\(\int \frac {e^{e^x} (-10+5 x-2 x^2-x^3+e^x (-10 x+9 x^2-4 x^3+x^4)+(-10+5 x+2 x^2-x^3+e^x (-10 x+9 x^2-4 x^3+x^4)) \log (4-4 x+x^2)+(-4 x+e^x (-4 x^2+2 x^3)+e^x (-4 x^2+2 x^3) \log (4-4 x+x^2)) \log (1+\log (4-4 x+x^2))+(-2+x+e^x (-2 x+x^2)+(-2+x+e^x (-2 x+x^2)) \log (4-4 x+x^2)) \log ^2(1+\log (4-4 x+x^2)))}{(5-2 x+x^2+2 x \log (1+\log (4-4 x+x^2))+\log ^2(1+\log (4-4 x+x^2))) (-10+9 x-4 x^2+x^3+(-10+9 x-4 x^2+x^3) \log (4-4 x+x^2)+(-4 x+2 x^2+(-4 x+2 x^2) \log (4-4 x+x^2)) \log (1+\log (4-4 x+x^2))+(-2+x+(-2+x) \log (4-4 x+x^2)) \log ^2(1+\log (4-4 x+x^2)))} \, dx\) [4308]

Optimal result

Integrand size = 346, antiderivative size = 29 \[ \int \frac {e^{e^x} \left (-10+5 x-2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )+\left (-10+5 x+2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+e^x \left (-4 x^2+2 x^3\right )+e^x \left (-4 x^2+2 x^3\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+e^x \left (-2 x+x^2\right )+\left (-2+x+e^x \left (-2 x+x^2\right )\right ) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )}{\left (5-2 x+x^2+2 x \log \left (1+\log \left (4-4 x+x^2\right )\right )+\log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right ) \left (-10+9 x-4 x^2+x^3+\left (-10+9 x-4 x^2+x^3\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+2 x^2+\left (-4 x+2 x^2\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+(-2+x) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )} \, dx=\frac {e^{e^x} x}{5-2 x+\left (x+\log \left (1+\log \left ((2-x)^2\right )\right )\right )^2} \]

[Out]

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

Rubi [F]

\[ \int \frac {e^{e^x} \left (-10+5 x-2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )+\left (-10+5 x+2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+e^x \left (-4 x^2+2 x^3\right )+e^x \left (-4 x^2+2 x^3\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+e^x \left (-2 x+x^2\right )+\left (-2+x+e^x \left (-2 x+x^2\right )\right ) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )}{\left (5-2 x+x^2+2 x \log \left (1+\log \left (4-4 x+x^2\right )\right )+\log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right ) \left (-10+9 x-4 x^2+x^3+\left (-10+9 x-4 x^2+x^3\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+2 x^2+\left (-4 x+2 x^2\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+(-2+x) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )} \, dx=\int \frac {e^{e^x} \left (-10+5 x-2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )+\left (-10+5 x+2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+e^x \left (-4 x^2+2 x^3\right )+e^x \left (-4 x^2+2 x^3\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+e^x \left (-2 x+x^2\right )+\left (-2+x+e^x \left (-2 x+x^2\right )\right ) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )}{\left (5-2 x+x^2+2 x \log \left (1+\log \left (4-4 x+x^2\right )\right )+\log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right ) \left (-10+9 x-4 x^2+x^3+\left (-10+9 x-4 x^2+x^3\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+2 x^2+\left (-4 x+2 x^2\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+(-2+x) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )} \, dx \]

[In]

