Integrand size = 267, antiderivative size = 31 \[ \int \frac {-7742196 x^8+7779240 x^7 \log ^2(2)+\left (-7461720 x^8+7482888 x^7 \log ^2(2)\right ) \log \left (-x+\log ^2(2)\right )+\left (-2874816 x^8+2878848 x^7 \log ^2(2)\right ) \log ^2\left (-x+\log ^2(2)\right )+\left (-553472 x^8+553728 x^7 \log ^2(2)\right ) \log ^3\left (-x+\log ^2(2)\right )+\left (-53248 x^8+53248 x^7 \log ^2(2)\right ) \log ^4\left (-x+\log ^2(2)\right )+\left (-2048 x^8+2048 x^7 \log ^2(2)\right ) \log ^5\left (-x+\log ^2(2)\right )}{-3125 x+3125 \log ^2(2)+\left (-3125 x+3125 \log ^2(2)\right ) \log \left (-x+\log ^2(2)\right )+\left (-1250 x+1250 \log ^2(2)\right ) \log ^2\left (-x+\log ^2(2)\right )+\left (-250 x+250 \log ^2(2)\right ) \log ^3\left (-x+\log ^2(2)\right )+\left (-25 x+25 \log ^2(2)\right ) \log ^4\left (-x+\log ^2(2)\right )+\left (-x+\log ^2(2)\right ) \log ^5\left (-x+\log ^2(2)\right )} \, dx=x^8 \left (5+\frac {-x+\frac {x}{5+\log \left (-x+\log ^2(2)\right )}}{x}\right )^4 \] Output:
((x/(5+ln(ln(2)^2-x))-x)/x+5)^4*x^8
Leaf count is larger than twice the leaf count of optimal. \(122\) vs. \(2(31)=62\).
Time = 10.06 (sec) , antiderivative size = 122, normalized size of antiderivative = 3.94 \[ \int \frac {-7742196 x^8+7779240 x^7 \log ^2(2)+\left (-7461720 x^8+7482888 x^7 \log ^2(2)\right ) \log \left (-x+\log ^2(2)\right )+\left (-2874816 x^8+2878848 x^7 \log ^2(2)\right ) \log ^2\left (-x+\log ^2(2)\right )+\left (-553472 x^8+553728 x^7 \log ^2(2)\right ) \log ^3\left (-x+\log ^2(2)\right )+\left (-53248 x^8+53248 x^7 \log ^2(2)\right ) \log ^4\left (-x+\log ^2(2)\right )+\left (-2048 x^8+2048 x^7 \log ^2(2)\right ) \log ^5\left (-x+\log ^2(2)\right )}{-3125 x+3125 \log ^2(2)+\left (-3125 x+3125 \log ^2(2)\right ) \log \left (-x+\log ^2(2)\right )+\left (-1250 x+1250 \log ^2(2)\right ) \log ^2\left (-x+\log ^2(2)\right )+\left (-250 x+250 \log ^2(2)\right ) \log ^3\left (-x+\log ^2(2)\right )+\left (-25 x+25 \log ^2(2)\right ) \log ^4\left (-x+\log ^2(2)\right )+\left (-x+\log ^2(2)\right ) \log ^5\left (-x+\log ^2(2)\right )} \, dx=\frac {194481 x^8-160000 \log ^{16}(2)+16 \left (9261 x^8-8000 \log ^{16}(2)\right ) \log \left (-x+\log ^2(2)\right )+96 \left (441 x^8-400 \log ^{16}(2)\right ) \log ^2\left (-x+\log ^2(2)\right )+256 \left (21 x^8-20 \log ^{16}(2)\right ) \log ^3\left (-x+\log ^2(2)\right )+256 \left (x^8-\log ^{16}(2)\right ) \log ^4\left (-x+\log ^2(2)\right )}{\left (5+\log \left (-x+\log ^2(2)\right )\right )^4} \] Input:
Integrate[(-7742196*x^8 + 7779240*x^7*Log[2]^2 + (-7461720*x^8 + 7482888*x ^7*Log[2]^2)*Log[-x + Log[2]^2] + (-2874816*x^8 + 2878848*x^7*Log[2]^2)*Lo g[-x + Log[2]^2]^2 + (-553472*x^8 + 553728*x^7*Log[2]^2)*Log[-x + Log[2]^2 ]^3 + (-53248*x^8 + 53248*x^7*Log[2]^2)*Log[-x + Log[2]^2]^4 + (-2048*x^8 + 2048*x^7*Log[2]^2)*Log[-x + Log[2]^2]^5)/(-3125*x + 3125*Log[2]^2 + (-31 25*x + 3125*Log[2]^2)*Log[-x + Log[2]^2] + (-1250*x + 1250*Log[2]^2)*Log[- x + Log[2]^2]^2 + (-250*x + 250*Log[2]^2)*Log[-x + Log[2]^2]^3 + (-25*x + 25*Log[2]^2)*Log[-x + Log[2]^2]^4 + (-x + Log[2]^2)*Log[-x + Log[2]^2]^5), x]
Output:
(194481*x^8 - 160000*Log[2]^16 + 16*(9261*x^8 - 8000*Log[2]^16)*Log[-x + L og[2]^2] + 96*(441*x^8 - 400*Log[2]^16)*Log[-x + Log[2]^2]^2 + 256*(21*x^8 - 20*Log[2]^16)*Log[-x + Log[2]^2]^3 + 256*(x^8 - Log[2]^16)*Log[-x + Log [2]^2]^4)/(5 + Log[-x + Log[2]^2])^4
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.
