Integrand size = 298, antiderivative size = 34 \[ \int \frac {6 x^2+2 x^3+\left (48 x+4 x^2-4 x^3\right ) \log (-4+x) \log (\log (-4+x))+\left (-2 x^2+\left (-40 x+2 x^2+2 x^3\right ) \log (-4+x) \log (\log (-4+x))\right ) \log \left (\frac {4}{x \log (\log (-4+x))}\right )+\left (8 x-2 x^2\right ) \log (-4+x) \log (\log (-4+x)) \log ^2\left (\frac {4}{x \log (\log (-4+x))}\right )}{\left (-324-351 x-180 x^2-24 x^3+8 x^4+4 x^5\right ) \log (-4+x) \log (\log (-4+x))+\left (432+324 x+84 x^2-16 x^3-8 x^4\right ) \log (-4+x) \log (\log (-4+x)) \log \left (\frac {4}{x \log (\log (-4+x))}\right )+\left (-216-90 x+4 x^2+8 x^3\right ) \log (-4+x) \log (\log (-4+x)) \log ^2\left (\frac {4}{x \log (\log (-4+x))}\right )+\left (48+4 x-4 x^2\right ) \log (-4+x) \log (\log (-4+x)) \log ^3\left (\frac {4}{x \log (\log (-4+x))}\right )+(-4+x) \log (-4+x) \log (\log (-4+x)) \log ^4\left (\frac {4}{x \log (\log (-4+x))}\right )} \, dx=\frac {x^2}{-x^2-\left (3+x-\log \left (\frac {4}{x \log (\log (-4+x))}\right )\right )^2} \]
Time = 0.20 (sec) , antiderivative size = 50, normalized size of antiderivative = 1.47 \[ \int \frac {6 x^2+2 x^3+\left (48 x+4 x^2-4 x^3\right ) \log (-4+x) \log (\log (-4+x))+\left (-2 x^2+\left (-40 x+2 x^2+2 x^3\right ) \log (-4+x) \log (\log (-4+x))\right ) \log \left (\frac {4}{x \log (\log (-4+x))}\right )+\left (8 x-2 x^2\right ) \log (-4+x) \log (\log (-4+x)) \log ^2\left (\frac {4}{x \log (\log (-4+x))}\right )}{\left (-324-351 x-180 x^2-24 x^3+8 x^4+4 x^5\right ) \log (-4+x) \log (\log (-4+x))+\left (432+324 x+84 x^2-16 x^3-8 x^4\right ) \log (-4+x) \log (\log (-4+x)) \log \left (\frac {4}{x \log (\log (-4+x))}\right )+\left (-216-90 x+4 x^2+8 x^3\right ) \log (-4+x) \log (\log (-4+x)) \log ^2\left (\frac {4}{x \log (\log (-4+x))}\right )+\left (48+4 x-4 x^2\right ) \log (-4+x) \log (\log (-4+x)) \log ^3\left (\frac {4}{x \log (\log (-4+x))}\right )+(-4+x) \log (-4+x) \log (\log (-4+x)) \log ^4\left (\frac {4}{x \log (\log (-4+x))}\right )} \, dx=-\frac {x^2}{9+6 x+2 x^2-2 (3+x) \log \left (\frac {4}{x \log (\log (-4+x))}\right )+\log ^2\left (\frac {4}{x \log (\log (-4+x))}\right )} \]
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]]*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]
-(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))
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {2 x^3+6 x^2+\left (8 x-2 x^2\right ) \log (x-4) \log (\log (x-4)) \log ^2\left (\frac {4}{x \log (\log (x-4))}\right )+\left (-4 x^3+4 x^2+48 x\right ) \log (x-4) \log (\log (x-4))+\left (\left (2 x^3+2 x^2-40 x\right ) \log (x-4) \log (\log (x-4))-2 x^2\right ) \log \left (\frac {4}{x \log (\log (x-4))}\right )}{\left (-4 x^2+4 x+48\right ) \log (x-4) \log (\log (x-4)) \log ^3\left (\frac {4}{x \log (\log (x-4))}\right )+\left (8 x^3+4 x^2-90 x-216\right ) \log (x-4) \log (\log (x-4)) \log ^2\left (\frac {4}{x \log (\log (x-4))}\right )+\left (-8 x^4-16 x^3+84 x^2+324 x+432\right ) \log (x-4) \log (\log (x-4)) \log \left (\frac {4}{x \log (\log (x-4))}\right )+\left (4 x^5+8 x^4-24 x^3-180 x^2-351 x-324\right ) \log (x-4) \log (\log (x-4))+(x-4) \log (x-4) \log (\log (x-4)) \log ^4\left (\frac {4}{x \log (\log (x-4))}\right )} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 x \left (x+(x-4) \log (x-4) \log (\log (x-4)) \left (\log \left (\frac {4}{x \log (\log (x-4))}\right )-2\right )\right ) \left (-x+\log \left (\frac {4}{x \log (\log (x-4))}\right )-3\right )}{(4-x) \log (x-4) \log (\log (x-4)) \left (2 x^2+6 x+\log ^2\left (\frac {4}{x \log (\log (x-4))}\right )-2 (x+3) \log \left (\frac {4}{x \log (\log (x-4))}\right )+9\right )^2}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 2 \int -\frac {x \left (x+(4-x) \log (x-4) \log (\log (x-4)) \left (2-\log \left (\frac {4}{x \log (\log (x-4))}\right )\right )\right ) \left (x-\log \left (\frac {4}{x \log (\log (x-4))}\right )+3\right )}{(4-x) \log (x-4) \log (\log (x-4)) \left (2 x^2+6 x+\log ^2\left (\frac {4}{x \log (\log (x-4))}\right )-2 (x+3) \log \left (\frac {4}{x \log (\log (x-4))}\right )+9\right )^2}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -2 \int \frac {x \left (x+(4-x) \log (x-4) \log (\log (x-4)) \left (2-\log \left (\frac {4}{x \log (\log (x-4))}\right )\right )\right ) \left (x-\log \left (\frac {4}{x \log (\log (x-4))}\right )+3\right )}{(4-x) \log (x-4) \log (\log (x-4)) \left (2 x^2+6 x+\log ^2\left (\frac {4}{x \log (\log (x-4))}\right )-2 (x+3) \log \left (\frac {4}{x \log (\log (x-4))}\right )+9\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {x}{2 x^2-2 \log \left (\frac {4}{x \log (\log (x-4))}\right ) x+6 x+\log ^2\left (\frac {4}{x \log (\log (x-4))}\right )-6 \log \left (\frac {4}{x \log (\log (x-4))}\right )+9}-\frac {x \left (2 \log (x-4) \log (\log (x-4)) x^3-4 \log (x-4) \log (\log (x-4)) x^2-\log (x-4) \log (\log (x-4)) \log \left (\frac {4}{x \log (\log (x-4))}\right ) x^2+x^2-13 \log (x-4) \log (\log (x-4)) x+3 \log (x-4) \log (\log (x-4)) \log \left (\frac {4}{x \log (\log (x-4))}\right ) x-\log \left (\frac {4}{x \log (\log (x-4))}\right ) x+3 x-12 \log (x-4) \log (\log (x-4))+4 \log (x-4) \log (\log (x-4)) \log \left (\frac {4}{x \log (\log (x-4))}\right )\right )}{(x-4) \log (x-4) \log (\log (x-4)) \left (2 x^2-2 \log \left (\frac {4}{x \log (\log (x-4))}\right ) x+6 x+\log ^2\left (\frac {4}{x \log (\log (x-4))}\right )-6 \log \left (\frac {4}{x \log (\log (x-4))}\right )+9\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {x \left (x+(x-4) \log (x-4) \log (\log (x-4)) \left (\log \left (\frac {4}{x \log (\log (x-4))}\right )-2\right )\right ) \left (x-\log \left (\frac {4}{x \log (\log (x-4))}\right )+3\right )}{(4-x) \log (x-4) \log (\log (x-4)) \left (2 x^2+6 x+\log ^2\left (\frac {4}{x \log (\log (x-4))}\right )-2 (x+3) \log \left (\frac {4}{x \log (\log (x-4))}\right )+9\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {x}{2 x^2-2 \log \left (\frac {4}{x \log (\log (x-4))}\right ) x+6 x+\log ^2\left (\frac {4}{x \log (\log (x-4))}\right )-6 \log \left (\frac {4}{x \log (\log (x-4))}\right )+9}-\frac {x \left (2 \log (x-4) \log (\log (x-4)) x^3-4 \log (x-4) \log (\log (x-4)) x^2-\log (x-4) \log (\log (x-4)) \log \left (\frac {4}{x \log (\log (x-4))}\right ) x^2+x^2-13 \log (x-4) \log (\log (x-4)) x+3 \log (x-4) \log (\log (x-4)) \log \left (\frac {4}{x \log (\log (x-4))}\right ) x-\log \left (\frac {4}{x \log (\log (x-4))}\right ) x+3 x-12 \log (x-4) \log (\log (x-4))+4 \log (x-4) \log (\log (x-4)) \log \left (\frac {4}{x \log (\log (x-4))}\right )\right )}{(x-4) \log (x-4) \log (\log (x-4)) \left (2 x^2-2 \log \left (\frac {4}{x \log (\log (x-4))}\right ) x+6 x+\log ^2\left (\frac {4}{x \log (\log (x-4))}\right )-6 \log \left (\frac {4}{x \log (\log (x-4))}\right )+9\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {x \left (x+(x-4) \log (x-4) \log (\log (x-4)) \left (\log \left (\frac {4}{x \log (\log (x-4))}\right )-2\right )\right ) \left (x-\log \left (\frac {4}{x \log (\log (x-4))}\right )+3\right )}{(4-x) \log (x-4) \log (\log (x-4)) \left (2 x^2+6 x+\log ^2\left (\frac {4}{x \log (\log (x-4))}\right )-2 (x+3) \log \left (\frac {4}{x \log (\log (x-4))}\right )+9\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {x}{2 x^2-2 \log \left (\frac {4}{x \log (\log (x-4))}\right ) x+6 