Int[(E^E^x*(-10 + 5*x - 2*x^2 - x^3 + E^x*(-10*x + 9*x^2 - 4*x^3 + x^4) + (-10 + 5*x + 2*x^2 - x^3 + E^x*(-10*
x + 9*x^2 - 4*x^3 + x^4))*Log[4 - 4*x + x^2] + (-4*x + E^x*(-4*x^2 + 2*x^3) + E^x*(-4*x^2 + 2*x^3)*Log[4 - 4*x
+ x^2])*Log[1 + Log[4 - 4*x + x^2]] + (-2 + x + E^x*(-2*x + x^2) + (-2 + x + E^x*(-2*x + x^2))*Log[4 - 4*x +
x^2])*Log[1 + Log[4 - 4*x + x^2]]^2))/((5 - 2*x + x^2 + 2*x*Log[1 + Log[4 - 4*x + x^2]] + Log[1 + Log[4 - 4*x
+ x^2]]^2)*(-10 + 9*x - 4*x^2 + x^3 + (-10 + 9*x - 4*x^2 + x^3)*Log[4 - 4*x + x^2] + (-4*x + 2*x^2 + (-4*x + 2
*x^2)*Log[4 - 4*x + x^2])*Log[1 + Log[4 - 4*x + x^2]] + (-2 + x + (-2 + x)*Log[4 - 4*x + x^2])*Log[1 + Log[4 -
4*x + x^2]]^2)),x]

[Out]

