\(\int \frac {(16 x-16 x^2+(96 x-48 x^2+(-32 x+16 x^2) \log (x)) \log (-3+\log (x))) \log ^3(-\frac {x^2 \log (3)}{(-2+2 x) \log (-3+\log (x))})+(24 x-24 x^2+(-8 x+8 x^2) \log (x)) \log (-3+\log (x)) \log ^4(-\frac {x^2 \log (3)}{(-2+2 x) \log (-3+\log (x))})}{(3-3 x+(-1+x) \log (x)) \log (-3+\log (x))} \, dx\) [6591]

Optimal result

Integrand size = 134, antiderivative size = 31 \[ \int \frac {\left (16 x-16 x^2+\left (96 x-48 x^2+\left (-32 x+16 x^2\right ) \log (x)\right ) \log (-3+\log (x))\right ) \log ^3\left (-\frac {x^2 \log (3)}{(-2+2 x) \log (-3+\log (x))}\right )+\left (24 x-24 x^2+\left (-8 x+8 x^2\right ) \log (x)\right ) \log (-3+\log (x)) \log ^4\left (-\frac {x^2 \log (3)}{(-2+2 x) \log (-3+\log (x))}\right )}{(3-3 x+(-1+x) \log (x)) \log (-3+\log (x))} \, dx=4 x^2 \log ^4\left (\frac {x^2 \log (3)}{2 (1-x) \log (-3+\log (x))}\right ) \]

[Out]

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

Rubi [F]

\[ \int \frac {\left (16 x-16 x^2+\left (96 x-48 x^2+\left (-32 x+16 x^2\right ) \log (x)\right ) \log (-3+\log (x))\right ) \log ^3\left (-\frac {x^2 \log (3)}{(-2+2 x) \log (-3+\log (x))}\right )+\left (24 x-24 x^2+\left (-8 x+8 x^2\right ) \log (x)\right ) \log (-3+\log (x)) \log ^4\left (-\frac {x^2 \log (3)}{(-2+2 x) \log (-3+\log (x))}\right )}{(3-3 x+(-1+x) \log (x)) \log (-3+\log (x))} \, dx=\int \frac {\left (16 x-16 x^2+\left (96 x-48 x^2+\left (-32 x+16 x^2\right ) \log (x)\right ) \log (-3+\log (x))\right ) \log ^3\left (-\frac {x^2 \log (3)}{(-2+2 x) \log (-3+\log (x))}\right )+\left (24 x-24 x^2+\left (-8 x+8 x^2\right ) \log (x)\right ) \log (-3+\log (x)) \log ^4\left (-\frac {x^2 \log (3)}{(-2+2 x) \log (-3+\log (x))}\right )}{(3-3 x+(-1+x) \log (x)) \log (-3+\log (x))} \, dx \]

[In]

Int[((16*x - 16*x^2 + (96*x - 48*x^2 + (-32*x + 16*x^2)*Log[x])*Log[-3 + Log[x]])*Log[-((x^2*Log[3])/((-2 + 2*
x)*Log[-3 + Log[x]]))]^3 + (24*x - 24*x^2 + (-8*x + 8*x^2)*Log[x])*Log[-3 + Log[x]]*Log[-((x^2*Log[3])/((-2 +
2*x)*Log[-3 + Log[x]]))]^4)/((3 - 3*x + (-1 + x)*Log[x])*Log[-3 + Log[x]]),x]

[Out]

