\(\int \frac {6 x^2+2 x^3+(48 x+4 x^2-4 x^3) \log (-4+x) \log (\log (-4+x))+(-2 x^2+(-40 x+2 x^2+2 x^3) \log (-4+x) \log (\log (-4+x))) \log (\frac {4}{x \log (\log (-4+x))})+(8 x-2 x^2) \log (-4+x) \log (\log (-4+x)) \log ^2(\frac {4}{x \log (\log (-4+x))})}{(-324-351 x-180 x^2-24 x^3+8 x^4+4 x^5) \log (-4+x) \log (\log (-4+x))+(432+324 x+84 x^2-16 x^3-8 x^4) \log (-4+x) \log (\log (-4+x)) \log (\frac {4}{x \log (\log (-4+x))})+(-216-90 x+4 x^2+8 x^3) \log (-4+x) \log (\log (-4+x)) \log ^2(\frac {4}{x \log (\log (-4+x))})+(48+4 x-4 x^2) \log (-4+x) \log (\log (-4+x)) \log ^3(\frac {4}{x \log (\log (-4+x))})+(-4+x) \log (-4+x) \log (\log (-4+x)) \log ^4(\frac {4}{x \log (\log (-4+x))})} \, dx\) [834]

Optimal result

Integrand size = 298, antiderivative size = 34 \[ \int \frac {6 x^2+2 x^3+\left (48 x+4 x^2-4 x^3\right ) \log (-4+x) \log (\log (-4+x))+\left (-2 x^2+\left (-40 x+2 x^2+2 x^3\right ) \log (-4+x) \log (\log (-4+x))\right ) \log \left (\frac {4}{x \log (\log (-4+x))}\right )+\left (8 x-2 x^2\right ) \log (-4+x) \log (\log (-4+x)) \log ^2\left (\frac {4}{x \log (\log (-4+x))}\right )}{\left (-324-351 x-180 x^2-24 x^3+8 x^4+4 x^5\right ) \log (-4+x) \log (\log (-4+x))+\left (432+324 x+84 x^2-16 x^3-8 x^4\right ) \log (-4+x) \log (\log (-4+x)) \log \left (\frac {4}{x \log (\log (-4+x))}\right )+\left (-216-90 x+4 x^2+8 x^3\right ) \log (-4+x) \log (\log (-4+x)) \log ^2\left (\frac {4}{x \log (\log (-4+x))}\right )+\left (48+4 x-4 x^2\right ) \log (-4+x) \log (\log (-4+x)) \log ^3\left (\frac {4}{x \log (\log (-4+x))}\right )+(-4+x) \log (-4+x) \log (\log (-4+x)) \log ^4\left (\frac {4}{x \log (\log (-4+x))}\right )} \, dx=\frac {x^2}{-x^2-\left (3+x-\log \left (\frac {4}{x \log (\log (-4+x))}\right )\right )^2} \]

[Out]

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

Rubi [F]

\[ \int \frac {6 x^2+2 x^3+\left (48 x+4 x^2-4 x^3\right ) \log (-4+x) \log (\log (-4+x))+\left (-2 x^2+\left (-40 x+2 x^2+2 x^3\right ) \log (-4+x) \log (\log (-4+x))\right ) \log \left (\frac {4}{x \log (\log (-4+x))}\right )+\left (8 x-2 x^2\right ) \log (-4+x) \log (\log (-4+x)) \log ^2\left (\frac {4}{x \log (\log (-4+x))}\right )}{\left (-324-351 x-180 x^2-24 x^3+8 x^4+4 x^5\right ) \log (-4+x) \log (\log (-4+x))+\left (432+324 x+84 x^2-16 x^3-8 x^4\right ) \log (-4+x) \log (\log (-4+x)) \log \left (\frac {4}{x \log (\log (-4+x))}\right )+\left (-216-90 x+4 x^2+8 x^3\right ) \log (-4+x) \log (\log (-4+x)) \log ^2\left (\frac {4}{x \log (\log (-4+x))}\right )+\left (48+4 x-4 x^2\right ) \log (-4+x) \log (\log (-4+x)) \log ^3\left (\frac {4}{x \log (\log (-4+x))}\right )+(-4+x) \log (-4+x) \log (\log (-4+x)) \log ^4\left (\frac {4}{x \log (\log (-4+x))}\right )} \, dx=\int \frac {6 x^2+2 x^3+\left (48 x+4 x^2-4 x^3\right ) \log (-4+x) \log (\log (-4+x))+\left (-2 x^2+\left (-40 x+2 x^2+2 x^3\right ) \log (-4+x) \log (\log (-4+x))\right ) \log \left (\frac {4}{x \log (\log (-4+x))}\right )+\left (8 x-2 x^2\right ) \log (-4+x) \log (\log (-4+x)) \log ^2\left (\frac {4}{x \log (\log (-4+x))}\right )}{\left (-324-351 x-180 x^2-24 x^3+8 x^4+4 x^5\right ) \log (-4+x) \log (\log (-4+x))+\left (432+324 x+84 x^2-16 x^3-8 x^4\right ) \log (-4+x) \log (\log (-4+x)) \log \left (\frac {4}{x \log (\log (-4+x))}\right )+\left (-216-90 x+4 x^2+8 x^3\right ) \log (-4+x) \log (\log (-4+x)) \log ^2\left (\frac {4}{x \log (\log (-4+x))}\right )+\left (48+4 x-4 x^2\right ) \log (-4+x) \log (\log (-4+x)) \log ^3\left (\frac {4}{x \log (\log (-4+x))}\right )+(-4+x) \log (-4+x) \log (\log (-4+x)) \log ^4\left (\frac {4}{x \log (\log (-4+x))}\right )} \, dx \]

[In]