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

Rubi steps \begin{align*} \text {integral}& = \int \frac {e^{e^x} \left (10-5 x+10 e^x x+2 x^2-9 e^x x^2+x^3+4 e^x x^3-e^x x^4-2 x \left (-2+e^x (-2+x) x\right ) \log \left (1+\log \left ((-2+x)^2\right )\right )-(-2+x) \left (1+e^x x\right ) \log ^2\left (1+\log \left ((-2+x)^2\right )\right )-(-2+x) \log \left ((-2+x)^2\right ) \left (5-x^2+e^x x \left (5-2 x+x^2\right )+2 e^x x^2 \log \left (1+\log \left ((-2+x)^2\right )\right )+\left (1+e^x x\right ) \log ^2\left (1+\log \left ((-2+x)^2\right )\right )\right )\right )}{(2-x) \left (1+\log \left ((-2+x)^2\right )\right ) \left (5-2 x+x^2+2 x \log \left (1+\log \left ((-2+x)^2\right )\right )+\log ^2\left (1+\log \left ((-2+x)^2\right )\right )\right )^2} \, dx \\ & = \int \left (-\frac {10 e^{e^x}}{(-2+x) \left (1+\log \left ((-2+x)^2\right )\right ) \left (5-2 x+x^2+2 x \log \left (1+\log \left ((-2+x)^2\right )\right )+\log ^2\left (1+\log \left ((-2+x)^2\right )\right )\right )^2}+\frac {5 e^{e^x} x}{(-2+x) \left (1+\log \left ((-2+x)^2\right )\right ) \left (5-2 x+x^2+2 x \log \left (1+\log \left ((-2+x)^2\right )\right )+\log ^2\left (1+\log \left ((-2+x)^2\right )\right )\right )^2}-\frac {2 e^{e^x} x^2}{(-2+x) \left (1+\log \left ((-2+x)^2\right )\right ) \left (5-2 x+x^2+2 x \log \left (1+\log \left ((-2+x)^2\right )\right )+\log ^2\left (1+\log \left ((-2+x)^2\right )\right )\right )^2}-\frac {e^{e^x} x^3}{(-2+x) \left (1+\log \left ((-2+x)^2\right )\right ) \left (5-2 x+x^2+2 x \log \left (1+\log \left ((-2+x)^2\right )\right )+\log ^2\left (1+\log \left ((-2+x)^2\right )\right )\right )^2}+\frac {5 e^{e^x} \log \left ((-2+x)^2\right )}{\left (1+\log \left ((-2+x)^2\right )\right ) \left (5-2 x+x^2+2 x \log \left (1+\log \left ((-2+x)^2\right )\right )+\log ^2\left (1+\log \left ((-2+x)^2\right )\right )\right )^2}-\frac {e^{e^x} x^2 \log \left ((-2+x)^2\right )}{\left (1+\log \left ((-2+x)^2\right )\right ) \left (5-2 x+x^2+2 x \log \left (1+\log \left ((-2+x)^2\right )\right )+\log ^2\left (1+\log \left ((-2+x)^2\right )\right )\right )^2}-\frac {4 e^{e^x} x \log \left (1+\log \left ((-2+x)^2\right )\right )}{(-2+x) \left (1+\log \left ((-2+x)^2\right )\right ) \left (5-2 x+x^2+2 x \log \left (1+\log \left ((-2+x)^2\right )\right )+\log ^2\left (1+\log \left ((-2+x)^2\right )\right )\right )^2}+\frac {e^{e^x} \log ^2\left (1+\log \left ((-2+x)^2\right )\right )}{\left (1+\log \left ((-2+x)^2\right )\right ) \left (5-2 x+x^2+2 x \log \left (1+\log \left ((-2+x)^2\right )\right )+\log ^2\left (1+\log \left ((-2+x)^2\right )\right )\right )^2}+\frac {e^{e^x} \log \left ((-2+x)^2\right ) \log ^2\left (1+\log \left ((-2+x)^2\right )\right )}{\left (1+\log \left ((-2+x)^2\right )\right ) \left (5-2 x+x^2+2 x \log \left (1+\log \left ((-2+x)^2\right )\right )+\log ^2\left (1+\log \left ((-2+x)^2\right )\right )\right )^2}+\frac {e^{e^x+x} x}{5-2 x+x^2+2 x \log \left (1+\log \left ((-2+x)^2\right )\right )+\log ^2\left (1+\log \left ((-2+x)^2\right )\right )}\right ) \, dx \\ & = -\left (2 \int \frac {e^{e^x} x^2}{(-2+x) \left (1+\log \left ((-2+x)^2\right )\right ) \left (5-2 x+x^2+2 x \log \left (1+\log \left ((-2+x)^2\right )\right )+\log ^2\left (1+\log \left ((-2+x)^2\right )\right )\right )^2} \, dx\right )-4 \int \frac {e^{e^x} x \log \left (1+\log \left ((-2+x)^2\right )\right )}{(-2+x) \left (1+\log \left ((-2+x)^2\right )\right ) \left (5-2 x+x^2+2 x \log \left (1+\log \left ((-2+x)^2\right )\right )+\log ^2\left (1+\log \left ((-2+x)^2\right )\right )\right )^2} \, dx+5 \int \frac {e^{e^x} x}{(-2+x) \left (1+\log \left ((-2+x)^2\right )\right ) \left (5-2 x+x^2+2 x \log \left (1+\log \left ((-2+x)^2\right )\right )+\log ^2\left (1+\log \left ((-2+x)^2\right )\right )\right )^2} \, dx+5 \int \frac {e^{e^x} \log \left ((-2+x)^2\right )}{\left (1+\log \left ((-2+x)^2\right )\right ) \left (5-2 x+x^2+2 x \log \left (1+\log \left ((-2+x)^2\right )\right )+\log ^2\left (1+\log \left ((-2+x)^2\right )\right )\right )^2} \, dx-10 \int \frac {e^{e^x}}{(-2+x) \left (1+\log \left ((-2+x)^2\right )\right ) \left (5-2 x+x^2+2 x \log \left (1+\log \left ((-2+x)^2\right )\right )+\log ^2\left (1+\log \left ((-2+x)^2\right )\right )\right )^2} \, dx-\int \frac {e^{e^x} x^3}{(-2+x) \left (1+\log \left ((-2+x)^2\right )\right ) \left (5-2 x+x^2+2 x \log \left (1+\log \left ((-2+x)^2\right )\right )+\log ^2\left (1+\log \left ((-2+x)^2\right )\right )\right )^2} \, dx-\int \frac {e^{e^x} x^2 \log \left ((-2+x)^2\right )}{\left (1+\log \left ((-2+x)^2\right )\right ) \left (5-2 x+x^2+2 x \log \left (1+\log \left ((-2+x)^2\right )\right )+\log ^2\left (1+\log \left ((-2+x)^2\right )\right )\right )^2} \, dx+\int \frac {e^{e^x} \log ^2\left (1+\log \left ((-2+x)^2\right )\right )}{\left (1+\log \left ((-2+x)^2\right )\right ) \left (5-2 x+x^2+2 x \log \left (1+\log \left ((-2+x)^2\right )\right )+\log ^2\left (1+\log \left ((-2+x)^2\right )\right )\right )^2} \, dx+\int \frac {e^{e^x} \log \left ((-2+x)^2\right ) \log ^2\left (1+\log \left ((-2+x)^2\right )\right )}{\left (1+\log \left ((-2+x)^2\right )\right ) \left (5-2 x+x^2+2 x \log \left (1+\log \left ((-2+x)^2\right )\right )+\log ^2\left (1+\log \left ((-2+x)^2\right )\right )\right )^2} \, dx+\int \frac {e^{e^x+x} x}{5-2 x+x^2+2 x \log \left (1+\log \left ((-2+x)^2\right )\right )+\log ^2\left (1+\log \left ((-2+x)^2\right )\right )} \, dx \\ & = \text {Too large to display} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.25 (sec) , antiderivative size = 40, normalized size of antiderivative = 1.38 \[ \int \frac {e^{e^x} \left (-10+5 x-2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )+\left (-10+5 x+2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+e^x \left (-4 x^2+2 x^3\right )+e^x \left (-4 x^2+2 x^3\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+e^x \left (-2 x+x^2\right )+\left (-2+x+e^x \left (-2 x+x^2\right )\right ) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )}{\left (5-2 x+x^2+2 x \log \left (1+\log \left (4-4 x+x^2\right )\right )+\log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right ) \left (-10+9 x-4 x^2+x^3+\left (-10+9 x-4 x^2+x^3\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+2 x^2+\left (-4 x+2 x^2\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+(-2+x) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )} \, dx=\frac {e^{e^x} x}{5-2 x+x^2+2 x \log \left (1+\log \left ((-2+x)^2\right )\right )+\log ^2\left (1+\log \left ((-2+x)^2\right )\right )} \]