48*Defer[Int][Log[-1/2*(x^2*Log[3])/((-1 + x)*Log[-3 + Log[x]])]^3/(-3 + Log[x]), x] + 48*Defer[Int][Log[-1/2*
(x^2*Log[3])/((-1 + x)*Log[-3 + Log[x]])]^3/((-1 + x)*(-3 + Log[x])), x] - 48*Defer[Int][(x*Log[-1/2*(x^2*Log[
3])/((-1 + x)*Log[-3 + Log[x]])]^3)/(-3 + Log[x]), x] - 16*Defer[Int][(Log[x]*Log[-1/2*(x^2*Log[3])/((-1 + x)*
Log[-3 + Log[x]])]^3)/(-3 + Log[x]), x] - 16*Defer[Int][(Log[x]*Log[-1/2*(x^2*Log[3])/((-1 + x)*Log[-3 + Log[x
]])]^3)/((-1 + x)*(-3 + Log[x])), x] + 16*Defer[Int][(x*Log[x]*Log[-1/2*(x^2*Log[3])/((-1 + x)*Log[-3 + Log[x]
])]^3)/(-3 + Log[x]), x] - 16*Defer[Int][(x*Log[-1/2*(x^2*Log[3])/((-1 + x)*Log[-3 + Log[x]])]^3)/((-3 + Log[x
])*Log[-3 + Log[x]]), x] + 8*Defer[Int][x*Log[-1/2*(x^2*Log[3])/((-1 + x)*Log[-3 + Log[x]])]^4, x]