Int[(6*x^2 + 2*x^3 + (48*x + 4*x^2 - 4*x^3)*Log[-4 + x]*Log[Log[-4 + x]] + (-2*x^2 + (-40*x + 2*x^2 + 2*x^3)*L
og[-4 + x]*Log[Log[-4 + x]])*Log[4/(x*Log[Log[-4 + x]])] + (8*x - 2*x^2)*Log[-4 + x]*Log[Log[-4 + x]]*Log[4/(x
*Log[Log[-4 + x]])]^2)/((-324 - 351*x - 180*x^2 - 24*x^3 + 8*x^4 + 4*x^5)*Log[-4 + x]*Log[Log[-4 + x]] + (432
+ 324*x + 84*x^2 - 16*x^3 - 8*x^4)*Log[-4 + x]*Log[Log[-4 + x]]*Log[4/(x*Log[Log[-4 + x]])] + (-216 - 90*x + 4
*x^2 + 8*x^3)*Log[-4 + x]*Log[Log[-4 + x]]*Log[4/(x*Log[Log[-4 + x]])]^2 + (48 + 4*x - 4*x^2)*Log[-4 + x]*Log[
Log[-4 + x]]*Log[4/(x*Log[Log[-4 + x]])]^3 + (-4 + x)*Log[-4 + x]*Log[Log[-4 + x]]*Log[4/(x*Log[Log[-4 + x]])]
^4),x]

[Out]

6*Defer[Int][x/(9 + 6*x + 2*x^2 - 6*Log[4/(x*Log[Log[-4 + x]])] - 2*x*Log[4/(x*Log[Log[-4 + x]])] + Log[4/(x*L
og[Log[-4 + x]])]^2)^2, x] + 8*Defer[Int][x^2/(9 + 6*x + 2*x^2 - 6*Log[4/(x*Log[Log[-4 + x]])] - 2*x*Log[4/(x*
Log[Log[-4 + x]])] + Log[4/(x*Log[Log[-4 + x]])]^2)^2, x] + 4*Defer[Int][x^3/(9 + 6*x + 2*x^2 - 6*Log[4/(x*Log
[Log[-4 + x]])] - 2*x*Log[4/(x*Log[Log[-4 + x]])] + Log[4/(x*Log[Log[-4 + x]])]^2)^2, x] + 56*Defer[Int][1/(Lo
g[-4 + x]*Log[Log[-4 + x]]*(9 + 6*x + 2*x^2 - 6*Log[4/(x*Log[Log[-4 + x]])] - 2*x*Log[4/(x*Log[Log[-4 + x]])]
+ Log[4/(x*Log[Log[-4 + x]])]^2)^2), x] + 224*Defer[Int][1/((-4 + x)*Log[-4 + x]*Log[Log[-4 + x]]*(9 + 6*x + 2
*x^2 - 6*Log[4/(x*Log[Log[-4 + x]])] - 2*x*Log[4/(x*Log[Log[-4 + x]])] + Log[4/(x*Log[Log[-4 + x]])]^2)^2), x]
+ 14*Defer[Int][x/(Log[-4 + x]*Log[Log[-4 + x]]*(9 + 6*x + 2*x^2 - 6*Log[4/(x*Log[Log[-4 + x]])] - 2*x*Log[4/
(x*Log[Log[-4 + x]])] + Log[4/(x*Log[Log[-4 + x]])]^2)^2), x] + 2*Defer[Int][x^2/(Log[-4 + x]*Log[Log[-4 + x]]
*(9 + 6*x + 2*x^2 - 6*Log[4/(x*Log[Log[-4 + x]])] - 2*x*Log[4/(x*Log[Log[-4 + x]])] + Log[4/(x*Log[Log[-4 + x]
])]^2)^2), x] - 2*Defer[Int][(x*Log[4/(x*Log[Log[-4 + x]])])/(9 + 6*x + 2*x^2 - 6*Log[4/(x*Log[Log[-4 + x]])]
- 2*x*Log[4/(x*Log[Log[-4 + x]])] + Log[4/(x*Log[Log[-4 + x]])]^2)^2, x] - 2*Defer[Int][(x^2*Log[4/(x*Log[Log[
-4 + x]])])/(9 + 6*x + 2*x^2 - 6*Log[4/(x*Log[Log[-4 + x]])] - 2*x*Log[4/(x*Log[Log[-4 + x]])] + Log[4/(x*Log[
Log[-4 + x]])]^2)^2, x] - 8*Defer[Int][Log[4/(x*Log[Log[-4 + x]])]/(Log[-4 + x]*Log[Log[-4 + x]]*(9 + 6*x + 2*
x^2 - 6*Log[4/(x*Log[Log[-4 + x]])] - 2*x*Log[4/(x*Log[Log[-4 + x]])] + Log[4/(x*Log[Log[-4 + x]])]^2)^2), x]
- 32*Defer[Int][Log[4/(x*Log[Log[-4 + x]])]/((-4 + x)*Log[-4 + x]*Log[Log[-4 + x]]*(9 + 6*x + 2*x^2 - 6*Log[4/
(x*Log[Log[-4 + x]])] - 2*x*Log[4/(x*Log[Log[-4 + x]])] + Log[4/(x*Log[Log[-4 + x]])]^2)^2), x] - 2*Defer[Int]
[(x*Log[4/(x*Log[Log[-4 + x]])])/(Log[-4 + x]*Log[Log[-4 + x]]*(9 + 6*x + 2*x^2 - 6*Log[4/(x*Log[Log[-4 + x]])
] - 2*x*Log[4/(x*Log[Log[-4 + x]])] + Log[4/(x*Log[Log[-4 + x]])]^2)^2), x] - 2*Defer[Int][x/(9 + 6*x + 2*x^2
- 6*Log[4/(x*Log[Log[-4 + x]])] - 2*x*Log[4/(x*Log[Log[-4 + x]])] + Log[4/(x*Log[Log[-4 + x]])]^2), x]