| \(\displaystyle \int \frac {-7742196 x^8+7779240 x^7 \log ^2(2)+\left (2878848 x^7 \log ^2(2)-2874816 x^8\right ) \log ^2\left (\log ^2(2)-x\right )+\left (7482888 x^7 \log ^2(2)-7461720 x^8\right ) \log \left (\log ^2(2)-x\right )+\left (2048 x^7 \log ^2(2)-2048 x^8\right ) \log ^5\left (\log ^2(2)-x\right )+\left (53248 x^7 \log ^2(2)-53248 x^8\right ) \log ^4\left (\log ^2(2)-x\right )+\left (553728 x^7 \log ^2(2)-553472 x^8\right ) \log ^3\left (\log ^2(2)-x\right )}{-3125 x+\left (1250 \log ^2(2)-1250 x\right ) \log ^2\left (\log ^2(2)-x\right )+\left (3125 \log ^2(2)-3125 x\right ) \log \left (\log ^2(2)-x\right )+\left (\log ^2(2)-x\right ) \log ^5\left (\log ^2(2)-x\right )+\left (25 \log ^2(2)-25 x\right ) \log ^4\left (\log ^2(2)-x\right )+\left (250 \log ^2(2)-250 x\right ) \log ^3\left (\log ^2(2)-x\right )+3125 \log ^2(2)} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {4 x^7 \left (4 \log \left (\log ^2(2)-x\right )+21\right )^3 \left (209 x+8 \left (x-\log ^2(2)\right ) \log ^2\left (\log ^2(2)-x\right )+82 \left (x-\log ^2(2)\right ) \log \left (\log ^2(2)-x\right )-210 \log ^2(2)\right )}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^5}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 4 \int \frac {x^7 \left (4 \log \left (\log ^2(2)-x\right )+21\right )^3 \left (8 \left (x-\log ^2(2)\right ) \log ^2\left (\log ^2(2)-x\right )+82 \left (x-\log ^2(2)\right ) \log \left (\log ^2(2)-x\right )+209 x-210 \log ^2(2)\right )}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^5}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 4 \int \left (-\frac {x^8}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^5}+\frac {512 x^7}{\log \left (\log ^2(2)-x\right )+5}+\frac {64 \left (2 x-3 \log ^2(2)\right ) x^7}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^2}-\frac {16 \left (x+2 \log ^2(2)\right ) x^7}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^3}-\frac {2 \left (5 x+\log ^2(2)\right ) x^7}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^4}+512 x^7\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 4 \int \frac {x^7 \left (4 \log \left (\log ^2(2)-x\right )+21\right )^3 \left (8 \left (x-\log ^2(2)\right ) \log ^2\left (\log ^2(2)-x\right )+82 \left (x-\log ^2(2)\right ) \log \left (\log ^2(2)-x\right )+209 x-210 \log ^2(2)\right )}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^5}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 4 \int \left (-\frac {x^8}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^5}+\frac {512 x^7}{\log \left (\log ^2(2)-x\right )+5}+\frac {64 \left (2 x-3 \log ^2(2)\right ) x^7}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^2}-\frac {16 \left (x+2 \log ^2(2)\right ) x^7}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^3}-\frac {2 \left (5 x+\log ^2(2)\right ) x^7}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^4}+512 x^7\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 4 \int \frac {x^7 \left (4 \log \left (\log ^2(2)-x\right )+21\right )^3 \left (8 \left (x-\log ^2(2)\right ) \log ^2\left (\log ^2(2)-x\right )+82 \left (x-\log ^2(2)\right ) \log \left (\log ^2(2)-x\right )+209 x-210 \log ^2(2)\right )}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^5}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 4 \int \left (-\frac {x^8}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^5}+\frac {512 x^7}{\log \left (\log ^2(2)-x\right )+5}+\frac {64 \left (2 x-3 \log ^2(2)\right ) x^7}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^2}-\frac {16 \left (x+2 \log ^2(2)\right ) x^7}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^3}-\frac {2 \left (5 x+\log ^2(2)\right ) x^7}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^4}+512 x^7\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 4 \int \frac {x^7 \left (4 \log \left (\log ^2(2)-x\right )+21\right )^3 \left (8 \left (x-\log ^2(2)\right ) \log ^2\left (\log ^2(2)-x\right )+82 \left (x-\log ^2(2)\right ) \log \left (\log ^2(2)-x\right )+209 x-210 \log ^2(2)\right )}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^5}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 4 \int \left (-\frac {x^8}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^5}+\frac {512 x^7}{\log \left (\log ^2(2)-x\right )+5}+\frac {64 \left (2 x-3 \log ^2(2)\right ) x^7}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^2}-\frac {16 \left (x+2 \log ^2(2)\right ) x^7}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^3}-\frac {2 \left (5 x+\log ^2(2)\right ) x^7}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^4}+512 x^7\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 4 \int \frac {x^7 \left (4 \log \left (\log ^2(2)-x\right )+21\right )^3 \left (8 \left (x-\log ^2(2)\right ) \log ^2\left (\log ^2(2)-x\right )+82 \left (x-\log ^2(2)\right ) \log \left (\log ^2(2)-x\right )+209 x-210 \log ^2(2)\right )}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^5}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 4 \int \left (-\frac {x^8}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^5}+\frac {512 x^7}{\log \left (\log ^2(2)-x\right )+5}+\frac {64 \left (2 x-3 \log ^2(2)\right ) x^7}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^2}-\frac {16 \left (x+2 \log ^2(2)\right ) x^7}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^3}-\frac {2 \left (5 x+\log ^2(2)\right ) x^7}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^4}+512 x^7\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 4 \int \frac {x^7 \left (4 \log \left (\log ^2(2)-x\right )+21\right )^3 \left (8 \left (x-\log ^2(2)\right ) \log ^2\left (\log ^2(2)-x\right )+82 \left (x-\log ^2(2)\right ) \log \left (\log ^2(2)-x\right )+209 x-210 \log ^2(2)\right )}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^5}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 4 \int \left (-\frac {x^8}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^5}+\frac {512 x^7}{\log \left (\log ^2(2)-x\right )+5}+\frac {64 \left (2 x-3 \log ^2(2)\right ) x^7}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^2}-\frac {16 \left (x+2 \log ^2(2)\right ) x^7}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^3}-\frac {2 \left (5 x+\log ^2(2)\right ) x^7}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^4}+512 x^7\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 4 \int \frac {x^7 \left (4 \log \left (\log ^2(2)-x\right )+21\right )^3 \left (8 \left (x-\log ^2(2)\right ) \log ^2\left (\log ^2(2)-x\right )+82 \left (x-\log ^2(2)\right ) \log \left (\log ^2(2)-x\right )+209 x-210 \log ^2(2)\right )}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^5}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 4 \int \left (-\frac {x^8}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^5}+\frac {512 x^7}{\log \left (\log ^2(2)-x\right )+5}+\frac {64 \left (2 x-3 \log ^2(2)\right ) x^7}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^2}-\frac {16 \left (x+2 \log ^2(2)\right ) x^7}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^3}-\frac {2 \left (5 x+\log ^2(2)\right ) x^7}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^4}+512 x^7\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 4 \int \frac {x^7 \left (4 \log \left (\log ^2(2)-x\right )+21\right )^3 \left (8 \left (x-\log ^2(2)\right ) \log ^2\left (\log ^2(2)-x\right )+82 \left (x-\log ^2(2)\right ) \log \left (\log ^2(2)-x\right )+209 x-210 \log ^2(2)\right )}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^5}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 4 \int \left (-\frac {x^8}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^5}+\frac {512 x^7}{\log \left (\log ^2(2)-x\right )+5}+\frac {64 \left (2 x-3 \log ^2(2)\right ) x^7}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^2}-\frac {16 \left (x+2 \log ^2(2)\right ) x^7}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^3}-\frac {2 \left (5 x+\log ^2(2)\right ) x^7}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^4}+512 x^7\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 4 \int \frac {x^7 \left (4 \log \left (\log ^2(2)-x\right )+21\right )^3 \left (8 \left (x-\log ^2(2)\right ) \log ^2\left (\log ^2(2)-x\right )+82 \left (x-\log ^2(2)\right ) \log \left (\log ^2(2)-x\right )+209 x-210 \log ^2(2)\right )}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^5}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 4 \int \left (-\frac {x^8}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^5}+\frac {512 x^7}{\log \left (\log ^2(2)-x\right )+5}+\frac {64 \left (2 x-3 \log ^2(2)\right ) x^7}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^2}-\frac {16 \left (x+2 \log ^2(2)\right ) x^7}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^3}-\frac {2 \left (5 x+\log ^2(2)\right ) x^7}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^4}+512 x^7\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 4 \int \frac {x^7 \left (4 \log \left (\log ^2(2)-x\right )+21\right )^3 \left (8 \left (x-\log ^2(2)\right ) \log ^2\left (\log ^2(2)-x\right )+82 \left (x-\log ^2(2)\right ) \log \left (\log ^2(2)-x\right )+209 x-210 \log ^2(2)\right )}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^5}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 4 \int \left (-\frac {x^8}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^5}+\frac {512 x^7}{\log \left (\log ^2(2)-x\right )+5}+\frac {64 \left (2 x-3 \log ^2(2)\right ) x^7}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^2}-\frac {16 \left (x+2 \log ^2(2)\right ) x^7}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^3}-\frac {2 \left (5 x+\log ^2(2)\right ) x^7}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^4}+512 x^7\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 4 \int \frac {x^7 \left (4 \log \left (\log ^2(2)-x\right )+21\right )^3 \left (8 \left (x-\log ^2(2)\right ) \log ^2\left (\log ^2(2)-x\right )+82 \left (x-\log ^2(2)\right ) \log \left (\log ^2(2)-x\right )+209 x-210 \log ^2(2)\right )}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^5}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 4 \int \left (-\frac {x^8}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^5}+\frac {512 x^7}{\log \left (\log ^2(2)-x\right )+5}+\frac {64 \left (2 x-3 \log ^2(2)\right ) x^7}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^2}-\frac {16 \left (x+2 \log ^2(2)\right ) x^7}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^3}-\frac {2 \left (5 x+\log ^2(2)\right ) x^7}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^4}+512 x^7\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 