Rubi steps \begin{align*} \text {integral}& = \int \frac {\left (16 x-16 x^2+\left (96 x-48 x^2+\left (-32 x+16 x^2\right ) \log (x)\right ) \log (-3+\log (x))\right ) \log ^3\left (-\frac {x^2 \log (3)}{(-2+2 x) \log (-3+\log (x))}\right )+\left (24 x-24 x^2+\left (-8 x+8 x^2\right ) \log (x)\right ) \log (-3+\log (x)) \log ^4\left (-\frac {x^2 \log (3)}{(-2+2 x) \log (-3+\log (x))}\right )}{(1-x) (3-\log (x)) \log (-3+\log (x))} \, dx \\ & = \int \frac {8 x \log ^3\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right ) \left (2-2 x+2 (-2+x) (-3+\log (x)) \log (-3+\log (x))+(-1+x) (-3+\log (x)) \log (-3+\log (x)) \log \left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right )\right )}{(1-x) (3-\log (x)) \log (-3+\log (x))} \, dx \\ & = 8 \int \frac {x \log ^3\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right ) \left (2-2 x+2 (-2+x) (-3+\log (x)) \log (-3+\log (x))+(-1+x) (-3+\log (x)) \log (-3+\log (x)) \log \left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right )\right )}{(1-x) (3-\log (x)) \log (-3+\log (x))} \, dx \\ & = 8 \int \left (\frac {2 x (1-x+6 \log (-3+\log (x))-3 x \log (-3+\log (x))-2 \log (x) \log (-3+\log (x))+x \log (x) \log (-3+\log (x))) \log ^3\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right )}{(-1+x) (-3+\log (x)) \log (-3+\log (x))}+x \log ^4\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right )\right ) \, dx \\ & = 8 \int x \log ^4\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right ) \, dx+16 \int \frac {x (1-x+6 \log (-3+\log (x))-3 x \log (-3+\log (x))-2 \log (x) \log (-3+\log (x))+x \log (x) \log (-3+\log (x))) \log ^3\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right )}{(-1+x) (-3+\log (x)) \log (-3+\log (x))} \, dx \\ & = 8 \int x \log ^4\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right ) \, dx+16 \int \frac {x (1-x+(-2+x) (-3+\log (x)) \log (-3+\log (x))) \log ^3\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right )}{(1-x) (3-\log (x)) \log (-3+\log (x))} \, dx \\ & = 8 \int x \log ^4\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right ) \, dx+16 \int \left (\frac {(1-x+6 \log (-3+\log (x))-3 x \log (-3+\log (x))-2 \log (x) \log (-3+\log (x))+x \log (x) \log (-3+\log (x))) \log ^3\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right )}{(-3+\log (x)) \log (-3+\log (x))}+\frac {(1-x+6 \log (-3+\log (x))-3 x \log (-3+\log (x))-2 \log (x) \log (-3+\log (x))+x \log (x) \log (-3+\log (x))) \log ^3\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right )}{(-1+x) (-3+\log (x)) \log (-3+\log (x))}\right ) \, dx \\ & = 8 \int x \log ^4\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right ) \, dx+16 \int \frac {(1-x+6 \log (-3+\log (x))-3 x \log (-3+\log (x))-2 \log (x) \log (-3+\log (x))+x \log (x) \log (-3+\log (x))) \log ^3\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right )}{(-3+\log (x)) \log (-3+\log (x))} \, dx+16 \int \frac {(1-x+6 \log (-3+\log (x))-3 x \log (-3+\log (x))-2 \log (x) \log (-3+\log (x))+x \log (x) \log (-3+\log (x))) \log ^3\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right )}{(-1+x) (-3+\log (x)) \log (-3+\log (x))} \, dx \\ & = 8 \int x \log ^4\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right ) \, dx+16 \int \frac {(-1+x-(-2+x) (-3+\log (x)) \log (-3+\log (x))) \log ^3\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right )}{(3-\log (x)) \log (-3+\log (x))} \, dx+16 \int \frac {(1-x+(-2+x) (-3+\log (x)) \log (-3+\log (x))) \log ^3\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right )}{(1-x) (3-\log (x)) \log (-3+\log (x))} \, dx \\ & = 8 \int x \log ^4\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right ) \, dx+16 \int \left (\frac {6 \log ^3\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right )}{-3+\log (x)}-\frac {3 x \log ^3\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right )}{-3+\log (x)}-\frac {2 \log (x) \log ^3\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right )}{-3+\log (x)}+\frac {x \log (x) \log ^3\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right )}{-3+\log (x)}+\frac {\log ^3\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right )}{(-3+\log (x)) \log (-3+\log (x))}-\frac {x \log ^3\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right )}{(-3+\log (x)) \log (-3+\log (x))}\right ) \, dx+16 \int \left (\frac {6 \log ^3\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right )}{(-1+x) (-3+\log (x))}-\frac {3 x \log ^3\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right )}{(-1+x) (-3+\log (x))}-\frac {2 \log (x) \log ^3\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right )}{(-1+x) (-3+\log (x))}+\frac {x \log (x) \log ^3\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right )}{(-1+x) (-3+\log (x))}+\frac {\log ^3\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right )}{(-1+x) (-3+\log (x)) \log (-3+\log (x))}-\frac {x \log ^3\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right )}{(-1+x) (-3+\log (x)) \log (-3+\log (x))}\right ) \, dx \\ & = 8 \int x \log ^4\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right ) \, dx+16 \int \frac {x \log (x) \log ^3\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right )}{-3+\log (x)} \, dx+16 \int \frac {x \log (x) \log ^3\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right )}{(-1+x) (-3+\log (x))} \, dx+16 \int \frac {\log ^3\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right )}{(-3+\log (x)) \log (-3+\log (x))} \, dx+16 \int \frac {\log ^3\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right )}{(-1+x) (-3+\log (x)) \log (-3+\log (x))} \, dx-16 \int \frac {x \log ^3\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right )}{(-3+\log (x)) \log (-3+\log (x))} \, dx-16 \int \frac {x \log ^3\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right )}{(-1+x) (-3+\log (x)) \log (-3+\log (x))} \, dx-32 \int \frac {\log (x) \log ^3\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right )}{-3+\log (x)} \, dx-32 \int \frac {\log (x) \log ^3\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right )}{(-1+x) (-3+\log (x))} \, dx-48 \int \frac {x \log ^3\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right )}{-3+\log (x)} \, dx-48 \int \frac {x \log ^3\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right )}{(-1+x) (-3+\log (x))} \, dx+96 \int \frac {\log ^3\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right )}{-3+\log (x)} \, dx+96 \int \frac {\log ^3\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right )}{(-1+x) (-3+\log (x))} \, dx \\ & = 8 \int x \log ^4\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right ) \, dx+16 \int \frac {x \log (x) \log ^3\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right )}{-3+\log (x)} \, dx+16 \int \frac {\log ^3\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right )}{(-3+\log (x)) \log (-3+\log (x))} \, dx+16 \int \frac {\log ^3\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right )}{(-1+x) (-3+\log (x)) \log (-3+\log (x))} \, dx-16 \int \frac {x \log ^3\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right )}{(-3+\log (x)) \log (-3+\log (x))} \, dx+16 \int \left (\frac {\log (x) \log ^3\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right )}{-3+\log (x)}+\frac {\log (x) \log ^3\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right )}{(-1+x) (-3+\log (x))}\right ) \, dx-16 \int \left (\frac {\log ^3\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right )}{(-3+\log (x)) \log (-3+\log (x))}+\frac {\log ^3\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right )}{(-1+x) (-3+\log (x)) \log (-3+\log (x))}\right ) \, dx-32 \int \frac {\log (x) \log ^3\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right )}{-3+\log (x)} \, dx-32 \int \frac {\log (x) \log ^3\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right )}{(-1+x) (-3+\log (x))} \, dx-48 \int \frac {x \log ^3\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right )}{-3+\log (x)} \, dx-48 \int \left (\frac {\log ^3\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right )}{-3+\log (x)}+\frac {\log ^3\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right )}{(-1+x) (-3+\log (x))}\right ) \, dx+96 \int \frac {\log ^3\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right )}{-3+\log (x)} \, dx+96 \int \frac {\log ^3\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right )}{(-1+x) (-3+\log (x))} \, dx \\ & = 8 \int x \log ^4\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right ) \, dx+16 \int \frac {\log (x) \log ^3\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right )}{-3+\log (x)} \, dx+16 \int \frac {\log (x) \log ^3\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right )}{(-1+x) (-3+\log (x))} \, dx+16 \int \frac {x \log (x) \log ^3\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right )}{-3+\log (x)} \, dx-16 \int \frac {x \log ^3\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right )}{(-3+\log (x)) \log (-3+\log (x))} \, dx-32 \int \frac {\log (x) \log ^3\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right )}{-3+\log (x)} \, dx-32 \int \frac {\log (x) \log ^3\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right )}{(-1+x) (-3+\log (x))} \, dx-48 \int \frac {\log ^3\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right )}{-3+\log (x)} \, dx-48 \int \frac {\log ^3\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right )}{(-1+x) (-3+\log (x))} \, dx-48 \int \frac {x \log ^3\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right )}{-3+\log (x)} \, dx+96 \int \frac {\log ^3\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right )}{-3+\log (x)} \, dx+96 \int \frac {\log ^3\left (-\frac {x^2 \log (3)}{2 (-1+x) \log (-3+\log (x))}\right )}{(-1+x) (-3+\log (x))} \, dx \\ \end{align*}