[In]

Integrate[(E^E^x*(-10 + 5*x - 2*x^2 - x^3 + E^x*(-10*x + 9*x^2 - 4*x^3 + x^4) + (-10 + 5*x + 2*x^2 - x^3 + E^x
*(-10*x + 9*x^2 - 4*x^3 + x^4))*Log[4 - 4*x + x^2] + (-4*x + E^x*(-4*x^2 + 2*x^3) + E^x*(-4*x^2 + 2*x^3)*Log[4
- 4*x + x^2])*Log[1 + Log[4 - 4*x + x^2]] + (-2 + x + E^x*(-2*x + x^2) + (-2 + x + E^x*(-2*x + x^2))*Log[4 -
4*x + x^2])*Log[1 + Log[4 - 4*x + x^2]]^2))/((5 - 2*x + x^2 + 2*x*Log[1 + Log[4 - 4*x + x^2]] + Log[1 + Log[4
- 4*x + x^2]]^2)*(-10 + 9*x - 4*x^2 + x^3 + (-10 + 9*x - 4*x^2 + x^3)*Log[4 - 4*x + x^2] + (-4*x + 2*x^2 + (-4
*x + 2*x^2)*Log[4 - 4*x + x^2])*Log[1 + Log[4 - 4*x + x^2]] + (-2 + x + (-2 + x)*Log[4 - 4*x + x^2])*Log[1 + L
og[4 - 4*x + x^2]]^2)),x]

[Out]

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

Maple [F]