Rubi steps \begin{align*} \text {integral}& = \int \frac {2 x \left (x+(-4+x) \log (-4+x) \log (\log (-4+x)) \left (-2+\log \left (\frac {4}{x \log (\log (-4+x))}\right )\right )\right ) \left (-3-x+\log \left (\frac {4}{x \log (\log (-4+x))}\right )\right )}{(4-x) \log (-4+x) \log (\log (-4+x)) \left (9+6 x+2 x^2-2 (3+x) \log \left (\frac {4}{x \log (\log (-4+x))}\right )+\log ^2\left (\frac {4}{x \log (\log (-4+x))}\right )\right )^2} \, dx \\ & = 2 \int \frac {x \left (x+(-4+x) \log (-4+x) \log (\log (-4+x)) \left (-2+\log \left (\frac {4}{x \log (\log (-4+x))}\right )\right )\right ) \left (-3-x+\log \left (\frac {4}{x \log (\log (-4+x))}\right )\right )}{(4-x) \log (-4+x) \log (\log (-4+x)) \left (9+6 x+2 x^2-2 (3+x) \log \left (\frac {4}{x \log (\log (-4+x))}\right )+\log ^2\left (\frac {4}{x \log (\log (-4+x))}\right )\right )^2} \, dx \\ & = 2 \int \left (\frac {x \left (3 x+x^2-12 \log (-4+x) \log (\log (-4+x))-13 x \log (-4+x) \log (\log (-4+x))-4 x^2 \log (-4+x) \log (\log (-4+x))+2 x^3 \log (-4+x) \log (\log (-4+x))-x \log \left (\frac {4}{x \log (\log (-4+x))}\right )+4 \log (-4+x) \log (\log (-4+x)) \log \left (\frac {4}{x \log (\log (-4+x))}\right )+3 x \log (-4+x) \log (\log (-4+x)) \log \left (\frac {4}{x \log (\log (-4+x))}\right )-x^2 \log (-4+x) \log (\log (-4+x)) \log \left (\frac {4}{x \log (\log (-4+x))}\right )\right )}{(-4+x) \log (-4+x) \log (\log (-4+x)) \left (9+6 x+2 x^2-6 \log \left (\frac {4}{x \log (\log (-4+x))}\right )-2 x \log \left (\frac {4}{x \log (\log (-4+x))}\right )+\log ^2\left (\frac {4}{x \log (\log (-4+x))}\right )\right )^2}-\frac {x}{9+6 x+2 x^2-6 \log \left (\frac {4}{x \log (\log (-4+x))}\right )-2 x \log \left (\frac {4}{x \log (\log (-4+x))}\right )+\log ^2\left (\frac {4}{x \log (\log (-4+x))}\right )}\right ) \, dx \\ & = 2 \int \frac {x \left (3 x+x^2-12 \log (-4+x) \log (\log (-4+x))-13 x \log (-4+x) \log (\log (-4+x))-4 x^2 \log (-4+x) \log (\log (-4+x))+2 x^3 \log (-4+x) \log (\log (-4+x))-x \log \left (\frac {4}{x \log (\log (-4+x))}\right )+4 \log (-4+x) \log (\log (-4+x)) \log \left (\frac {4}{x \log (\log (-4+x))}\right )+3 x \log (-4+x) \log (\log (-4+x)) \log \left (\frac {4}{x \log (\log (-4+x))}\right )-x^2 \log (-4+x) \log (\log (-4+x)) \log \left (\frac {4}{x \log (\log (-4+x))}\right )\right )}{(-4+x) \log (-4+x) \log (\log (-4+x)) \left (9+6 x+2 x^2-6 \log \left (\frac {4}{x \log (\log (-4+x))}\right )-2 x \log \left (\frac {4}{x \log (\log (-4+x))}\right )+\log ^2\left (\frac {4}{x \log (\log (-4+x))}\right )\right )^2} \, dx-2 \int \frac {x}{9+6 x+2 x^2-6 \log \left (\frac {4}{x \log (\log (-4+x))}\right )-2 x \log \left (\frac {4}{x \log (\log (-4+x))}\right )+\log ^2\left (\frac {4}{x \log (\log (-4+x))}\right )} \, dx \\ & = -\left (2 \int \frac {x}{9+6 x+2 x^2-6 \log \left (\frac {4}{x \log (\log (-4+x))}\right )-2 x \log \left (\frac {4}{x \log (\log (-4+x))}\right )+\log ^2\left (\frac {4}{x \log (\log (-4+x))}\right )} \, dx\right )+2 \int \frac {x \left (-x \left (3+x-\log \left (\frac {4}{x \log (\log (-4+x))}\right )\right )-(-4+x) \log (-4+x) \log (\log (-4+x)) \left (3+4 x+2 x^2-(1+x) \log \left (\frac {4}{x \log (\log (-4+x))}\right )\right )\right )}{(4-x) \log (-4+x) \log (\log (-4+x)) \left (9+6 x+2 x^2-2 (3+x) \log \left (\frac {4}{x \log (\log (-4+x))}\right )+\log ^2\left (\frac {4}{x \log (\log (-4+x))}\right )\right )^2} \, dx \\ & = -\left (2 \int \frac {x}{9+6 x+2 x^2-6 \log \left (\frac {4}{x \log (\log (-4+x))}\right )-2 x \log \left (\frac {4}{x \log (\log (-4+x))}\right )+\log ^2\left (\frac {4}{x \log (\log (-4+x))}\right )} \, dx\right )+2 \int \left (\frac {3 x+x^2-12 \log (-4+x) \log (\log (-4+x))-13 x \log (-4+x) \log (\log (-4+x))-4 x^2 \log (-4+x) \log (\log (-4+x))+2 x^3 \log (-4+x) \log (\log (-4+x))-x \log \left (\frac {4}{x \log (\log (-4+x))}\right )+4 \log (-4+x) \log (\log (-4+x)) \log \left (\frac {4}{x \log (\log (-4+x))}\right )+3 x \log (-4+x) \log (\log (-4+x)) \log \left (\frac {4}{x \log (\log (-4+x))}\right )-x^2 \log (-4+x) \log (\log (-4+x)) \log \left (\frac {4}{x \log (\log (-4+x))}\right )}{\log (-4+x) \log (\log (-4+x)) \left (9+6 x+2 x^2-6 \log \left (\frac {4}{x \log (\log (-4+x))}\right )-2 x \log \left (\frac {4}{x \log (\log (-4+x))}\right )+\log ^2\left (\frac {4}{x \log (\log (-4+x))}\right )\right )^2}+\frac {4 \left (3 x+x^2-12 \log (-4+x) \log (\log (-4+x))-13 x \log (-4+x) \log (\log (-4+x))-4 x^2 \log (-4+x) \log (\log (-4+x))+2 