Mathematica [F]

\[ \int \frac {\left (16 x-16 x^2+\left (96 x-48 x^2+\left (-32 x+16 x^2\right ) \log (x)\right ) \log (-3+\log (x))\right ) \log ^3\left (-\frac {x^2 \log (3)}{(-2+2 x) \log (-3+\log (x))}\right )+\left (24 x-24 x^2+\left (-8 x+8 x^2\right ) \log (x)\right ) \log (-3+\log (x)) \log ^4\left (-\frac {x^2 \log (3)}{(-2+2 x) \log (-3+\log (x))}\right )}{(3-3 x+(-1+x) \log (x)) \log (-3+\log (x))} \, dx=\int \frac {\left (16 x-16 x^2+\left (96 x-48 x^2+\left (-32 x+16 x^2\right ) \log (x)\right ) \log (-3+\log (x))\right ) \log ^3\left (-\frac {x^2 \log (3)}{(-2+2 x) \log (-3+\log (x))}\right )+\left (24 x-24 x^2+\left (-8 x+8 x^2\right ) \log (x)\right ) \log (-3+\log (x)) \log ^4\left (-\frac {x^2 \log (3)}{(-2+2 x) \log (-3+\log (x))}\right )}{(3-3 x+(-1+x) \log (x)) \log (-3+\log (x))} \, dx \]

[In]