x+\log ^2\left (\frac {4}{x \log (\log (x-4))}\right )-6 \log \left (\frac {4}{x \log (\log (x-4))}\right )+9}-\frac {x \left (2 \log (x-4) \log (\log (x-4)) x^3-4 \log (x-4) \log (\log (x-4)) x^2-\log (x-4) \log (\log (x-4)) \log \left (\frac {4}{x \log (\log (x-4))}\right ) x^2+x^2-13 \log (x-4) \log (\log (x-4)) x+3 \log (x-4) \log (\log (x-4)) \log \left (\frac {4}{x \log (\log (x-4))}\right ) x-\log \left (\frac {4}{x \log (\log (x-4))}\right ) x+3 x-12 \log (x-4) \log (\log (x-4))+4 \log (x-4) \log (\log (x-4)) \log \left (\frac {4}{x \log (\log (x-4))}\right )\right )}{(x-4) \log (x-4) \log (\log (x-4)) \left (2 x^2-2 \log \left (\frac {4}{x \log (\log (x-4))}\right ) x+6 x+\log ^2\left (\frac {4}{x \log (\log (x-4))}\right )-6 \log \left (\frac {4}{x \log (\log (x-4))}\right )+9\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {x \left (x+(x-4) \log (x-4) \log (\log (x-4)) \left (\log \left (\frac {4}{x \log (\log (x-4))}\right )-2\right )\right ) \left (x-\log \left (\frac {4}{x \log (\log (x-4))}\right )+3\right )}{(4-x) \log (x-4) \log (\log (x-4)) \left (2 x^2+6 x+\log ^2\left (\frac {4}{x \log (\log (x-4))}\right )-2 (x+3) \log \left (\frac {4}{x \log (\log (x-4))}\right )+9\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {x}{2 x^2-2 \log \left (\frac {4}{x \log (\log (x-4))}\right ) x+6 x+\log ^2\left (\frac {4}{x \log (\log (x-4))}\right )-6 \log \left (\frac {4}{x \log (\log (x-4))}\right )+9}-\frac {x \left (2 \log (x-4) \log (\log (x-4)) x^3-4 \log (x-4) \log (\log (x-4)) x^2-\log (x-4) \log (\log (x-4)) \log \left (\frac {4}{x \log (\log (x-4))}\right ) x^2+x^2-13 \log (x-4) \log (\log (x-4)) x+3 \log (x-4) \log (\log (x-4)) \log \left (\frac {4}{x \log (\log (x-4))}\right ) x-\log \left (\frac {4}{x \log (\log (x-4))}\right ) x+3 x-12 \log (x-4) \log (\log (x-4))+4 \log (x-4) \log (\log (x-4)) \log \left (\frac {4}{x \log (\log (x-4))}\right )\right )}{(x-4) \log (x-4) \log (\log (x-4)) \left (2 x^2-2 \log \left (\frac {4}{x \log (\log (x-4))}\right ) x+6 x+\log ^2\left (\frac {4}{x \log (\log (x-4))}\right )-6 \log \left (\frac {4}{x \log (\log (x-4))}\right )+9\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {x \left (x+(x-4) \log (x-4) \log (\log (x-4)) \left (\log \left (\frac {4}{x \log (\log (x-4))}\right )-2\right )\right ) \left (x-\log \left (\frac {4}{x \log (\log (x-4))}\right )+3\right )}{(4-x) \log (x-4) \log (\log (x-4)) \left (2 x^2+6 x+\log ^2\left (\frac {4}{x \log (\log (x-4))}\right )-2 (x+3) \log \left (\frac {4}{x \log (\log (x-4))}\right )+9\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {x}{2 x^2-2 \log \left (\frac {4}{x \log (\log (x-4))}\right ) x+6 x+\log ^2\left (\frac {4}{x \log (\log (x-4))}\right )-6 \log \left (\frac {4}{x \log (\log (x-4))}\right )+9}-\frac {x \left (2 \log (x-4) \log (\log (x-4)) x^3-4 \log (x-4) \log (\log (x-4)) x^2-\log (x-4) \log (\log (x-4)) \log \left (\frac {4}{x \log (\log (x-4))}\right ) x^2+x^2-13 \log (x-4) \log (\log (x-4)) x+3 \log (x-4) \log (\log (x-4)) \log \left (\frac {4}{x \log (\log (x-4))}\right ) x-\log \left (\frac {4}{x \log (\log (x-4))}\right ) x+3 x-12 \log (x-4) \log (\log (x-4))+4 \log (x-4) \log (\log (x-4)) \log \left (\frac {4}{x \log (\log (x-4))}\right )\right )}{(x-4) \log (x-4) \log (\log (x-4)) \left (2 x^2-2 \log \left (\frac {4}{x \log (\log (x-4))}\right ) x+6 x+\log ^2\left (\frac {4}{x \log (\log (x-4))}\right )-6 \log \left (\frac {4}{x \log (\log (x-4))}\right )+9\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {x \left (x+(x-4) \log (x-4) \log (\log (x-4)) \left (\log \left (\frac {4}{x \log (\log (x-4))}\right )-2\right )\right ) \left (x-\log \left (\frac {4}{x \log (\log (x-4))}\right )+3\right )}{(4-x) \log (x-4) \log (\log (x-4)) \left (2 x^2+6 x+\log ^2\left (\frac {4}{x \log (\log (x-4))}\right )-2 (x+3) \log \left (\frac {4}{x \log (\log (x-4))}\right )+9\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {x}{2 x^2-2 \log \left (\frac {4}{x \log (\log (x-4))}\right ) x+6 x+\log ^2\left (\frac {4}{x \log (\log (x-4))}\right )-6 \log \left (\frac {4}{x \log (\log (x-4))}\right )+9}-\frac {x \left (2 \log (x-4) \log (\log (x-4)) x^3-4 \log (x-4) \log (\log (x-4)) x^2-\log (x-4) \log (\log (x-4)) \log \left (\frac {4}{x \log (\log (x-4))}\right ) x^2+x^2-13 \log (x-4) \log (\log (x-4)) x+3 \log (x-4) \log (\log (x-4)) \log \left (\frac {4}{x \log (\log (x-4))}\right ) x-\log \left (\frac {4}{x \log (\log (x-4))}\right ) x+3 x-12 \log (x-4) \log (\log (x-4))+4 \log (x-4) \log (\log (x-4)) \log \left (\frac {4}{x \log (\log (x-4))}\right )\right )}{(x-4) \log (x-4) \log (\log (x-4)) \left (2 x^2-2 \log \left (\frac {4}{x \log (\log (x-4))}\right ) x+6 x+\log ^2\left (\frac {4}{x \log (\log (x-4))}\right )-6 \log \left (\frac {4}{x \log (\log (x-4))}\right )+9\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {x \left (x+(x-4) \log (x-4) \log (\log (x-4)) \left (\log \left (\frac {4}{x \log (\log (x-4))}\right )-2\right )\right ) \left (x-\log \left (\frac {4}{x \log (\log (x-4))}\right )+3\right )}{(4-x) \log (x-4) \log (\log (x-4)) \left (2 x^2+6 x+\log ^2\left (\frac {4}{x \log (\log (x-4))}\right )-2 (x+3) \log \left (\frac {4}{x \log (\log (x-4))}\right )+9\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {x}{2 x^2-2 \log \left (\frac {4}{x \log (\log (x-4))}\right ) x+6 x+\log ^2\left (\frac {4}{x \log (\log (x-4))}\right )-6 \log \left (\frac {4}{x \log (\log (x-4))}\right )+9}-\frac {x \left (2 \log (x-4) \log (\log (x-4)) x^3-4 \log (x-4) \log (\log (x-4)) x^2-\log (x-4) \log (\log (x-4)) \log \left (\frac {4}{x \log (\log (x-4))}\right ) x^2+x^2-13 \log (x-4) \log (\log (x-4)) x+3 \log (x-4) \log (\log (x-4)) \log \left (\frac {4}{x \log (\log (x-4))}\right ) x-\log \left (\frac {4}{x \log (\log (x-4))}\right ) x+3 x-12 \log (x-4) \log (\log (x-4))+4 \log (x-4) \log (\log (x-4)) \log \left (\frac {4}{x \log (\log (x-4))}\right )\right )}{(x-4) \log (x-4) \log (\log (x-4)) \left (2 x^2-2 \log \left (\frac {4}{x \log (\log (x-4))}\right ) x+6 x+\log ^2\left (\frac {4}{x \log (\log (x-4))}\right )-6 \log \left (\frac {4}{x \log (\log (x-4))}\right )+9\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {x \left (x+(x-4) \log (x-4) \log (\log (x-4)) \left (\log \left (\frac {4}{x \log (\log (x-4))}\right )-2\right )\right ) \left (x-\log \left (\frac {4}{x \log (\log (x-4))}\right )+3\right )}{(4-x) \log (x-4) \log (\log (x-4)) \left (2 x^2+6 x+\log ^2\left (\frac {4}{x \log (\log (x-4))}\right )-2 (x+3) \log \left (\frac {4}{x \log (\log (x-4))}\right )+9\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {x}{2 x^2-2 \log \left (\frac {4}{x \log (\log (x-4))}\right ) x+6 x+\log ^2\left (\frac {4}{x \log (\log (x-4))}\right )-6 \log \left (\frac {4}{x \log (\log (x-4))}\right )+9}-\frac {x \left (2 \log (x-4) \log (\log (x-4)) x^3-4 \log (x-4) \log (\log (x-4)) x^2-\log (x-4) \log (\log (x-4)) \log \left (\frac {4}{x \log (\log (x-4))}\right ) x^2+x^2-13 \log (x-4) \log (\log (x-4)) x+3 \log (x-4) \log (\log (x-4)) \log \left (\frac {4}{x \log (\log (x-4))}\right ) x-\log \left (\frac {4}{x \log (\log (x-4))}\right ) x+3 x-12 \log (x-4) \log (\log (x-4))+4 \log (x-4) \log (\log (x-4)) \log \left (\frac {4}{x \log (\log (x-4))}\right )\right )}{(x-4) \log (x-4) \log (\log (x-4)) \left (2 x^2-2 \log \left (\frac {4}{x \log (\log (x-4))}\right ) x+6 x+\log ^2\left (\frac {4}{x \log (\log (x-4))}\right )-6 \log \left (\frac {4}{x \log (\log (x-4))}\right )+9\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {x \left (x+(x-4) \log (x-4) \log (\log (x-4)) \left (\log \left (\frac {4}{x \log (\log (x-4))}\right )-2\right )\right ) \left (x-\log \left (\frac {4}{x \log (\log (x-4))}\right )+3\right )}{(4-x) \log (x-4) \log (\log (x-4)) \left (2 x^2+6 x+\log ^2\left (\frac {4}{x \log (\log (x-4))}\right )-2 (x+3) \log \left (\frac {4}{x \log (\log (x-4))}\right )+9\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {x}{2 x^2-2 \log \left (\frac {4}{x \log (\log (x-4))}\right ) x+6 x+\log ^2\left (\frac {4}{x \log (\log (x-4))}\right )-6 \log \left (\frac {4}{x \log (\log (x-4))}\right )+9}-\frac {x \left (2 \log (x-4) \log (\log (x-4)) x^3-4 \log (x-4) \log (\log (x-4)) x^2-\log (x-4) \log (\log (x-4)) \log \left (\frac {4}{x \log (\log (x-4))}\right ) x^2+x^2-13 \log (x-4) \log (\log (x-4)) x+3 \log (x-4) \log (\log (x-4)) \log \left (\frac {4}{x \log (\log (x-4))}\right ) x-\log \left (\frac {4}{x \log (\log (x-4))}\right ) x+3 x-12 \log (x-4) \log (\log (x-4))+4 \log (x-4) \log (\log (x-4)) \log \left (\frac {4}{x \log (\log (x-4))}\right )\right )}{(x-4) \log (x-4) \log (\log (x-4)) \left (2 x^2-2 \log \left (\frac {4}{x \log (\log (x-4))}\right ) x+6 x+\log ^2\left (\frac {4}{x \log (\log (x-4))}\right )-6 \log \left (\frac {4}{x \log (\log (x-4))}\right )+9\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {x \left (x+(x-4) \log (x-4) \log (\log (x-4)) \left (\log \left (\frac {4}{x \log (\log (x-4))}\right )-2\right )\right ) \left (x-\log \left (\frac {4}{x \log (\log (x-4))}\right )+3\right )}{(4-x) \log (x-4) \log (\log (x-4)) \left (2 x^2+6 x+\log ^2\left (\frac {4}{x \log (\log (x-4))}\right )-2 (x+3) \log \left (\frac {4}{x \log (\log (x-4))}\right )+9\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {x}{2 x^2-2 \log \left (\frac {4}{x \log (\log (x-4))}\right ) x+6 x+\log ^2\left (\frac {4}{x \log (\log (x-4))}\right )-6 \log \left (\frac {4}{x \log (\log (x-4))}\right )+9}-\frac {x \left (2 \log (x-4) \log (\log (x-4)) x^3-4 \log (x-4) \log (\log (x-4)) x^2-\log (x-4) \log (\log (x-4)) \log \left (\frac {4}{x \log (\log (x-4))}\right ) x^2+x^2-13 \log (x-4) \log (\log (x-4)) x+3 \log (x-4) \log (\log (x-4)) \log \left (\frac {4}{x \log (\log (x-4))}\right ) x-\log \left (\frac {4}{x \log (\log (x-4))}\right ) x+3 x-12 \log (x-4) \log (\log (x-4))+4 \log (x-4) \log (\log (x-4)) \log \left (\frac {4}{x \log (\log (x-4))}\right )\right )}{(x-4) \log (x-4) \log (\log (x-4)) \left (2 x^2-2 \log \left (\frac {4}{x \log (\log (x-4))}\right ) x+6 x+\log ^2\left (\frac {4}{x \log (\log (x-4))}\right )-6 \log \left (\frac {4}{x \log (\log (x-4))}\right )+9\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {x \left (x+(x-4) \log (x-4) \log (\log (x-4)) \left (\log \left (\frac {4}{x \log (\log (x-4))}\right )-2\right )\right ) \left (x-\log \left (\frac {4}{x \log (\log (x-4))}\right )+3\right )}{(4-x) \log (x-4) \log (\log (x-4)) \left (2 x^2+6 x+\log ^2\left (\frac {4}{x \log (\log (x-4))}\right )-2 (x+3) \log \left (\frac {4}{x \log (\log (x-4))}\right )+9\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {x}{2 x^2-2 \log \left (\frac {4}{x \log (\log (x-4))}\right ) x+6 x+\log ^2\left (\frac {4}{x \log (\log (x-4))}\right )-6 \log \left (\frac {4}{x \log (\log (x-4))}\right )+9}-\frac {x \left (2 \log (x-4) \log (\log (x-4)) x^3-4 \log (x-4) \log (\log (x-4)) x^2-\log (x-4) \log (\log (x-4)) \log \left (\frac {4}{x \log (\log (x-4))}\right ) x^2+x^2-13 \log (x-4) \log (\log (x-4)) x+3 \log (x-4) \log (\log (x-4)) \log \left (\frac {4}{x \log (\log (x-4))}\right ) x-\log \left (\frac {4}{x \log (\log (x-4))}\right ) x+3 x-12 \log (x-4) \log (\log (x-4))+4 \log (x-4) \log (\log (x-4)) \log \left (\frac {4}{x \log (\log (x-4))}\right )\right )}{(x-4) \log (x-4) \log (\log (x-4)) \left (2 x^2-2 \log \left (\frac {4}{x \log (\log (x-4))}\right ) x+6 x+\log ^2\left (\frac {4}{x \log (\log (x-4))}\right )-6 \log \left (\frac {4}{x \log (\log (x-4))}\right )+9\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {x \left (x+(x-4) \log (x-4) \log (\log (x-4)) \left (\log \left (\frac {4}{x \log (\log (x-4))}\right )-2\right )\right ) \left (x-\log \left (\frac {4}{x \log (\log (x-4))}\right )+3\right )}{(4-x) \log (x-4) \log (\log (x-4)) \left (2 x^2+6 x+\log ^2\left (\frac {4}{x \log (\log (x-4))}\right )-2 (x+3) \log \left (\frac {4}{x \log (\log (x-4))}\right )+9\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {x}{2 x^2-2 \log \left (\frac {4}{x \log (\log (x-4))}\right ) x+6 x+\log ^2\left (\frac {4}{x \log (\log (x-4))}\right )-6 \log \left (\frac {4}{x \log (\log (x-4))}\right )+9}-\frac {x \left (2 \log (x-4) \log (\log (x-4)) x^3-4 \log (x-4) \log (\log (x-4)) x^2-\log (x-4) \log (\log (x-4)) \log \left (\frac {4}{x \log (\log (x-4))}\right ) x^2+x^2-13 \log (x-4) \log (\log (x-4)) x+3 \log (x-4) \log (\log (x-4)) \log \left (\frac {4}{x \log (\log (x-4))}\right ) x-\log \left (\frac {4}{x \log (\log (x-4))}\right ) x+3 x-12 \log (x-4) \log (\log (x-4))+4 \log (x-4) \log (\log (x-4)) \log \left (\frac {4}{x \log (\log (x-4))}\right )\right )}{(x-4) \log (x-4) \log (\log (x-4)) \left (2 x^2-2 \log \left (\frac {4}{x \log (\log (x-4))}\right ) x+6 x+\log ^2\left (\frac {4}{x \log (\log (x-4))}\right )-6 \log \left (\frac {4}{x \log (\log (x-4))}\right )+9\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {x \left (x+(x-4) \log (x-4) \log (\log (x-4)) \left (\log \left (\frac {4}{x \log (\log (x-4))}\right )-2\right )\right ) \left (x-\log \left (\frac {4}{x \log (\log (x-4))}\right )+3\right )}{(4-x) \log (x-4) \log (\log (x-4)) \left (2 x^2+6 x+\log ^2\left (\frac {4}{x \log (\log (x-4))}\right )-2 (x+3) \log \left (\frac {4}{x \log (\log (x-4))}\right )+9\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {x}{2 x^2-2 \log \left (\frac {4}{x \log (\log (x-4))}\right ) x+6 x+\log ^2\left (\frac {4}{x \log (\log (x-4))}\right )-6 \log \left (\frac {4}{x \log (\log (x-4))}\right )+9}-\frac {x \left (2 \log (x-4) \log (\log (x-4)) x^3-4 \log (x-4) \log (\log (x-4)) x^2-\log (x-4) \log (\log (x-4)) \log \left (\frac {4}{x \log (\log (x-4))}\right ) x^2+x^2-13 \log (x-4) \log (\log (x-4)) x+3 \log (x-4) \log (\log (x-4)) \log \left (\frac {4}{x \log (\log (x-4))}\right ) x-\log \left (\frac {4}{x \log (\log (x-4))}\right ) x+3 x-12 \log (x-4) \log (\log (x-4))+4 \log (x-4) \log (\log (x-4)) \log \left (\frac {4}{x \log (\log (x-4))}\right )\right )}{(x-4) \log (x-4) \log (\log (x-4)) \left (2 x^2-2 \log \left (\frac {4}{x \log (\log (x-4))}\right ) x+6 x+\log ^2\left (\frac {4}{x \log (\log (x-4))}\right )-6 \log \left (\frac {4}{x \log (\log (x-4))}\right )+9\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -2 \int \frac {x \left (x+(x-4) \log (x-4) \log (\log (x-4)) \left (\log \left (\frac {4}{x \log (\log (x-4))}\right )-2\right )\right ) \left (x-\log \left (\frac {4}{x \log (\log (x-4))}\right )+3\right )}{(4-x) \log (x-4) \log (\log (x-4)) \left (2 x^2+6 x+\log ^2\left (\frac {4}{x \log (\log (x-4))}\right )-2 (x+3) \log \left (\frac {4}{x \log (\log (x-4))}\right )+9\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 \int \left (\frac {x}{2 x^2-2 \log \left (\frac {4}{x \log (\log (x-4))}\right ) x+6 x+\log ^2\left (\frac {4}{x \log (\log (x-4))}\right )-6 \log \left (\frac {4}{x \log (\log (x-4))}\right )+9}-\frac {x \left (2 \log (x-4) \log (\log (x-4)) x^3-4 \log (x-4) \log (\log (x-4)) x^2-\log (x-4) \log (\log (x-4)) \log \left (\frac {4}{x \log (\log (x-4))}\right ) x^2+x^2-13 \log (x-4) \log (\log (x-4)) x+3 \log (x-4) \log (\log (x-4)) \log \left (\frac {4}{x \log (\log (x-4))}\right ) x-\log \left (\frac {4}{x \log (\log (x-4))}\right ) x+3 x-12 \log (x-4) \log (\log (x-4))+4 \log (x-4) \log (\log (x-4)) \log \left (\frac {4}{x \log (\log (x-4))}\right )\right )}{(x-4) \log (x-4) \log (\log (x-4)) \left (2 x^2-2 \log \left (\frac {4}{x \log (\log (x-4))}\right ) x+6 x+\log ^2\left (\frac {4}{x \log (\log (x-4))}\right )-6 \log \left (\frac {4}{x \log (\log (x-4))}\right )+9\right )^2}\right )dx\) |
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)*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]]*Log[4/(x*L og[Log[-4 + x]])]^2)/((-324 - 351*x - 180*x^2 - 24*x^3 + 8*x^4 + 4*x^5)*Lo g[-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]
3.9.34.3.1 Defintions of rubi rules used
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
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 | \(\text {Expression too large to display}\) | \(1024\) |
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)*l n(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)
Time = 0.26 (sec) , antiderivative size = 50, normalized size of antiderivative = 1.47 \[ \int \frac {6 x^2+2 x^3+\left (48 x+4 x^2-4 x^3\right ) \log (-4+x) \log (\log (-4+x))+\left (-2 x^2+\left (-40 x+2 x^2+2 x^3\right ) \log (-4+x) \log (\log (-4+x))\right ) \log \left (\frac {4}{x \log (\log (-4+x))}\right )+\left (8 x-2 x^2\right ) \log (-4+x) \log (\log (-4+x)) \log ^2\left (\frac {4}{x \log (\log (-4+x))}\right )}{\left (-324-351 x-180 x^2-24 x^3+8 x^4+4 x^5\right ) \log (-4+x) \log (\log (-4+x))+\left (432+324 x+84 x^2-16 x^3-8 x^4\right ) \log (-4+x) \log (\log (-4+x)) \log \left (\frac {4}{x \log (\log (-4+x))}\right )+\left (-216-90 x+4 x^2+8 x^3\right ) \log (-4+x) \log (\log (-4+x)) \log ^2\left (\frac {4}{x \log (\log (-4+x))}\right )+\left (48+4 x-4 x^2\right ) \log (-4+x) \log (\log (-4+x)) \log ^3\left (\frac {4}{x \log (\log (-4+x))}\right )+(-4+x) \log (-4+x) \log (\log (-4+x)) \log ^4\left (\frac {4}{x \log (\log (-4+x))}\right )} \, dx=-\frac {x^{2}}{2 \, x^{2} - 2 \, {\left (x + 3\right )} \log \left (\frac {4}{x \log \left (\log \left (x - 4\right )\right )}\right ) + \log \left (\frac {4}{x \log \left (\log \left (x - 4\right )\right )}\right )^{2} + 6 \, x + 9} \]
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(l og(x-4))*log(4/x/log(log(x-4)))^4+(-4*x^2+4*x+48)*log(x-4)*log(log(x-4))*l og(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=\
Time = 0.43 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.35 \[ \int \frac {6 x^2+2 x^3+\left (48 x+4 x^2-4 x^3\right ) \log (-4+x) \log (\log (-4+x))+\left (-2 x^2+\left (-40 x+2 x^2+2 x^3\right ) \log (-4+x) \log (\log (-4+x))\right ) \log \left (\frac {4}{x \log (\log (-4+x))}\right )+\left (8 x-2 x^2\right ) \log (-4+x) \log (\log (-4+x)) \log ^2\left (\frac {4}{x \log (\log (-4+x))}\right )}{\left (-324-351 x-180 x^2-24 x^3+8 x^4+4 x^5\right ) \log (-4+x) \log (\log (-4+x))+\left (432+324 x+84 x^2-16 x^3-8 x^4\right ) \log (-4+x) \log (\log (-4+x)) \log \left (\frac {4}{x \log (\log (-4+x))}\right )+\left (-216-90 x+4 x^2+8 x^3\right ) \log (-4+x) \log (\log (-4+x)) \log ^2\left (\frac {4}{x \log (\log (-4+x))}\right )+\left (48+4 x-4 x^2\right ) \log (-4+x) \log (\log (-4+x)) \log ^3\left (\frac {4}{x \log (\log (-4+x))}\right )+(-4+x) \log (-4+x) \log (\log (-4+x)) \log ^4\left (\frac {4}{x \log (\log (-4+x))}\right )} \, dx=- \frac {x^{2}}{2 x^{2} + 6 x + \left (- 2 x - 6\right ) \log {\left (\frac {4}{x \log {\left (\log {\left (x - 4 \right )} \right )}} \right )} + \log {\left (\frac {4}{x \log {\left (\log {\left (x - 4 \right )} \right )}} \right )}^{2} + 9} \]