4 \int \frac {x^7 \left (4 \log \left (\log ^2(2)-x\right )+21\right )^3 \left (8 \left (x-\log ^2(2)\right ) \log ^2\left (\log ^2(2)-x\right )+82 \left (x-\log ^2(2)\right ) \log \left (\log ^2(2)-x\right )+209 x-210 \log ^2(2)\right )}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^5}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 4 \int \left (-\frac {x^8}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^5}+\frac {512 x^7}{\log \left (\log ^2(2)-x\right )+5}+\frac {64 \left (2 x-3 \log ^2(2)\right ) x^7}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^2}-\frac {16 \left (x+2 \log ^2(2)\right ) x^7}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^3}-\frac {2 \left (5 x+\log ^2(2)\right ) x^7}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^4}+512 x^7\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 4 \int \frac {x^7 \left (4 \log \left (\log ^2(2)-x\right )+21\right )^3 \left (8 \left (x-\log ^2(2)\right ) \log ^2\left (\log ^2(2)-x\right )+82 \left (x-\log ^2(2)\right ) \log \left (\log ^2(2)-x\right )+209 x-210 \log ^2(2)\right )}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^5}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 4 \int \left (-\frac {x^8}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^5}+\frac {512 x^7}{\log \left (\log ^2(2)-x\right )+5}+\frac {64 \left (2 x-3 \log ^2(2)\right ) x^7}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^2}-\frac {16 \left (x+2 \log ^2(2)\right ) x^7}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^3}-\frac {2 \left (5 x+\log ^2(2)\right ) x^7}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^4}+512 x^7\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 4 \int \frac {x^7 \left (4 \log \left (\log ^2(2)-x\right )+21\right )^3 \left (8 \left (x-\log ^2(2)\right ) \log ^2\left (\log ^2(2)-x\right )+82 \left (x-\log ^2(2)\right ) \log \left (\log ^2(2)-x\right )+209 x-210 \log ^2(2)\right )}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^5}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 4 \int \left (-\frac {x^8}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^5}+\frac {512 x^7}{\log \left (\log ^2(2)-x\right )+5}+\frac {64 \left (2 x-3 \log ^2(2)\right ) x^7}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^2}-\frac {16 \left (x+2 \log ^2(2)\right ) x^7}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^3}-\frac {2 \left (5 x+\log ^2(2)\right ) x^7}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^4}+512 x^7\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 4 \int \frac {x^7 \left (4 \log \left (\log ^2(2)-x\right )+21\right )^3 \left (8 \left (x-\log ^2(2)\right ) \log ^2\left (\log ^2(2)-x\right )+82 \left (x-\log ^2(2)\right ) \log \left (\log ^2(2)-x\right )+209 x-210 \log ^2(2)\right )}{\left (x-\log ^2(2)\right ) \left (\log \left (\log ^2(2)-x\right )+5\right )^5}dx\) |
Input:
Int[(-7742196*x^8 + 7779240*x^7*Log[2]^2 + (-7461720*x^8 + 7482888*x^7*Log [2]^2)*Log[-x + Log[2]^2] + (-2874816*x^8 + 2878848*x^7*Log[2]^2)*Log[-x + Log[2]^2]^2 + (-553472*x^8 + 553728*x^7*Log[2]^2)*Log[-x + Log[2]^2]^3 + (-53248*x^8 + 53248*x^7*Log[2]^2)*Log[-x + Log[2]^2]^4 + (-2048*x^8 + 2048 *x^7*Log[2]^2)*Log[-x + Log[2]^2]^5)/(-3125*x + 3125*Log[2]^2 + (-3125*x + 3125*Log[2]^2)*Log[-x + Log[2]^2] + (-1250*x + 1250*Log[2]^2)*Log[-x + Lo g[2]^2]^2 + (-250*x + 250*Log[2]^2)*Log[-x + Log[2]^2]^3 + (-25*x + 25*Log [2]^2)*Log[-x + Log[2]^2]^4 + (-x + Log[2]^2)*Log[-x + Log[2]^2]^5),x]
Output:
$Aborted
Time = 2.63 (sec) , antiderivative size = 63, normalized size of antiderivative = 2.03
| method | result | size |
| risch | \(256 x^{8}+\frac {x^{8} \left (256 \ln \left (\ln \left (2\right )^{2}-x \right )^{3}+3936 \ln \left (\ln \left (2\right )^{2}-x \right )^{2}+20176 \ln \left (\ln \left (2\right )^{2}-x \right )+34481\right )}{{\left (5+\ln \left (\ln \left (2\right )^{2}-x \right )\right )}^{4}}\) | \(63\) |
| parallelrisch | \(\frac {256 \ln \left (\ln \left (2\right )^{2}-x \right )^{4} x^{8}+5376 \ln \left (\ln \left (2\right )^{2}-x \right )^{3} x^{8}+42336 \ln \left (\ln \left (2\right )^{2}-x \right )^{2} x^{8}+148176 \ln \left (\ln \left (2\right )^{2}-x \right ) x^{8}+194481 x^{8}}{\ln \left (\ln \left (2\right )^{2}-x \right )^{4}+20 \ln \left (\ln \left (2\right )^{2}-x \right )^{3}+150 \ln \left (\ln \left (2\right )^{2}-x \right )^{2}+500 \ln \left (\ln \left (2\right )^{2}-x \right )+625}\) | \(122\) |
| derivativedivides | \(\text {Expression too large to display}\) | \(1022\) |
| default | \(\text {Expression too large to display}\) | \(1022\) |
Input:
int(((2048*x^7*ln(2)^2-2048*x^8)*ln(ln(2)^2-x)^5+(53248*x^7*ln(2)^2-53248* x^8)*ln(ln(2)^2-x)^4+(553728*x^7*ln(2)^2-553472*x^8)*ln(ln(2)^2-x)^3+(2878 848*x^7*ln(2)^2-2874816*x^8)*ln(ln(2)^2-x)^2+(7482888*x^7*ln(2)^2-7461720* x^8)*ln(ln(2)^2-x)+7779240*x^7*ln(2)^2-7742196*x^8)/((ln(2)^2-x)*ln(ln(2)^ 2-x)^5+(25*ln(2)^2-25*x)*ln(ln(2)^2-x)^4+(250*ln(2)^2-250*x)*ln(ln(2)^2-x) ^3+(1250*ln(2)^2-1250*x)*ln(ln(2)^2-x)^2+(3125*ln(2)^2-3125*x)*ln(ln(2)^2- x)+3125*ln(2)^2-3125*x),x,method=_RETURNVERBOSE)
Output:
256*x^8+x^8*(256*ln(ln(2)^2-x)^3+3936*ln(ln(2)^2-x)^2+20176*ln(ln(2)^2-x)+ 34481)/(5+ln(ln(2)^2-x))^4
Leaf count of result is larger than twice the leaf count of optimal. 121 vs. \(2 (30) = 60\).