Integrate[((16*x - 16*x^2 + (96*x - 48*x^2 + (-32*x + 16*x^2)*Log[x])*Log[-3 + Log[x]])*Log[-((x^2*Log[3])/((-
2 + 2*x)*Log[-3 + Log[x]]))]^3 + (24*x - 24*x^2 + (-8*x + 8*x^2)*Log[x])*Log[-3 + Log[x]]*Log[-((x^2*Log[3])/(
(-2 + 2*x)*Log[-3 + Log[x]]))]^4)/((3 - 3*x + (-1 + x)*Log[x])*Log[-3 + Log[x]]),x]

[Out]

Integrate[((16*x - 16*x^2 + (96*x - 48*x^2 + (-32*x + 16*x^2)*Log[x])*Log[-3 + Log[x]])*Log[-((x^2*Log[3])/((-
2 + 2*x)*Log[-3 + Log[x]]))]^3 + (24*x - 24*x^2 + (-8*x + 8*x^2)*Log[x])*Log[-3 + Log[x]]*Log[-((x^2*Log[3])/(
(-2 + 2*x)*Log[-3 + Log[x]]))]^4)/((3 - 3*x + (-1 + x)*Log[x])*Log[-3 + Log[x]]), x]

Maple [A] (verified)

Time = 54.86 (sec) , antiderivative size = 30, normalized size of antiderivative = 0.97

method	result	size
parallelrisch	\(4 \ln \left (-\frac {x^{2} \ln \left (3\right )}{\left (-2+2 x \right ) \ln \left (\ln \left (x \right )-3\right )}\right )^{4} x^{2}\)	\(30\)
risch	\(\text {Expression too large to display}\)	\(278332\)

[In]

int((((8*x^2-8*x)*ln(x)-24*x^2+24*x)*ln(ln(x)-3)*ln(-x^2*ln(3)/(-2+2*x)/ln(ln(x)-3))^4+(((16*x^2-32*x)*ln(x)-4
8*x^2+96*x)*ln(ln(x)-3)-16*x^2+16*x)*ln(-x^2*ln(3)/(-2+2*x)/ln(ln(x)-3))^3)/((-1+x)*ln(x)-3*x+3)/ln(ln(x)-3),x
,method=_RETURNVERBOSE)

[Out]

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

Fricas [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.87 \[ \int \frac {\left (16 x-16 x^2+\left (96 x-48 x^2+\left (-32 x+16 x^2\right ) \log (x)\right ) \log (-3+\log (x))\right ) \log ^3\left (-\frac {x^2 \log (3)}{(-2+2 x) \log (-3+\log (x))}\right )+\left (24 x-24 x^2+\left (-8 x+8 x^2\right ) \log (x)\right ) \log (-3+\log (x)) \log ^4\left (-\frac {x^2 \log (3)}{(-2+2 x) \log (-3+\log (x))}\right )}{(3-3 x+(-1+x) \log (x)) \log (-3+\log (x))} \, dx=4 \, x^{2} \log \left (-\frac {x^{2} \log \left (3\right )}{2 \, {\left (x - 1\right )} \log \left (\log \left (x\right ) - 3\right )}\right )^{4} \]

[In]

integrate((((8*x^2-8*x)*log(x)-24*x^2+24*x)*log(log(x)-3)*log(-x^2*log(3)/(-2+2*x)/log(log(x)-3))^4+(((16*x^2-
32*x)*log(x)-48*x^2+96*x)*log(log(x)-3)-16*x^2+16*x)*log(-x^2*log(3)/(-2+2*x)/log(log(x)-3))^3)/((-1+x)*log(x)
-3*x+3)/log(log(x)-3),x, algorithm="fricas")

[Out]

4*x^2*log(-1/2*x^2*log(3)/((x - 1)*log(log(x) - 3)))^4

Sympy [F(-2)]