x^3 \log (-4+x) \log (\log (-4+x))-x \log \left (\frac {4}{x \log (\log (-4+x))}\right )+4 \log (-4+x) \log (\log (-4+x)) \log \left (\frac {4}{x \log (\log (-4+x))}\right )+3 x \log (-4+x) \log (\log (-4+x)) \log \left (\frac {4}{x \log (\log (-4+x))}\right )-x^2 \log (-4+x) \log (\log (-4+x)) \log \left (\frac {4}{x \log (\log (-4+x))}\right )\right )}{(-4+x) \log (-4+x) \log (\log (-4+x)) \left (9+6 x+2 x^2-6 \log \left (\frac {4}{x \log (\log (-4+x))}\right )-2 x \log \left (\frac {4}{x \log (\log (-4+x))}\right )+\log ^2\left (\frac {4}{x \log (\log (-4+x))}\right )\right )^2}\right ) \, dx \\ & = 2 \int \frac {3 x+x^2-12 \log (-4+x) \log (\log (-4+x))-13 x \log (-4+x) \log (\log (-4+x))-4 x^2 \log (-4+x) \log (\log (-4+x))+2 x^3 \log (-4+x) \log (\log (-4+x))-x \log \left (\frac {4}{x \log (\log (-4+x))}\right )+4 \log (-4+x) \log (\log (-4+x)) \log \left (\frac {4}{x \log (\log (-4+x))}\right )+3 x \log (-4+x) \log (\log (-4+x)) \log \left (\frac {4}{x \log (\log (-4+x))}\right )-x^2 \log (-4+x) \log (\log (-4+x)) \log \left (\frac {4}{x \log (\log (-4+x))}\right )}{\log (-4+x) \log (\log (-4+x)) \left (9+6 x+2 x^2-6 \log \left (\frac {4}{x \log (\log (-4+x))}\right )-2 x \log \left (\frac {4}{x \log (\log (-4+x))}\right )+\log ^2\left (\frac {4}{x \log (\log (-4+x))}\right )\right )^2} \, dx-2 \int \frac {x}{9+6 x+2 x^2-6 \log \left (\frac {4}{x \log (\log (-4+x))}\right )-2 x \log \left (\frac {4}{x \log (\log (-4+x))}\right )+\log ^2\left (\frac {4}{x \log (\log (-4+x))}\right )} \, dx+8 \int \frac {3 x+x^2-12 \log (-4+x) \log (\log (-4+x))-13 x \log (-4+x) \log (\log (-4+x))-4 x^2 \log (-4+x) \log (\log (-4+x))+2 x^3 \log (-4+x) \log (\log (-4+x))-x \log \left (\frac {4}{x \log (\log (-4+x))}\right )+4 \log (-4+x) \log (\log (-4+x)) \log \left (\frac {4}{x \log (\log (-4+x))}\right )+3 x \log (-4+x) \log (\log (-4+x)) \log \left (\frac {4}{x \log (\log (-4+x))}\right )-x^2 \log (-4+x) \log (\log (-4+x)) \log \left (\frac {4}{x \log (\log (-4+x))}\right )}{(-4+x) \log (-4+x) \log (\log (-4+x)) \left (9+6 x+2 x^2-6 \log \left (\frac {4}{x \log (\log (-4+x))}\right )-2 x \log \left (\frac {4}{x \log (\log (-4+x))}\right )+\log ^2\left (\frac {4}{x \log (\log (-4+x))}\right )\right )^2} \, dx \\ & = -\left (2 \int \frac {x}{9+6 x+2 x^2-6 \log \left (\frac {4}{x \log (\log (-4+x))}\right )-2 x \log \left (\frac {4}{x \log (\log (-4+x))}\right )+\log ^2\left (\frac {4}{x \log (\log (-4+x))}\right )} \, dx\right )+2 \int \frac {x \left (3+x-\log \left (\frac {4}{x \log (\log (-4+x))}\right )\right )+(-4+x) \log (-4+x) \log (\log (-4+x)) \left (3+4 x+2 x^2-(1+x) \log \left (\frac {4}{x \log (\log (-4+x))}\right )\right )}{\log (-4+x) \log (\log (-4+x)) \left (9+6 x+2 x^2-2 (3+x) \log \left (\frac {4}{x \log (\log (-4+x))}\right )+\log ^2\left (\frac {4}{x \log (\log (-4+x))}\right )\right )^2} \, dx+8 \int \frac {-x \left (3+x-\log \left (\frac {4}{x \log (\log (-4+x))}\right )\right )-(-4+x) \log (-4+x) \log (\log (-4+x)) \left (3+4 x+2 x^2-(1+x) \log \left (\frac {4}{x \log (\log (-4+x))}\right )\right )}{(4-x) \log (-4+x) \log (\log (-4+x)) \left (9+6 x+2 x^2-2 (3+x) \log \left (\frac {4}{x \log (\log (-4+x))}\right )+\log ^2\left (\frac {4}{x \log (\log (-4+x))}\right )\right )^2} \, dx \\ & = \text {Too large to display} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.20 (sec) , antiderivative size = 50, normalized size of antiderivative = 1.47 \[ \int \frac {6 x^2+2 x^3+\left (48 x+4 x^2-4 x^3\right ) \log (-4+x) \log (\log (-4+x))+\left (-2 x^2+\left (-40 x+2 x^2+2 x^3\right ) \log (-4+x) \log (\log (-4+x))\right ) \log \left (\frac {4}{x \log (\log (-4+x))}\right )+\left (8 x-2 x^2\right ) \log (-4+x) \log (\log (-4+x)) \log ^2\left (\frac {4}{x \log (\log (-4+x))}\right )}{\left (-324-351 x-180 x^2-24 x^3+8 x^4+4 x^5\right ) \log (-4+x) \log (\log (-4+x))+\left (432+324 x+84 x^2-16 x^3-8 x^4\right ) \log (-4+x) \log (\log (-4+x)) \log \left (\frac {4}{x \log (\log (-4+x))}\right )+\left (-216-90 x+4 x^2+8 x^3\right ) \log (-4+x) \log (\log (-4+x)) \log ^2\left (\frac {4}{x \log (\log (-4+x))}\right )+\left (48+4 x-4 x^2\right ) \log (-4+x) \log (\log (-4+x)) \log ^3\left (\frac {4}{x \log (\log (-4+x))}\right )+(-4+x) \log (-4+x) \log (\log (-4+x)) \log ^4\left (\frac {4}{x \log (\log (-4+x))}\right )} \, dx=-\frac {x^2}{9+6 x+2 x^2-2 (3+x) \log \left (\frac {4}{x \log (\log (-4+x))}\right )+\log ^2\left (\frac {4}{x \log (\log (-4+x))}\right )} \]