\[\int \frac {\left (\left (\left (\left (x^{2}-2 x \right ) {\mathrm e}^{x}+x -2\right ) \ln \left (x^{2}-4 x +4\right )+\left (x^{2}-2 x \right ) {\mathrm e}^{x}+x -2\right ) {\ln \left (\ln \left (x^{2}-4 x +4\right )+1\right )}^{2}+\left (\left (2 x^{3}-4 x^{2}\right ) {\mathrm e}^{x} \ln \left (x^{2}-4 x +4\right )+\left (2 x^{3}-4 x^{2}\right ) {\mathrm e}^{x}-4 x \right ) \ln \left (\ln \left (x^{2}-4 x +4\right )+1\right )+\left (\left (x^{4}-4 x^{3}+9 x^{2}-10 x \right ) {\mathrm e}^{x}-x^{3}+2 x^{2}+5 x -10\right ) \ln \left (x^{2}-4 x +4\right )+\left (x^{4}-4 x^{3}+9 x^{2}-10 x \right ) {\mathrm e}^{x}-x^{3}-2 x^{2}+5 x -10\right ) {\mathrm e}^{-\ln \left ({\ln \left (\ln \left (x^{2}-4 x +4\right )+1\right )}^{2}+2 x \ln \left (\ln \left (x^{2}-4 x +4\right )+1\right )+x^{2}-2 x +5\right )+{\mathrm e}^{x}}}{\left (\left (-2+x \right ) \ln \left (x^{2}-4 x +4\right )+x -2\right ) {\ln \left (\ln \left (x^{2}-4 x +4\right )+1\right )}^{2}+\left (\left (2 x^{2}-4 x \right ) \ln \left (x^{2}-4 x +4\right )+2 x^{2}-4 x \right ) \ln \left (\ln \left (x^{2}-4 x +4\right )+1\right )+\left (x^{3}-4 x^{2}+9 x -10\right ) \ln \left (x^{2}-4 x +4\right )+x^{3}-4 x^{2}+9 x -10}d x\]

[In]

int(((((x^2-2*x)*exp(x)+x-2)*ln(x^2-4*x+4)+(x^2-2*x)*exp(x)+x-2)*ln(ln(x^2-4*x+4)+1)^2+((2*x^3-4*x^2)*exp(x)*l
n(x^2-4*x+4)+(2*x^3-4*x^2)*exp(x)-4*x)*ln(ln(x^2-4*x+4)+1)+((x^4-4*x^3+9*x^2-10*x)*exp(x)-x^3+2*x^2+5*x-10)*ln
(x^2-4*x+4)+(x^4-4*x^3+9*x^2-10*x)*exp(x)-x^3-2*x^2+5*x-10)*exp(-ln(ln(ln(x^2-4*x+4)+1)^2+2*x*ln(ln(x^2-4*x+4)
+1)+x^2-2*x+5)+exp(x))/(((-2+x)*ln(x^2-4*x+4)+x-2)*ln(ln(x^2-4*x+4)+1)^2+((2*x^2-4*x)*ln(x^2-4*x+4)+2*x^2-4*x)
*ln(ln(x^2-4*x+4)+1)+(x^3-4*x^2+9*x-10)*ln(x^2-4*x+4)+x^3-4*x^2+9*x-10),x)

[Out]

int(((((x^2-2*x)*exp(x)+x-2)*ln(x^2-4*x+4)+(x^2-2*x)*exp(x)+x-2)*ln(ln(x^2-4*x+4)+1)^2+((2*x^3-4*x^2)*exp(x)*l
n(x^2-4*x+4)+(2*x^3-4*x^2)*exp(x)-4*x)*ln(ln(x^2-4*x+4)+1)+((x^4-4*x^3+9*x^2-10*x)*exp(x)-x^3+2*x^2+5*x-10)*ln
(x^2-4*x+4)+(x^4-4*x^3+9*x^2-10*x)*exp(x)-x^3-2*x^2+5*x-10)*exp(-ln(ln(ln(x^2-4*x+4)+1)^2+2*x*ln(ln(x^2-4*x+4)
+1)+x^2-2*x+5)+exp(x))/(((-2+x)*ln(x^2-4*x+4)+x-2)*ln(ln(x^2-4*x+4)+1)^2+((2*x^2-4*x)*ln(x^2-4*x+4)+2*x^2-4*x)
*ln(ln(x^2-4*x+4)+1)+(x^3-4*x^2+9*x-10)*ln(x^2-4*x+4)+x^3-4*x^2+9*x-10),x)