Exception generated. \[ \int \frac {\left (16 x-16 x^2+\left (96 x-48 x^2+\left (-32 x+16 x^2\right ) \log (x)\right ) \log (-3+\log (x))\right ) \log ^3\left (-\frac {x^2 \log (3)}{(-2+2 x) \log (-3+\log (x))}\right )+\left (24 x-24 x^2+\left (-8 x+8 x^2\right ) \log (x)\right ) \log (-3+\log (x)) \log ^4\left (-\frac {x^2 \log (3)}{(-2+2 x) \log (-3+\log (x))}\right )}{(3-3 x+(-1+x) \log (x)) \log (-3+\log (x))} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((((8*x**2-8*x)*ln(x)-24*x**2+24*x)*ln(ln(x)-3)*ln(-x**2*ln(3)/(-2+2*x)/ln(ln(x)-3))**4+(((16*x**2-32
*x)*ln(x)-48*x**2+96*x)*ln(ln(x)-3)-16*x**2+16*x)*ln(-x**2*ln(3)/(-2+2*x)/ln(ln(x)-3))**3)/((-1+x)*ln(x)-3*x+3
)/ln(ln(x)-3),x)

[Out]

Exception raised: TypeError >> '>' not supported between instances of 'Poly' and 'int'

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 668 vs. \(2 (27) = 54\).

Time = 0.38 (sec) , antiderivative size = 668, normalized size of antiderivative = 21.55 \[ \int \frac {\left (16 x-16 x^2+\left (96 x-48 x^2+\left (-32 x+16 x^2\right ) \log (x)\right ) \log (-3+\log (x))\right ) \log ^3\left (-\frac {x^2 \log (3)}{(-2+2 x) \log (-3+\log (x))}\right )+\left (24 x-24 x^2+\left (-8 x+8 x^2\right ) \log (x)\right ) \log (-3+\log (x)) \log ^4\left (-\frac {x^2 \log (3)}{(-2+2 x) \log (-3+\log (x))}\right )}{(3-3 x+(-1+x) \log (x)) \log (-3+\log (x))} \, dx=\text {Too large to display} \]

[In]

integrate((((8*x^2-8*x)*log(x)-24*x^2+24*x)*log(log(x)-3)*log(-x^2*log(3)/(-2+2*x)/log(log(x)-3))^4+(((16*x^2-
32*x)*log(x)-48*x^2+96*x)*log(log(x)-3)-16*x^2+16*x)*log(-x^2*log(3)/(-2+2*x)/log(log(x)-3))^3)/((-1+x)*log(x)
-3*x+3)/log(log(x)-3),x, algorithm="maxima")

[Out]

-128*x^2*(log(2) - log(log(3)))*log(x)^3 + 64*x^2*log(x)^4 + 4*x^2*log(-x + 1)^4 + 4*x^2*log(log(log(x) - 3))^
4 + 96*(log(2)^2 - 2*log(2)*log(log(3)) + log(log(3))^2)*x^2*log(x)^2 - 32*(log(2)^3 - 3*log(2)^2*log(log(3))
+ 3*log(2)*log(log(3))^2 - log(log(3))^3)*x^2*log(x) + 16*(x^2*(log(2) - log(log(3))) - 2*x^2*log(x))*log(-x +
1)^3 + 16*(x^2*(log(2) - log(log(3))) - 2*x^2*log(x) + x^2*log(-x + 1))*log(log(log(x) - 3))^3 + 4*(log(2)^4
- 4*log(2)^3*log(log(3)) + 6*log(2)^2*log(log(3))^2 - 4*log(2)*log(log(3))^3 + log(log(3))^4)*x^2 - 24*(4*x^2*
(log(2) - log(log(3)))*log(x) - 4*x^2*log(x)^2 - (log(2)^2 - 2*log(2)*log(log(3)) + log(log(3))^2)*x^2)*log(-x
+ 1)^2 - 24*(4*x^2*(log(2) - log(log(3)))*log(x) - 4*x^2*log(x)^2 - x^2*log(-x + 1)^2 - (log(2)^2 - 2*log(2)*
log(log(3)) + log(log(3))^2)*x^2 - 2*(x^2*(log(2) - log(log(3))) - 2*x^2*log(x))*log(-x + 1))*log(log(log(x) -
3))^2 + 16*(12*x^2*(log(2) - log(log(3)))*log(x)^2 - 8*x^2*log(x)^3 - 6*(log(2)^2 - 2*log(2)*log(log(3)) + lo
g(log(3))^2)*x^2*log(x) + (log(2)^3 - 3*log(2)^2*log(log(3)) + 3*log(2)*log(log(3))^2 - log(log(3))^3)*x^2)*lo
g(-x + 1) + 16*(12*x^2*(log(2) - log(log(3)))*log(x)^2 - 8*x^2*log(x)^3 + x^2*log(-x + 1)^3 - 6*(log(2)^2 - 2*
log(2)*log(log(3)) + log(log(3))^2)*x^2*log(x) + (log(2)^3 - 3*log(2)^2*log(log(3)) + 3*log(2)*log(log(3))^2 -
log(log(3))^3)*x^2 + 3*(x^2*(log(2) - log(log(3))) - 2*x^2*log(x))*log(-x + 1)^2 - 3*(4*x^2*(log(2) - log(log
(3)))*log(x) - 4*x^2*log(x)^2 - (log(2)^2 - 2*log(2)*log(log(3)) + log(log(3))^2)*x^2)*log(-x + 1))*log(log(lo
g(x) - 3))