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(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)
-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)
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 \[ \int \frac {6 x^2+2 x^3+\left (48 x+4 x^2-4 x^3\right ) \log (-4+x) \log (\log (-4+x))+\left (-2 x^2+\left (-40 x+2 x^2+2 x^3\right ) \log (-4+x) \log (\log (-4+x))\right ) \log \left (\frac {4}{x \log (\log (-4+x))}\right )+\left (8 x-2 x^2\right ) \log (-4+x) \log (\log (-4+x)) \log ^2\left (\frac {4}{x \log (\log (-4+x))}\right )}{\left (-324-351 x-180 x^2-24 x^3+8 x^4+4 x^5\right ) \log (-4+x) \log (\log (-4+x))+\left (432+324 x+84 x^2-16 x^3-8 x^4\right ) \log (-4+x) \log (\log (-4+x)) \log \left (\frac {4}{x \log (\log (-4+x))}\right )+\left (-216-90 x+4 x^2+8 x^3\right ) \log (-4+x) \log (\log (-4+x)) \log ^2\left (\frac {4}{x \log (\log (-4+x))}\right )+\left (48+4 x-4 x^2\right ) \log (-4+x) \log (\log (-4+x)) \log ^3\left (\frac {4}{x \log (\log (-4+x))}\right )+(-4+x) \log (-4+x) \log (\log (-4+x)) \log ^4\left (\frac {4}{x \log (\log (-4+x))}\right )} \, dx=-\frac {x^{2}}{2 \, x^{2} - 2 \, x {\left (2 \, \log \left (2\right ) - 3\right )} + 4 \, \log \left (2\right )^{2} + 2 \, {\left (x - 2 \, \log \left (2\right ) + 3\right )} \log \left (x\right ) + \log \left (x\right )^{2} + 2 \, {\left (x - 2 \, \log \left (2\right ) + \log \left (x\right ) + 3\right )} \log \left (\log \left (\log \left (x - 4\right )\right )\right ) + \log \left (\log \left (\log \left (x - 4\right )\right )\right )^{2} - 12 \, \log \left (2\right ) + 9} \]
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(l og(x-4))*log(4/x/log(log(x-4)))^4+(-4*x^2+4*x+48)*log(x-4)*log(log(x-4))*l og(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=\
-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(lo g(log(x - 4)))^2 - 12*log(2) + 9)
Timed out. \[ \int \frac {6 x^2+2 x^3+\left (48 x+4 x^2-4 x^3\right ) \log (-4+x) \log (\log (-4+x))+\left (-2 x^2+\left (-40 x+2 x^2+2 x^3\right ) \log (-4+x) \log (\log (-4+x))\right ) \log \left (\frac {4}{x \log (\log (-4+x))}\right )+\left (8 x-2 x^2\right ) \log (-4+x) \log (\log (-4+x)) \log ^2\left (\frac {4}{x \log (\log (-4+x))}\right )}{\left (-324-351 x-180 x^2-24 x^3+8 x^4+4 x^5\right ) \log (-4+x) \log (\log (-4+x))+\left (432+324 x+84 x^2-16 x^3-8 x^4\right ) \log (-4+x) \log (\log (-4+x)) \log \left (\frac {4}{x \log (\log (-4+x))}\right )+\left (-216-90 x+4 x^2+8 x^3\right ) \log (-4+x) \log (\log (-4+x)) \log ^2\left (\frac {4}{x \log (\log (-4+x))}\right )+\left (48+4 x-4 x^2\right ) \log (-4+x) \log (\log (-4+x)) \log ^3\left (\frac {4}{x \log (\log (-4+x))}\right )+(-4+x) \log (-4+x) \log (\log (-4+x)) \log ^4\left (\frac {4}{x \log (\log (-4+x))}\right )} \, dx=\text {Timed out} \]
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(l og(x-4))*log(4/x/log(log(x-4)))^4+(-4*x^2+4*x+48)*log(x-4)*log(log(x-4))*l og(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=\
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 \]
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)
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)