[In]

Integrate[(6*x^2 + 2*x^3 + (48*x + 4*x^2 - 4*x^3)*Log[-4 + x]*Log[Log[-4 + x]] + (-2*x^2 + (-40*x + 2*x^2 + 2*
x^3)*Log[-4 + x]*Log[Log[-4 + x]])*Log[4/(x*Log[Log[-4 + x]])] + (8*x - 2*x^2)*Log[-4 + x]*Log[Log[-4 + x]]*Lo
g[4/(x*Log[Log[-4 + x]])]^2)/((-324 - 351*x - 180*x^2 - 24*x^3 + 8*x^4 + 4*x^5)*Log[-4 + x]*Log[Log[-4 + x]] +
(432 + 324*x + 84*x^2 - 16*x^3 - 8*x^4)*Log[-4 + x]*Log[Log[-4 + x]]*Log[4/(x*Log[Log[-4 + x]])] + (-216 - 90
*x + 4*x^2 + 8*x^3)*Log[-4 + x]*Log[Log[-4 + x]]*Log[4/(x*Log[Log[-4 + x]])]^2 + (48 + 4*x - 4*x^2)*Log[-4 + x
]*Log[Log[-4 + x]]*Log[4/(x*Log[Log[-4 + x]])]^3 + (-4 + x)*Log[-4 + x]*Log[Log[-4 + x]]*Log[4/(x*Log[Log[-4 +
x]])]^4),x]

[Out]

-(x^2/(9 + 6*x + 2*x^2 - 2*(3 + x)*Log[4/(x*Log[Log[-4 + x]])] + Log[4/(x*Log[Log[-4 + x]])]^2))

Maple [A] (verified)

Time = 85.45 (sec) , antiderivative size = 64, normalized size of antiderivative = 1.88

method	result	size
parallelrisch	\(-\frac {x^{2}}{2 x^{2}-2 \ln \left (\frac {4}{x \ln \left (\ln \left (x -4\right )\right )}\right ) x +\ln \left (\frac {4}{x \ln \left (\ln \left (x -4\right )\right )}\right )^{2}+6 x -6 \ln \left (\frac {4}{x \ln \left (\ln \left (x -4\right )\right )}\right )+9}\)	\(64\)
risch	\(\text {Expression too large to display}\)	\(1024\)

[In]

int(((-2*x^2+8*x)*ln(x-4)*ln(ln(x-4))*ln(4/x/ln(ln(x-4)))^2+((2*x^3+2*x^2-40*x)*ln(x-4)*ln(ln(x-4))-2*x^2)*ln(
4/x/ln(ln(x-4)))+(-4*x^3+4*x^2+48*x)*ln(x-4)*ln(ln(x-4))+2*x^3+6*x^2)/((x-4)*ln(x-4)*ln(ln(x-4))*ln(4/x/ln(ln(
x-4)))^4+(-4*x^2+4*x+48)*ln(x-4)*ln(ln(x-4))*ln(4/x/ln(ln(x-4)))^3+(8*x^3+4*x^2-90*x-216)*ln(x-4)*ln(ln(x-4))*
ln(4/x/ln(ln(x-4)))^2+(-8*x^4-16*x^3+84*x^2+324*x+432)*ln(x-4)*ln(ln(x-4))*ln(4/x/ln(ln(x-4)))+(4*x^5+8*x^4-24
*x^3-180*x^2-351*x-324)*ln(x-4)*ln(ln(x-4))),x,method=_RETURNVERBOSE)

[Out]

-x^2/(2*x^2-2*ln(4/x/ln(ln(x-4)))*x+ln(4/x/ln(ln(x-4)))^2+6*x-6*ln(4/x/ln(ln(x-4)))+9)