Giac [F(-1)]

Timed out. \[ \int \frac {\left (16 x-16 x^2+\left (96 x-48 x^2+\left (-32 x+16 x^2\right ) \log (x)\right ) \log (-3+\log (x))\right ) \log ^3\left (-\frac {x^2 \log (3)}{(-2+2 x) \log (-3+\log (x))}\right )+\left (24 x-24 x^2+\left (-8 x+8 x^2\right ) \log (x)\right ) \log (-3+\log (x)) \log ^4\left (-\frac {x^2 \log (3)}{(-2+2 x) \log (-3+\log (x))}\right )}{(3-3 x+(-1+x) \log (x)) \log (-3+\log (x))} \, dx=\text {Timed out} \]

[In]

integrate((((8*x^2-8*x)*log(x)-24*x^2+24*x)*log(log(x)-3)*log(-x^2*log(3)/(-2+2*x)/log(log(x)-3))^4+(((16*x^2-
32*x)*log(x)-48*x^2+96*x)*log(log(x)-3)-16*x^2+16*x)*log(-x^2*log(3)/(-2+2*x)/log(log(x)-3))^3)/((-1+x)*log(x)
-3*x+3)/log(log(x)-3),x, algorithm="giac")

[Out]

Timed out

Mupad [B] (verification not implemented)

Time = 12.55 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.87 \[ \int \frac {\left (16 x-16 x^2+\left (96 x-48 x^2+\left (-32 x+16 x^2\right ) \log (x)\right ) \log (-3+\log (x))\right ) \log ^3\left (-\frac {x^2 \log (3)}{(-2+2 x) \log (-3+\log (x))}\right )+\left (24 x-24 x^2+\left (-8 x+8 x^2\right ) \log (x)\right ) \log (-3+\log (x)) \log ^4\left (-\frac {x^2 \log (3)}{(-2+2 x) \log (-3+\log (x))}\right )}{(3-3 x+(-1+x) \log (x)) \log (-3+\log (x))} \, dx=4\,x^2\,{\ln \left (-\frac {x^2\,\ln \left (3\right )}{2\,\ln \left (\ln \left (x\right )-3\right )\,\left (x-1\right )}\right )}^4 \]

[In]

int(-(log(-(x^2*log(3))/(log(log(x) - 3)*(2*x - 2)))^3*(log(log(x) - 3)*(log(x)*(32*x - 16*x^2) - 96*x + 48*x^
2) - 16*x + 16*x^2) + log(log(x) - 3)*log(-(x^2*log(3))/(log(log(x) - 3)*(2*x - 2)))^4*(log(x)*(8*x - 8*x^2) -
24*x + 24*x^2))/(log(log(x) - 3)*(log(x)*(x - 1) - 3*x + 3)),x)

[Out]

4*x^2*log(-(x^2*log(3))/(2*log(log(x) - 3)*(x - 1)))^4