\left (2\,x^4+4\,x^3\right )+4\,x^3-2\,x^4\right )+\ln \left (2\right )\,\left (18\,x^4+60\,x^3+50\,x^2\right )\right )\,\ln \left (x\right )+{\ln \left (2\right )}^2\,\left (81\,x^4+540\,x^3+1350\,x^2+1500\,x+625\right )-{\mathrm {e}}^x\,\left ({\ln \left (2\right )}^2\,\left (18\,x^4+60\,x^3+50\,x^2\right )+\ln \left (2\right )\,\left (18\,x^4+96\,x^3+170\,x^2+100\,x\right )+10\,x^2-22\,x^3-18\,x^4\right )+{\mathrm {e}}^{2\,x}\,\left (x^4\,{\ln \left (2\right )}^2+\ln \left (2\right )\,\left (x^4+4\,x^3\right )+4\,x^2+4\,x^3\right )+\ln \left (2\right )\,\left (81\,x^4+540\,x^3+1350\,x^2+1500\,x+625\right )}{{\ln \left (2\right )}^2\,\left (81\,x^4+540\,x^3+1350\,x^2+1500\,x+625\right )+\ln \left (x\right )\,\left ({\ln \left (2\right )}^2\,\left (18\,x^4+60\,x^3+50\,x^2\right )-{\mathrm {e}}^x\,\left (2\,{\ln \left (2\right )}^2\,x^4+4\,\ln \left (2\right )\,x^3\right )\right )-{\mathrm {e}}^x\,\left ({\ln \left (2\right )}^2\,\left (18\,x^4+60\,x^3+50\,x^2\right )+\ln \left (2\right )\,\left (36\,x^3+120\,x^2+100\,x\right )\right )+{\mathrm {e}}^{2\,x}\,\left ({\ln \left (2\right )}^2\,x^4+4\,\ln \left (2\right )\,x^3+4\,x^2\right )+x^4\,{\ln \left (2\right )}^2\,{\ln \left (x\right )}^2} \,d x \]

[In]

int((log(2)^2*(1500*x + 1350*x^2 + 540*x^3 + 81*x^4 + 625) - exp(x)*(log(2)^2*(50*x^2 + 60*x^3 + 18*x^4) + log
(2)*(100*x + 170*x^2 + 96*x^3 + 18*x^4) + 10*x^2 - 22*x^3 - 18*x^4) + log(x)*(log(2)^2*(50*x^2 + 60*x^3 + 18*x
^4) - exp(x)*(2*x^4*log(2)^2 + log(2)*(4*x^3 + 2*x^4) + 4*x^3 - 2*x^4) + log(2)*(50*x^2 + 60*x^3 + 18*x^4)) +
exp(2*x)*(x^4*log(2)^2 + log(2)*(4*x^3 + x^4) + 4*x^2 + 4*x^3) + log(2)*(1500*x + 1350*x^2 + 540*x^3 + 81*x^4
+ 625) + log(x)^2*(x^4*log(2)^2 + x^4*log(2)))/(log(2)^2*(1500*x + 1350*x^2 + 540*x^3 + 81*x^4 + 625) + log(x)
*(log(2)^2*(50*x^2 + 60*x^3 + 18*x^4) - exp(x)*(2*x^4*log(2)^2 + 4*x^3*log(2))) - exp(x)*(log(2)^2*(50*x^2 + 6
0*x^3 + 18*x^4) + log(2)*(100*x + 120*x^2 + 36*x^3)) + exp(2*x)*(x^4*log(2)^2 + 4*x^3*log(2) + 4*x^2) + x^4*lo
g(2)^2*log(x)^2),x)

[Out]

int((log(2)^2*(1500*x + 1350*x^2 + 540*x^3 + 81*x^4 + 625) - exp(x)*(log(2)^2*(50*x^2 + 60*x^3 + 18*x^4) + log
(2)*(100*x + 170*x^2 + 96*x^3 + 18*x^4) + 10*x^2 - 22*x^3 - 18*x^4) + log(x)*(log(2)^2*(50*x^2 + 60*x^3 + 18*x
^4) - exp(x)*(2*x^4*log(2)^2 + log(2)*(4*x^3 + 2*x^4) + 4*x^3 - 2*x^4) + log(2)*(50*x^2 + 60*x^3 + 18*x^4)) +
exp(2*x)*(x^4*log(2)^2 + log(2)*(4*x^3 + x^4) + 4*x^2 + 4*x^3) + log(2)*(1500*x + 1350*x^2 + 540*x^3 + 81*x^4
+ 625) + log(x)^2*(x^4*log(2)^2 + x^4*log(2)))/(log(2)^2*(1500*x + 1350*x^2 + 540*x^3 + 81*x^4 + 625) + log(x)
*(log(2)^2*(50*x^2 + 60*x^3 + 18*x^4) - exp(x)*(2*x^4*log(2)^2 + 4*x^3*log(2))) - exp(x)*(log(2)^2*(50*x^2 + 6
0*x^3 + 18*x^4) + log(2)*(100*x + 120*x^2 + 36*x^3)) + exp(2*x)*(x^4*log(2)^2 + 4*x^3*log(2) + 4*x^2) + x^4*lo
g(2)^2*log(x)^2), x)