Fricas [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.59 \[ \int \frac {e^{e^x} \left (-10+5 x-2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )+\left (-10+5 x+2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+e^x \left (-4 x^2+2 x^3\right )+e^x \left (-4 x^2+2 x^3\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+e^x \left (-2 x+x^2\right )+\left (-2+x+e^x \left (-2 x+x^2\right )\right ) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )}{\left (5-2 x+x^2+2 x \log \left (1+\log \left (4-4 x+x^2\right )\right )+\log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right ) \left (-10+9 x-4 x^2+x^3+\left (-10+9 x-4 x^2+x^3\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+2 x^2+\left (-4 x+2 x^2\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+(-2+x) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )} \, dx=x e^{\left (e^{x} - \log \left (x^{2} + 2 \, x \log \left (\log \left (x^{2} - 4 \, x + 4\right ) + 1\right ) + \log \left (\log \left (x^{2} - 4 \, x + 4\right ) + 1\right )^{2} - 2 \, x + 5\right )\right )} \]

[In]

integrate(((((x^2-2*x)*exp(x)+x-2)*log(x^2-4*x+4)+(x^2-2*x)*exp(x)+x-2)*log(log(x^2-4*x+4)+1)^2+((2*x^3-4*x^2)
*exp(x)*log(x^2-4*x+4)+(2*x^3-4*x^2)*exp(x)-4*x)*log(log(x^2-4*x+4)+1)+((x^4-4*x^3+9*x^2-10*x)*exp(x)-x^3+2*x^
2+5*x-10)*log(x^2-4*x+4)+(x^4-4*x^3+9*x^2-10*x)*exp(x)-x^3-2*x^2+5*x-10)*exp(-log(log(log(x^2-4*x+4)+1)^2+2*x*
log(log(x^2-4*x+4)+1)+x^2-2*x+5)+exp(x))/(((-2+x)*log(x^2-4*x+4)+x-2)*log(log(x^2-4*x+4)+1)^2+((2*x^2-4*x)*log
(x^2-4*x+4)+2*x^2-4*x)*log(log(x^2-4*x+4)+1)+(x^3-4*x^2+9*x-10)*log(x^2-4*x+4)+x^3-4*x^2+9*x-10),x, algorithm=
"fricas")

[Out]

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

Sympy [A] (verification not implemented)

Time = 0.59 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.59 \[ \int \frac {e^{e^x} \left (-10+5 x-2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )+\left (-10+5 x+2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+e^x \left (-4 x^2+2 x^3\right )+e^x \left (-4 x^2+2 x^3\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+e^x \left (-2 x+x^2\right )+\left (-2+x+e^x \left (-2 x+x^2\right )\right ) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )}{\left (5-2 x+x^2+2 x \log \left (1+\log \left (4-4 x+x^2\right )\right )+\log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right ) \left (-10+9 x-4 x^2+x^3+\left (-10+9 x-4 x^2+x^3\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+2 x^2+\left (-4 x+2 x^2\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+(-2+x) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )} \, dx=\frac {x e^{e^{x}}}{x^{2} + 2 x \log {\left (\log {\left (x^{2} - 4 x + 4 \right )} + 1 \right )} - 2 x + \log {\left (\log {\left (x^{2} - 4 x + 4 \right )} + 1 \right )}^{2} + 5} \]

[In]

integrate(((((x**2-2*x)*exp(x)+x-2)*ln(x**2-4*x+4)+(x**2-2*x)*exp(x)+x-2)*ln(ln(x**2-4*x+4)+1)**2+((2*x**3-4*x
**2)*exp(x)*ln(x**2-4*x+4)+(2*x**3-4*x**2)*exp(x)-4*x)*ln(ln(x**2-4*x+4)+1)+((x**4-4*x**3+9*x**2-10*x)*exp(x)-
x**3+2*x**2+5*x-10)*ln(x**2-4*x+4)+(x**4-4*x**3+9*x**2-10*x)*exp(x)-x**3-2*x**2+5*x-10)*exp(-ln(ln(ln(x**2-4*x
+4)+1)**2+2*x*ln(ln(x**2-4*x+4)+1)+x**2-2*x+5)+exp(x))/(((-2+x)*ln(x**2-4*x+4)+x-2)*ln(ln(x**2-4*x+4)+1)**2+((
2*x**2-4*x)*ln(x**2-4*x+4)+2*x**2-4*x)*ln(ln(x**2-4*x+4)+1)+(x**3-4*x**2+9*x-10)*ln(x**2-4*x+4)+x**3-4*x**2+9*
x-10),x)