Time = 0.09 (sec) , antiderivative size = 121, normalized size of antiderivative = 3.90 \[ \int \frac {-7742196 x^8+7779240 x^7 \log ^2(2)+\left (-7461720 x^8+7482888 x^7 \log ^2(2)\right ) \log \left (-x+\log ^2(2)\right )+\left (-2874816 x^8+2878848 x^7 \log ^2(2)\right ) \log ^2\left (-x+\log ^2(2)\right )+\left (-553472 x^8+553728 x^7 \log ^2(2)\right ) \log ^3\left (-x+\log ^2(2)\right )+\left (-53248 x^8+53248 x^7 \log ^2(2)\right ) \log ^4\left (-x+\log ^2(2)\right )+\left (-2048 x^8+2048 x^7 \log ^2(2)\right ) \log ^5\left (-x+\log ^2(2)\right )}{-3125 x+3125 \log ^2(2)+\left (-3125 x+3125 \log ^2(2)\right ) \log \left (-x+\log ^2(2)\right )+\left (-1250 x+1250 \log ^2(2)\right ) \log ^2\left (-x+\log ^2(2)\right )+\left (-250 x+250 \log ^2(2)\right ) \log ^3\left (-x+\log ^2(2)\right )+\left (-25 x+25 \log ^2(2)\right ) \log ^4\left (-x+\log ^2(2)\right )+\left (-x+\log ^2(2)\right ) \log ^5\left (-x+\log ^2(2)\right )} \, dx=\frac {256 \, x^{8} \log \left (\log \left (2\right )^{2} - x\right )^{4} + 5376 \, x^{8} \log \left (\log \left (2\right )^{2} - x\right )^{3} + 42336 \, x^{8} \log \left (\log \left (2\right )^{2} - x\right )^{2} + 148176 \, x^{8} \log \left (\log \left (2\right )^{2} - x\right ) + 194481 \, x^{8}}{\log \left (\log \left (2\right )^{2} - x\right )^{4} + 20 \, \log \left (\log \left (2\right )^{2} - x\right )^{3} + 150 \, \log \left (\log \left (2\right )^{2} - x\right )^{2} + 500 \, \log \left (\log \left (2\right )^{2} - x\right ) + 625} \] Input:
integrate(((2048*x^7*log(2)^2-2048*x^8)*log(log(2)^2-x)^5+(53248*x^7*log(2 )^2-53248*x^8)*log(log(2)^2-x)^4+(553728*x^7*log(2)^2-553472*x^8)*log(log( 2)^2-x)^3+(2878848*x^7*log(2)^2-2874816*x^8)*log(log(2)^2-x)^2+(7482888*x^ 7*log(2)^2-7461720*x^8)*log(log(2)^2-x)+7779240*x^7*log(2)^2-7742196*x^8)/ ((log(2)^2-x)*log(log(2)^2-x)^5+(25*log(2)^2-25*x)*log(log(2)^2-x)^4+(250* log(2)^2-250*x)*log(log(2)^2-x)^3+(1250*log(2)^2-1250*x)*log(log(2)^2-x)^2 +(3125*log(2)^2-3125*x)*log(log(2)^2-x)+3125*log(2)^2-3125*x),x, algorithm ="fricas")
Output:
(256*x^8*log(log(2)^2 - x)^4 + 5376*x^8*log(log(2)^2 - x)^3 + 42336*x^8*lo g(log(2)^2 - x)^2 + 148176*x^8*log(log(2)^2 - x) + 194481*x^8)/(log(log(2) ^2 - x)^4 + 20*log(log(2)^2 - x)^3 + 150*log(log(2)^2 - x)^2 + 500*log(log (2)^2 - x) + 625)
Leaf count of result is larger than twice the leaf count of optimal. 99 vs. \(2 (20) = 40\).
Time = 0.11 (sec) , antiderivative size = 99, normalized size of antiderivative = 3.19 \[ \int \frac {-7742196 x^8+7779240 x^7 \log ^2(2)+\left (-7461720 x^8+7482888 x^7 \log ^2(2)\right ) \log \left (-x+\log ^2(2)\right )+\left (-2874816 x^8+2878848 x^7 \log ^2(2)\right ) \log ^2\left (-x+\log ^2(2)\right )+\left (-553472 x^8+553728 x^7 \log ^2(2)\right ) \log ^3\left (-x+\log ^2(2)\right )+\left (-53248 x^8+53248 x^7 \log ^2(2)\right ) \log ^4\left (-x+\log ^2(2)\right )+\left (-2048 x^8+2048 x^7 \log ^2(2)\right ) \log ^5\left (-x+\log ^2(2)\right )}{-3125 x+3125 \log ^2(2)+\left (-3125 x+3125 \log ^2(2)\right ) \log \left (-x+\log ^2(2)\right )+\left (-1250 x+1250 \log ^2(2)\right ) \log ^2\left (-x+\log ^2(2)\right )+\left (-250 x+250 \log ^2(2)\right ) \log ^3\left (-x+\log ^2(2)\right )+\left (-25 x+25 \log ^2(2)\right ) \log ^4\left (-x+\log ^2(2)\right )+\left (-x+\log ^2(2)\right ) \log ^5\left (-x+\log ^2(2)\right )} \, dx=256 x^{8} + \frac {256 x^{8} \log {\left (- x + \log {\left (2 \right )}^{2} \right )}^{3} + 3936 x^{8} \log {\left (- x + \log {\left (2 \right )}^{2} \right )}^{2} + 20176 x^{8} \log {\left (- x + \log {\left (2 \right )}^{2} \right )} + 34481 x^{8}}{\log {\left (- x + \log {\left (2 \right )}^{2} \right )}^{4} + 20 \log {\left (- x + \log {\left (2 \right )}^{2} \right )}^{3} + 150 \log {\left (- x + \log {\left (2 \right )}^{2} \right )}^{2} + 500 \log {\left (- x + \log {\left (2 \right )}^{2} \right )} + 625} \] Input:
integrate(((2048*x**7*ln(2)**2-2048*x**8)*ln(ln(2)**2-x)**5+(53248*x**7*ln (2)**2-53248*x**8)*ln(ln(2)**2-x)**4+(553728*x**7*ln(2)**2-553472*x**8)*ln (ln(2)**2-x)**3+(2878848*x**7*ln(2)**2-2874816*x**8)*ln(ln(2)**2-x)**2+(74 82888*x**7*ln(2)**2-7461720*x**8)*ln(ln(2)**2-x)+7779240*x**7*ln(2)**2-774 2196*x**8)/((ln(2)**2-x)*ln(ln(2)**2-x)**5+(25*ln(2)**2-25*x)*ln(ln(2)**2- x)**4+(250*ln(2)**2-250*x)*ln(ln(2)**2-x)**3+(1250*ln(2)**2-1250*x)*ln(ln( 2)**2-x)**2+(3125*ln(2)**2-3125*x)*ln(ln(2)**2-x)+3125*ln(2)**2-3125*x),x)
Output:
256*x**8 + (256*x**8*log(-x + log(2)**2)**3 + 3936*x**8*log(-x + log(2)**2 )**2 + 20176*x**8*log(-x + log(2)**2) + 34481*x**8)/(log(-x + log(2)**2)** 4 + 20*log(-x + log(2)**2)**3 + 150*log(-x + log(2)**2)**2 + 500*log(-x + log(2)**2) + 625)
Leaf count of result is larger than twice the leaf count of optimal. 121 vs. \(2 (30) = 60\).