Fricas [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 50, normalized size of antiderivative = 1.47 \[ \int \frac {6 x^2+2 x^3+\left (48 x+4 x^2-4 x^3\right ) \log (-4+x) \log (\log (-4+x))+\left (-2 x^2+\left (-40 x+2 x^2+2 x^3\right ) \log (-4+x) \log (\log (-4+x))\right ) \log \left (\frac {4}{x \log (\log (-4+x))}\right )+\left (8 x-2 x^2\right ) \log (-4+x) \log (\log (-4+x)) \log ^2\left (\frac {4}{x \log (\log (-4+x))}\right )}{\left (-324-351 x-180 x^2-24 x^3+8 x^4+4 x^5\right ) \log (-4+x) \log (\log (-4+x))+\left (432+324 x+84 x^2-16 x^3-8 x^4\right ) \log (-4+x) \log (\log (-4+x)) \log \left (\frac {4}{x \log (\log (-4+x))}\right )+\left (-216-90 x+4 x^2+8 x^3\right ) \log (-4+x) \log (\log (-4+x)) \log ^2\left (\frac {4}{x \log (\log (-4+x))}\right )+\left (48+4 x-4 x^2\right ) \log (-4+x) \log (\log (-4+x)) \log ^3\left (\frac {4}{x \log (\log (-4+x))}\right )+(-4+x) \log (-4+x) \log (\log (-4+x)) \log ^4\left (\frac {4}{x \log (\log (-4+x))}\right )} \, dx=-\frac {x^{2}}{2 \, x^{2} - 2 \, {\left (x + 3\right )} \log \left (\frac {4}{x \log \left (\log \left (x - 4\right )\right )}\right ) + \log \left (\frac {4}{x \log \left (\log \left (x - 4\right )\right )}\right )^{2} + 6 \, x + 9} \]

[In]

integrate(((-2*x^2+8*x)*log(x-4)*log(log(x-4))*log(4/x/log(log(x-4)))^2+((2*x^3+2*x^2-40*x)*log(x-4)*log(log(x
-4))-2*x^2)*log(4/x/log(log(x-4)))+(-4*x^3+4*x^2+48*x)*log(x-4)*log(log(x-4))+2*x^3+6*x^2)/((x-4)*log(x-4)*log
(log(x-4))*log(4/x/log(log(x-4)))^4+(-4*x^2+4*x+48)*log(x-4)*log(log(x-4))*log(4/x/log(log(x-4)))^3+(8*x^3+4*x
^2-90*x-216)*log(x-4)*log(log(x-4))*log(4/x/log(log(x-4)))^2+(-8*x^4-16*x^3+84*x^2+324*x+432)*log(x-4)*log(log
(x-4))*log(4/x/log(log(x-4)))+(4*x^5+8*x^4-24*x^3-180*x^2-351*x-324)*log(x-4)*log(log(x-4))),x, algorithm="fri
cas")

[Out]

-x^2/(2*x^2 - 2*(x + 3)*log(4/(x*log(log(x - 4)))) + log(4/(x*log(log(x - 4))))^2 + 6*x + 9)

Sympy [A] (verification not implemented)

Time = 0.43 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.35 \[ \int \frac {6 x^2+2 x^3+\left (48 x+4 x^2-4 x^3\right ) \log (-4+x) \log (\log (-4+x))+\left (-2 x^2+\left (-40 x+2 x^2+2 x^3\right ) \log (-4+x) \log (\log (-4+x))\right ) \log \left (\frac {4}{x \log (\log (-4+x))}\right )+\left (8 x-2 x^2\right ) \log (-4+x) \log (\log (-4+x)) \log ^2\left (\frac {4}{x \log (\log (-4+x))}\right )}{\left (-324-351 x-180 x^2-24 x^3+8 x^4+4 x^5\right ) \log (-4+x) \log (\log (-4+x))+\left (432+324 x+84 x^2-16 x^3-8 x^4\right ) \log (-4+x) \log (\log (-4+x)) \log \left (\frac {4}{x \log (\log (-4+x))}\right )+\left (-216-90 x+4 x^2+8 x^3\right ) \log (-4+x) \log (\log (-4+x)) \log ^2\left (\frac {4}{x \log (\log (-4+x))}\right )+\left (48+4 x-4 x^2\right ) \log (-4+x) \log (\log (-4+x)) \log ^3\left (\frac {4}{x \log (\log (-4+x))}\right )+(-4+x) \log (-4+x) \log (\log (-4+x)) \log ^4\left (\frac {4}{x \log (\log (-4+x))}\right )} \, dx=- \frac {x^{2}}{2 x^{2} + 6 x + \left (- 2 x - 6\right ) \log {\left (\frac {4}{x \log {\left (\log {\left (x - 4 \right )} \right )}} \right )} + \log {\left (\frac {4}{x \log {\left (\log {\left (x - 4 \right )} \right )}} \right )}^{2} + 9} \]

[In]

integrate(((-2*x**2+8*x)*ln(x-4)*ln(ln(x-4))*ln(4/x/ln(ln(x-4)))**2+((2*x**3+2*x**2-40*x)*ln(x-4)*ln(ln(x-4))-
2*x**2)*ln(4/x/ln(ln(x-4)))+(-4*x**3+4*x**2+48*x)*ln(x-4)*ln(ln(x-4))+2*x**3+6*x**2)/((x-4)*ln(x-4)*ln(ln(x-4)
)*ln(4/x/ln(ln(x-4)))**4+(-4*x**2+4*x+48)*ln(x-4)*ln(ln(x-4))*ln(4/x/ln(ln(x-4)))**3+(8*x**3+4*x**2-90*x-216)*
ln(x-4)*ln(ln(x-4))*ln(4/x/ln(ln(x-4)))**2+(-8*x**4-16*x**3+84*x**2+324*x+432)*ln(x-4)*ln(ln(x-4))*ln(4/x/ln(l
n(x-4)))+(4*x**5+8*x**4-24*x**3-180*x**2-351*x-324)*ln(x-4)*ln(ln(x-4))),x)

[Out]

-x**2/(2*x**2 + 6*x + (-2*x - 6)*log(4/(x*log(log(x - 4)))) + log(4/(x*log(log(x - 4))))**2 + 9)

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 73 vs. \(2 (31) = 62\).