[Out]

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

Maxima [A] (verification not implemented)

none

Time = 0.38 (sec) , antiderivative size = 38, normalized size of antiderivative = 1.31 \[ \int \frac {e^{e^x} \left (-10+5 x-2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )+\left (-10+5 x+2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+e^x \left (-4 x^2+2 x^3\right )+e^x \left (-4 x^2+2 x^3\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+e^x \left (-2 x+x^2\right )+\left (-2+x+e^x \left (-2 x+x^2\right )\right ) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )}{\left (5-2 x+x^2+2 x \log \left (1+\log \left (4-4 x+x^2\right )\right )+\log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right ) \left (-10+9 x-4 x^2+x^3+\left (-10+9 x-4 x^2+x^3\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+2 x^2+\left (-4 x+2 x^2\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+(-2+x) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )} \, dx=\frac {x e^{\left (e^{x}\right )}}{x^{2} + 2 \, x \log \left (2 \, \log \left (x - 2\right ) + 1\right ) + \log \left (2 \, \log \left (x - 2\right ) + 1\right )^{2} - 2 \, x + 5} \]

[In]

integrate(((((x^2-2*x)*exp(x)+x-2)*log(x^2-4*x+4)+(x^2-2*x)*exp(x)+x-2)*log(log(x^2-4*x+4)+1)^2+((2*x^3-4*x^2)
*exp(x)*log(x^2-4*x+4)+(2*x^3-4*x^2)*exp(x)-4*x)*log(log(x^2-4*x+4)+1)+((x^4-4*x^3+9*x^2-10*x)*exp(x)-x^3+2*x^
2+5*x-10)*log(x^2-4*x+4)+(x^4-4*x^3+9*x^2-10*x)*exp(x)-x^3-2*x^2+5*x-10)*exp(-log(log(log(x^2-4*x+4)+1)^2+2*x*
log(log(x^2-4*x+4)+1)+x^2-2*x+5)+exp(x))/(((-2+x)*log(x^2-4*x+4)+x-2)*log(log(x^2-4*x+4)+1)^2+((2*x^2-4*x)*log
(x^2-4*x+4)+2*x^2-4*x)*log(log(x^2-4*x+4)+1)+(x^3-4*x^2+9*x-10)*log(x^2-4*x+4)+x^3-4*x^2+9*x-10),x, algorithm=
"maxima")

[Out]

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

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 106 vs. \(2 (27) = 54\).

Time = 3.02 (sec) , antiderivative size = 106, normalized size of antiderivative = 3.66 \[ \int \frac {e^{e^x} \left (-10+5 x-2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )+\left (-10+5 x+2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+e^x \left (-4 x^2+2 x^3\right )+e^x \left (-4 x^2+2 x^3\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+e^x \left (-2 x+x^2\right )+\left (-2+x+e^x \left (-2 x+x^2\right )\right ) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )}{\left (5-2 x+x^2+2 x \log \left (1+\log \left (4-4 x+x^2\right )\right )+\log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right ) \left (-10+9 x-4 x^2+x^3+\left (-10+9 x-4 x^2+x^3\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+2 x^2+\left (-4 x+2 x^2\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+(-2+x) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )} \, dx=\frac {2 \, x e^{\left (x + e^{x}\right )}}{x^{2} e^{x} + 2 \, x e^{x} \log \left (\log \left (x^{2} - 4 \, x + 4\right ) + 1\right ) + e^{x} \log \left (\log \left (x^{2} - 4 \, x + 4\right ) + 1\right )^{2} - 2 \, x e^{x} + 5 \, e^{x}} + \frac {2 \, x e^{\left (e^{x}\right )}}{x^{2} + 2 \, x \log \left (\log \left (x^{2} - 4 \, x + 4\right ) + 1\right ) + \log \left (\log \left (x^{2} - 4 \, x + 4\right ) + 1\right )^{2} - 2 \, x + 5} \]