Time = 0.20 (sec) , antiderivative size = 121, normalized size of antiderivative = 3.90 \[ \int \frac {-7742196 x^8+7779240 x^7 \log ^2(2)+\left (-7461720 x^8+7482888 x^7 \log ^2(2)\right ) \log \left (-x+\log ^2(2)\right )+\left (-2874816 x^8+2878848 x^7 \log ^2(2)\right ) \log ^2\left (-x+\log ^2(2)\right )+\left (-553472 x^8+553728 x^7 \log ^2(2)\right ) \log ^3\left (-x+\log ^2(2)\right )+\left (-53248 x^8+53248 x^7 \log ^2(2)\right ) \log ^4\left (-x+\log ^2(2)\right )+\left (-2048 x^8+2048 x^7 \log ^2(2)\right ) \log ^5\left (-x+\log ^2(2)\right )}{-3125 x+3125 \log ^2(2)+\left (-3125 x+3125 \log ^2(2)\right ) \log \left (-x+\log ^2(2)\right )+\left (-1250 x+1250 \log ^2(2)\right ) \log ^2\left (-x+\log ^2(2)\right )+\left (-250 x+250 \log ^2(2)\right ) \log ^3\left (-x+\log ^2(2)\right )+\left (-25 x+25 \log ^2(2)\right ) \log ^4\left (-x+\log ^2(2)\right )+\left (-x+\log ^2(2)\right ) \log ^5\left (-x+\log ^2(2)\right )} \, dx=\frac {256 \, x^{8} \log \left (\log \left (2\right )^{2} - x\right )^{4} + 5376 \, x^{8} \log \left (\log \left (2\right )^{2} - x\right )^{3} + 42336 \, x^{8} \log \left (\log \left (2\right )^{2} - x\right )^{2} + 148176 \, x^{8} \log \left (\log \left (2\right )^{2} - x\right ) + 194481 \, x^{8}}{\log \left (\log \left (2\right )^{2} - x\right )^{4} + 20 \, \log \left (\log \left (2\right )^{2} - x\right )^{3} + 150 \, \log \left (\log \left (2\right )^{2} - x\right )^{2} + 500 \, \log \left (\log \left (2\right )^{2} - x\right ) + 625} \] Input:
integrate(((2048*x^7*log(2)^2-2048*x^8)*log(log(2)^2-x)^5+(53248*x^7*log(2 )^2-53248*x^8)*log(log(2)^2-x)^4+(553728*x^7*log(2)^2-553472*x^8)*log(log( 2)^2-x)^3+(2878848*x^7*log(2)^2-2874816*x^8)*log(log(2)^2-x)^2+(7482888*x^ 7*log(2)^2-7461720*x^8)*log(log(2)^2-x)+7779240*x^7*log(2)^2-7742196*x^8)/ ((log(2)^2-x)*log(log(2)^2-x)^5+(25*log(2)^2-25*x)*log(log(2)^2-x)^4+(250* log(2)^2-250*x)*log(log(2)^2-x)^3+(1250*log(2)^2-1250*x)*log(log(2)^2-x)^2 +(3125*log(2)^2-3125*x)*log(log(2)^2-x)+3125*log(2)^2-3125*x),x, algorithm ="maxima")
Output:
(256*x^8*log(log(2)^2 - x)^4 + 5376*x^8*log(log(2)^2 - x)^3 + 42336*x^8*lo g(log(2)^2 - x)^2 + 148176*x^8*log(log(2)^2 - x) + 194481*x^8)/(log(log(2) ^2 - x)^4 + 20*log(log(2)^2 - x)^3 + 150*log(log(2)^2 - x)^2 + 500*log(log (2)^2 - x) + 625)
Leaf count of result is larger than twice the leaf count of optimal. 968 vs. \(2 (30) = 60\).