Time = 0.65 (sec) , antiderivative size = 73, normalized size of antiderivative = 2.15 \[ \int \frac {6 x^2+2 x^3+\left (48 x+4 x^2-4 x^3\right ) \log (-4+x) \log (\log (-4+x))+\left (-2 x^2+\left (-40 x+2 x^2+2 x^3\right ) \log (-4+x) \log (\log (-4+x))\right ) \log \left (\frac {4}{x \log (\log (-4+x))}\right )+\left (8 x-2 x^2\right ) \log (-4+x) \log (\log (-4+x)) \log ^2\left (\frac {4}{x \log (\log (-4+x))}\right )}{\left (-324-351 x-180 x^2-24 x^3+8 x^4+4 x^5\right ) \log (-4+x) \log (\log (-4+x))+\left (432+324 x+84 x^2-16 x^3-8 x^4\right ) \log (-4+x) \log (\log (-4+x)) \log \left (\frac {4}{x \log (\log (-4+x))}\right )+\left (-216-90 x+4 x^2+8 x^3\right ) \log (-4+x) \log (\log (-4+x)) \log ^2\left (\frac {4}{x \log (\log (-4+x))}\right )+\left (48+4 x-4 x^2\right ) \log (-4+x) \log (\log (-4+x)) \log ^3\left (\frac {4}{x \log (\log (-4+x))}\right )+(-4+x) \log (-4+x) \log (\log (-4+x)) \log ^4\left (\frac {4}{x \log (\log (-4+x))}\right )} \, dx=-\frac {x^{2}}{2 \, x^{2} - 2 \, x {\left (2 \, \log \left (2\right ) - 3\right )} + 4 \, \log \left (2\right )^{2} + 2 \, {\left (x - 2 \, \log \left (2\right ) + 3\right )} \log \left (x\right ) + \log \left (x\right )^{2} + 2 \, {\left (x - 2 \, \log \left (2\right ) + \log \left (x\right ) + 3\right )} \log \left (\log \left (\log \left (x - 4\right )\right )\right ) + \log \left (\log \left (\log \left (x - 4\right )\right )\right )^{2} - 12 \, \log \left (2\right ) + 9} \]

[In]

integrate(((-2*x^2+8*x)*log(x-4)*log(log(x-4))*log(4/x/log(log(x-4)))^2+((2*x^3+2*x^2-40*x)*log(x-4)*log(log(x
-4))-2*x^2)*log(4/x/log(log(x-4)))+(-4*x^3+4*x^2+48*x)*log(x-4)*log(log(x-4))+2*x^3+6*x^2)/((x-4)*log(x-4)*log
(log(x-4))*log(4/x/log(log(x-4)))^4+(-4*x^2+4*x+48)*log(x-4)*log(log(x-4))*log(4/x/log(log(x-4)))^3+(8*x^3+4*x
^2-90*x-216)*log(x-4)*log(log(x-4))*log(4/x/log(log(x-4)))^2+(-8*x^4-16*x^3+84*x^2+324*x+432)*log(x-4)*log(log
(x-4))*log(4/x/log(log(x-4)))+(4*x^5+8*x^4-24*x^3-180*x^2-351*x-324)*log(x-4)*log(log(x-4))),x, algorithm="max
ima")

[Out]

-x^2/(2*x^2 - 2*x*(2*log(2) - 3) + 4*log(2)^2 + 2*(x - 2*log(2) + 3)*log(x) + log(x)^2 + 2*(x - 2*log(2) + log
(x) + 3)*log(log(log(x - 4))) + log(log(log(x - 4)))^2 - 12*log(2) + 9)

Giac [F(-1)]

Timed out. \[ \int \frac {6 x^2+2 x^3+\left (48 x+4 x^2-4 x^3\right ) \log (-4+x) \log (\log (-4+x))+\left (-2 x^2+\left (-40 x+2 x^2+2 x^3\right ) \log (-4+x) \log (\log (-4+x))\right ) \log \left (\frac {4}{x \log (\log (-4+x))}\right )+\left (8 x-2 x^2\right ) \log (-4+x) \log (\log (-4+x)) \log ^2\left (\frac {4}{x \log (\log (-4+x))}\right )}{\left (-324-351 x-180 x^2-24 x^3+8 x^4+4 x^5\right ) \log (-4+x) \log (\log (-4+x))+\left (432+324 x+84 x^2-16 x^3-8 x^4\right ) \log (-4+x) \log (\log (-4+x)) \log \left (\frac {4}{x \log (\log (-4+x))}\right )+\left (-216-90 x+4 x^2+8 x^3\right ) \log (-4+x) \log (\log (-4+x)) \log ^2\left (\frac {4}{x \log (\log (-4+x))}\right )+\left (48+4 x-4 x^2\right ) \log (-4+x) \log (\log (-4+x)) \log ^3\left (\frac {4}{x \log (\log (-4+x))}\right )+(-4+x) \log (-4+x) \log (\log (-4+x)) \log ^4\left (\frac {4}{x \log (\log (-4+x))}\right )} \, dx=\text {Timed out} \]

[In]

integrate(((-2*x^2+8*x)*log(x-4)*log(log(x-4))*log(4/x/log(log(x-4)))^2+((2*x^3+2*x^2-40*x)*log(x-4)*log(log(x
-4))-2*x^2)*log(4/x/log(log(x-4)))+(-4*x^3+4*x^2+48*x)*log(x-4)*log(log(x-4))+2*x^3+6*x^2)/((x-4)*log(x-4)*log
(log(x-4))*log(4/x/log(log(x-4)))^4+(-4*x^2+4*x+48)*log(x-4)*log(log(x-4))*log(4/x/log(log(x-4)))^3+(8*x^3+4*x
^2-90*x-216)*log(x-4)*log(log(x-4))*log(4/x/log(log(x-4)))^2+(-8*x^4-16*x^3+84*x^2+324*x+432)*log(x-4)*log(log
(x-4))*log(4/x/log(log(x-4)))+(4*x^5+8*x^4-24*x^3-180*x^2-351*x-324)*log(x-4)*log(log(x-4))),x, algorithm="gia
c")