[In]

integrate(((((x^2-2*x)*exp(x)+x-2)*log(x^2-4*x+4)+(x^2-2*x)*exp(x)+x-2)*log(log(x^2-4*x+4)+1)^2+((2*x^3-4*x^2)
*exp(x)*log(x^2-4*x+4)+(2*x^3-4*x^2)*exp(x)-4*x)*log(log(x^2-4*x+4)+1)+((x^4-4*x^3+9*x^2-10*x)*exp(x)-x^3+2*x^
2+5*x-10)*log(x^2-4*x+4)+(x^4-4*x^3+9*x^2-10*x)*exp(x)-x^3-2*x^2+5*x-10)*exp(-log(log(log(x^2-4*x+4)+1)^2+2*x*
log(log(x^2-4*x+4)+1)+x^2-2*x+5)+exp(x))/(((-2+x)*log(x^2-4*x+4)+x-2)*log(log(x^2-4*x+4)+1)^2+((2*x^2-4*x)*log
(x^2-4*x+4)+2*x^2-4*x)*log(log(x^2-4*x+4)+1)+(x^3-4*x^2+9*x-10)*log(x^2-4*x+4)+x^3-4*x^2+9*x-10),x, algorithm=
"giac")

[Out]

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

Mupad [B] (verification not implemented)

Time = 11.41 (sec) , antiderivative size = 44, normalized size of antiderivative = 1.52 \[ \int \frac {e^{e^x} \left (-10+5 x-2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )+\left (-10+5 x+2 x^2-x^3+e^x \left (-10 x+9 x^2-4 x^3+x^4\right )\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+e^x \left (-4 x^2+2 x^3\right )+e^x \left (-4 x^2+2 x^3\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+e^x \left (-2 x+x^2\right )+\left (-2+x+e^x \left (-2 x+x^2\right )\right ) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )}{\left (5-2 x+x^2+2 x \log \left (1+\log \left (4-4 x+x^2\right )\right )+\log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right ) \left (-10+9 x-4 x^2+x^3+\left (-10+9 x-4 x^2+x^3\right ) \log \left (4-4 x+x^2\right )+\left (-4 x+2 x^2+\left (-4 x+2 x^2\right ) \log \left (4-4 x+x^2\right )\right ) \log \left (1+\log \left (4-4 x+x^2\right )\right )+\left (-2+x+(-2+x) \log \left (4-4 x+x^2\right )\right ) \log ^2\left (1+\log \left (4-4 x+x^2\right )\right )\right )} \, dx=\frac {x\,{\mathrm {e}}^{{\mathrm {e}}^x}}{{\ln \left (\ln \left (x^2-4\,x+4\right )+1\right )}^2+x^2+x\,\left (2\,\ln \left (\ln \left (x^2-4\,x+4\right )+1\right )-2\right )+5} \]

[In]

int(-(exp(exp(x) - log(2*x*log(log(x^2 - 4*x + 4) + 1) - 2*x + log(log(x^2 - 4*x + 4) + 1)^2 + x^2 + 5))*(exp(
x)*(10*x - 9*x^2 + 4*x^3 - x^4) - 5*x + log(x^2 - 4*x + 4)*(exp(x)*(10*x - 9*x^2 + 4*x^3 - x^4) - 5*x - 2*x^2
+ x^3 + 10) + log(log(x^2 - 4*x + 4) + 1)*(4*x + exp(x)*(4*x^2 - 2*x^3) + exp(x)*log(x^2 - 4*x + 4)*(4*x^2 - 2
*x^3)) + log(log(x^2 - 4*x + 4) + 1)^2*(exp(x)*(2*x - x^2) - x + log(x^2 - 4*x + 4)*(exp(x)*(2*x - x^2) - x +
2) + 2) + 2*x^2 + x^3 + 10))/(9*x + log(x^2 - 4*x + 4)*(9*x - 4*x^2 + x^3 - 10) - log(log(x^2 - 4*x + 4) + 1)*
(4*x + log(x^2 - 4*x + 4)*(4*x - 2*x^2) - 2*x^2) + log(log(x^2 - 4*x + 4) + 1)^2*(x + log(x^2 - 4*x + 4)*(x -
2) - 2) - 4*x^2 + x^3 - 10),x)

[Out]

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