Time = 0.16 (sec) , antiderivative size = 968, normalized size of antiderivative = 31.23 \[ \int \frac {-7742196 x^8+7779240 x^7 \log ^2(2)+\left (-7461720 x^8+7482888 x^7 \log ^2(2)\right ) \log \left (-x+\log ^2(2)\right )+\left (-2874816 x^8+2878848 x^7 \log ^2(2)\right ) \log ^2\left (-x+\log ^2(2)\right )+\left (-553472 x^8+553728 x^7 \log ^2(2)\right ) \log ^3\left (-x+\log ^2(2)\right )+\left (-53248 x^8+53248 x^7 \log ^2(2)\right ) \log ^4\left (-x+\log ^2(2)\right )+\left (-2048 x^8+2048 x^7 \log ^2(2)\right ) \log ^5\left (-x+\log ^2(2)\right )}{-3125 x+3125 \log ^2(2)+\left (-3125 x+3125 \log ^2(2)\right ) \log \left (-x+\log ^2(2)\right )+\left (-1250 x+1250 \log ^2(2)\right ) \log ^2\left (-x+\log ^2(2)\right )+\left (-250 x+250 \log ^2(2)\right ) \log ^3\left (-x+\log ^2(2)\right )+\left (-25 x+25 \log ^2(2)\right ) \log ^4\left (-x+\log ^2(2)\right )+\left (-x+\log ^2(2)\right ) \log ^5\left (-x+\log ^2(2)\right )} \, dx=\text {Too large to display} \] Input:
integrate(((2048*x^7*log(2)^2-2048*x^8)*log(log(2)^2-x)^5+(53248*x^7*log(2 )^2-53248*x^8)*log(log(2)^2-x)^4+(553728*x^7*log(2)^2-553472*x^8)*log(log( 2)^2-x)^3+(2878848*x^7*log(2)^2-2874816*x^8)*log(log(2)^2-x)^2+(7482888*x^ 7*log(2)^2-7461720*x^8)*log(log(2)^2-x)+7779240*x^7*log(2)^2-7742196*x^8)/ ((log(2)^2-x)*log(log(2)^2-x)^5+(25*log(2)^2-25*x)*log(log(2)^2-x)^4+(250* log(2)^2-250*x)*log(log(2)^2-x)^3+(1250*log(2)^2-1250*x)*log(log(2)^2-x)^2 +(3125*log(2)^2-3125*x)*log(log(2)^2-x)+3125*log(2)^2-3125*x),x, algorithm ="giac")
Output:
-2048*(log(2)^2 - x)*log(2)^14 + 7168*(log(2)^2 - x)^2*log(2)^12 - 14336*( log(2)^2 - x)^3*log(2)^10 + 17920*(log(2)^2 - x)^4*log(2)^8 - 14336*(log(2 )^2 - x)^5*log(2)^6 + 7168*(log(2)^2 - x)^6*log(2)^4 - 2048*(log(2)^2 - x) ^7*log(2)^2 + 256*(log(2)^2 - x)^8 + (256*log(2)^16*log(log(2)^2 - x)^3 + 3936*log(2)^16*log(log(2)^2 - x)^2 - 2048*(log(2)^2 - x)*log(2)^14*log(log (2)^2 - x)^3 + 20176*log(2)^16*log(log(2)^2 - x) - 31488*(log(2)^2 - x)*lo g(2)^14*log(log(2)^2 - x)^2 + 7168*(log(2)^2 - x)^2*log(2)^12*log(log(2)^2 - x)^3 + 34481*log(2)^16 - 161408*(log(2)^2 - x)*log(2)^14*log(log(2)^2 - x) + 110208*(log(2)^2 - x)^2*log(2)^12*log(log(2)^2 - x)^2 - 14336*(log(2 )^2 - x)^3*log(2)^10*log(log(2)^2 - x)^3 - 275848*(log(2)^2 - x)*log(2)^14 + 564928*(log(2)^2 - x)^2*log(2)^12*log(log(2)^2 - x) - 220416*(log(2)^2 - x)^3*log(2)^10*log(log(2)^2 - x)^2 + 17920*(log(2)^2 - x)^4*log(2)^8*log (log(2)^2 - x)^3 + 965468*(log(2)^2 - x)^2*log(2)^12 - 1129856*(log(2)^2 - x)^3*log(2)^10*log(log(2)^2 - x) + 275520*(log(2)^2 - x)^4*log(2)^8*log(l og(2)^2 - x)^2 - 14336*(log(2)^2 - x)^5*log(2)^6*log(log(2)^2 - x)^3 - 193 0936*(log(2)^2 - x)^3*log(2)^10 + 1412320*(log(2)^2 - x)^4*log(2)^8*log(lo g(2)^2 - x) - 220416*(log(2)^2 - x)^5*log(2)^6*log(log(2)^2 - x)^2 + 7168* (log(2)^2 - x)^6*log(2)^4*log(log(2)^2 - x)^3 + 2413670*(log(2)^2 - x)^4*l og(2)^8 - 1129856*(log(2)^2 - x)^5*log(2)^6*log(log(2)^2 - x) + 110208*(lo g(2)^2 - x)^6*log(2)^4*log(log(2)^2 - x)^2 - 2048*(log(2)^2 - x)^7*log(...