[Out]

Timed out

Mupad [F(-1)]

Timed out. \[ \int \frac {6 x^2+2 x^3+\left (48 x+4 x^2-4 x^3\right ) \log (-4+x) \log (\log (-4+x))+\left (-2 x^2+\left (-40 x+2 x^2+2 x^3\right ) \log (-4+x) \log (\log (-4+x))\right ) \log \left (\frac {4}{x \log (\log (-4+x))}\right )+\left (8 x-2 x^2\right ) \log (-4+x) \log (\log (-4+x)) \log ^2\left (\frac {4}{x \log (\log (-4+x))}\right )}{\left (-324-351 x-180 x^2-24 x^3+8 x^4+4 x^5\right ) \log (-4+x) \log (\log (-4+x))+\left (432+324 x+84 x^2-16 x^3-8 x^4\right ) \log (-4+x) \log (\log (-4+x)) \log \left (\frac {4}{x \log (\log (-4+x))}\right )+\left (-216-90 x+4 x^2+8 x^3\right ) \log (-4+x) \log (\log (-4+x)) \log ^2\left (\frac {4}{x \log (\log (-4+x))}\right )+\left (48+4 x-4 x^2\right ) \log (-4+x) \log (\log (-4+x)) \log ^3\left (\frac {4}{x \log (\log (-4+x))}\right )+(-4+x) \log (-4+x) \log (\log (-4+x)) \log ^4\left (\frac {4}{x \log (\log (-4+x))}\right )} \, dx=\int \frac {6\,x^2-\ln \left (\frac {4}{x\,\ln \left (\ln \left (x-4\right )\right )}\right )\,\left (2\,x^2-\ln \left (x-4\right )\,\ln \left (\ln \left (x-4\right )\right )\,\left (2\,x^3+2\,x^2-40\,x\right )\right )+2\,x^3+\ln \left (x-4\right )\,\ln \left (\ln \left (x-4\right )\right )\,\left (-4\,x^3+4\,x^2+48\,x\right )+\ln \left (x-4\right )\,\ln \left (\ln \left (x-4\right )\right )\,{\ln \left (\frac {4}{x\,\ln \left (\ln \left (x-4\right )\right )}\right )}^2\,\left (8\,x-2\,x^2\right )}{\ln \left (x-4\right )\,\ln \left (\ln \left (x-4\right )\right )\,\left (x-4\right )\,{\ln \left (\frac {4}{x\,\ln \left (\ln \left (x-4\right )\right )}\right )}^4+\ln \left (x-4\right )\,\ln \left (\ln \left (x-4\right )\right )\,\left (-4\,x^2+4\,x+48\right )\,{\ln \left (\frac {4}{x\,\ln \left (\ln \left (x-4\right )\right )}\right )}^3-\ln \left (x-4\right )\,\ln \left (\ln \left (x-4\right )\right )\,\left (-8\,x^3-4\,x^2+90\,x+216\right )\,{\ln \left (\frac {4}{x\,\ln \left (\ln \left (x-4\right )\right )}\right )}^2+\ln \left (x-4\right )\,\ln \left (\ln \left (x-4\right )\right )\,\left (-8\,x^4-16\,x^3+84\,x^2+324\,x+432\right )\,\ln \left (\frac {4}{x\,\ln \left (\ln \left (x-4\right )\right )}\right )-\ln \left (x-4\right )\,\ln \left (\ln \left (x-4\right )\right )\,\left (-4\,x^5-8\,x^4+24\,x^3+180\,x^2+351\,x+324\right )} \,d x \]

[In]

int((6*x^2 - log(4/(x*log(log(x - 4))))*(2*x^2 - log(x - 4)*log(log(x - 4))*(2*x^2 - 40*x + 2*x^3)) + 2*x^3 +
log(x - 4)*log(log(x - 4))*(48*x + 4*x^2 - 4*x^3) + log(x - 4)*log(log(x - 4))*log(4/(x*log(log(x - 4))))^2*(8
*x - 2*x^2))/(log(x - 4)*log(log(x - 4))*log(4/(x*log(log(x - 4))))^4*(x - 4) - log(x - 4)*log(log(x - 4))*log
(4/(x*log(log(x - 4))))^2*(90*x - 4*x^2 - 8*x^3 + 216) - log(x - 4)*log(log(x - 4))*(351*x + 180*x^2 + 24*x^3
- 8*x^4 - 4*x^5 + 324) + log(x - 4)*log(log(x - 4))*log(4/(x*log(log(x - 4))))^3*(4*x - 4*x^2 + 48) + log(x -
4)*log(log(x - 4))*log(4/(x*log(log(x - 4))))*(324*x + 84*x^2 - 16*x^3 - 8*x^4 + 432)),x)

[Out]

int((6*x^2 - log(4/(x*log(log(x - 4))))*(2*x^2 - log(x - 4)*log(log(x - 4))*(2*x^2 - 40*x + 2*x^3)) + 2*x^3 +
log(x - 4)*log(log(x - 4))*(48*x + 4*x^2 - 4*x^3) + log(x - 4)*log(log(x - 4))*log(4/(x*log(log(x - 4))))^2*(8
*x - 2*x^2))/(log(x - 4)*log(log(x - 4))*log(4/(x*log(log(x - 4))))^4*(x - 4) - log(x - 4)*log(log(x - 4))*log
(4/(x*log(log(x - 4))))^2*(90*x - 4*x^2 - 8*x^3 + 216) - log(x - 4)*log(log(x - 4))*(351*x + 180*x^2 + 24*x^3
- 8*x^4 - 4*x^5 + 324) + log(x - 4)*log(log(x - 4))*log(4/(x*log(log(x - 4))))^3*(4*x - 4*x^2 + 48) + log(x -
4)*log(log(x - 4))*log(4/(x*log(log(x - 4))))*(324*x + 84*x^2 - 16*x^3 - 8*x^4 + 432)), x)