Time = 7.95 (sec) , antiderivative size = 1087, normalized size of antiderivative = 35.06 \[ \int \frac {-7742196 x^8+7779240 x^7 \log ^2(2)+\left (-7461720 x^8+7482888 x^7 \log ^2(2)\right ) \log \left (-x+\log ^2(2)\right )+\left (-2874816 x^8+2878848 x^7 \log ^2(2)\right ) \log ^2\left (-x+\log ^2(2)\right )+\left (-553472 x^8+553728 x^7 \log ^2(2)\right ) \log ^3\left (-x+\log ^2(2)\right )+\left (-53248 x^8+53248 x^7 \log ^2(2)\right ) \log ^4\left (-x+\log ^2(2)\right )+\left (-2048 x^8+2048 x^7 \log ^2(2)\right ) \log ^5\left (-x+\log ^2(2)\right )}{-3125 x+3125 \log ^2(2)+\left (-3125 x+3125 \log ^2(2)\right ) \log \left (-x+\log ^2(2)\right )+\left (-1250 x+1250 \log ^2(2)\right ) \log ^2\left (-x+\log ^2(2)\right )+\left (-250 x+250 \log ^2(2)\right ) \log ^3\left (-x+\log ^2(2)\right )+\left (-25 x+25 \log ^2(2)\right ) \log ^4\left (-x+\log ^2(2)\right )+\left (-x+\log ^2(2)\right ) \log ^5\left (-x+\log ^2(2)\right )} \, dx=\text {Too large to display} \] Input:
int(-(7779240*x^7*log(2)^2 + log(log(2)^2 - x)*(7482888*x^7*log(2)^2 - 746 1720*x^8) + log(log(2)^2 - x)^5*(2048*x^7*log(2)^2 - 2048*x^8) + log(log(2 )^2 - x)^4*(53248*x^7*log(2)^2 - 53248*x^8) + log(log(2)^2 - x)^3*(553728* x^7*log(2)^2 - 553472*x^8) + log(log(2)^2 - x)^2*(2878848*x^7*log(2)^2 - 2 874816*x^8) - 7742196*x^8)/(3125*x + log(log(2)^2 - x)*(3125*x - 3125*log( 2)^2) + log(log(2)^2 - x)^5*(x - log(2)^2) + log(log(2)^2 - x)^4*(25*x - 2 5*log(2)^2) + log(log(2)^2 - x)^3*(250*x - 250*log(2)^2) + log(log(2)^2 - x)^2*(1250*x - 1250*log(2)^2) - 3125*log(2)^2),x)
Output:
(83397377*x^6*log(2)^4)/3 - (72798895*x^7*log(2)^2)/3 - 13680940*x^5*log(2 )^6 + 2413670*x^4*log(2)^8 - ((256*log(log(2)^2 - x)^4*(x - log(2)^2)*(42* x^5*log(2)^4 - 105*x^6*log(2)^2 + 64*x^7))/3 - (x^5*log(log(2)^2 - x)*(249 65017*x^2*log(2)^2 - 20865859*x*log(2)^4 + 5685162*log(2)^6 - 9784128*x^3) )/3 - (x^5*(32678991*x^2*log(2)^2 - 26979281*x*log(2)^4 + 7241010*log(2)^6 - 12939712*x^3))/3 + (32*log(log(2)^2 - x)^3*(x - log(2)^2)*(6846*x^5*log (2)^4 - 17507*x^6*log(2)^2 + 10880*x^7))/3 + (112*log(log(2)^2 - x)^2*(x - log(2)^2)*(14946*x^5*log(2)^4 - 39069*x^6*log(2)^2 + 24736*x^7))/3)/(10*l og(log(2)^2 - x) + log(log(2)^2 - x)^2 + 25) + log(log(2)^2 - x)*((4635668 8*x^6*log(2)^4)/3 - 13219344*x^7*log(2)^2 - 7784896*x^5*log(2)^6 + 1412320 *x^4*log(2)^8 + (12419072*x^8)/3) + ((log(log(2)^2 - x)*(x - log(2)^2)*(18 3506575*x^6*log(2)^2 - 128543058*x^5*log(2)^4 + 28425810*x^4*log(2)^6 - 83 813888*x^7))/3 - (2*x^4*(205747241*x^2*log(2)^4 - 178617825*x^3*log(2)^2 - 101882949*x*log(2)^6 + 18102525*log(2)^8 + 56650912*x^4))/3 + (256*log(lo g(2)^2 - x)^4*(x - log(2)^2)*(1183*x^6*log(2)^2 - 882*x^5*log(2)^4 + 210*x ^4*log(2)^6 - 512*x^7))/3 + (32*log(log(2)^2 - x)^3*(x - log(2)^2)*(202069 *x^6*log(2)^2 - 147462*x^5*log(2)^4 + 34230*x^4*log(2)^6 - 89088*x^7))/3 + (16*log(log(2)^2 - x)^2*(x - log(2)^2)*(3231487*x^6*log(2)^2 - 2309706*x^ 5*log(2)^4 + 523110*x^4*log(2)^6 - 1450496*x^7))/3)/(log(log(2)^2 - x) + 5 ) + log(log(2)^2 - x)^3*((528640*x^6*log(2)^4)/3 - 144640*x^7*log(2)^2 ...
Time = 0.16 (sec) , antiderivative size = 108, normalized size of antiderivative = 3.48 \[ \int \frac {-7742196 x^8+7779240 x^7 \log ^2(2)+\left (-7461720 x^8+7482888 x^7 \log ^2(2)\right ) \log \left (-x+\log ^2(2)\right )+\left (-2874816 x^8+2878848 x^7 \log ^2(2)\right ) \log ^2\left (-x+\log ^2(2)\right )+\left (-553472 x^8+553728 x^7 \log ^2(2)\right ) \log ^3\left (-x+\log ^2(2)\right )+\left (-53248 x^8+53248 x^7 \log ^2(2)\right ) \log ^4\left (-x+\log ^2(2)\right )+\left (-2048 x^8+2048 x^7 \log ^2(2)\right ) \log ^5\left (-x+\log ^2(2)\right )}{-3125 x+3125 \log ^2(2)+\left (-3125 x+3125 \log ^2(2)\right ) \log \left (-x+\log ^2(2)\right )+\left (-1250 x+1250 \log ^2(2)\right ) \log ^2\left (-x+\log ^2(2)\right )+\left (-250 x+250 \log ^2(2)\right ) \log ^3\left (-x+\log ^2(2)\right )+\left (-25 x+25 \log ^2(2)\right ) \log ^4\left (-x+\log ^2(2)\right )+\left (-x+\log ^2(2)\right ) \log ^5\left (-x+\log ^2(2)\right )} \, dx=\frac {x^{8} \left (256 \mathrm {log}\left (\mathrm {log}\left (2\right )^{2}-x \right )^{4}+5376 \mathrm {log}\left (\mathrm {log}\left (2\right )^{2}-x \right )^{3}+42336 \mathrm {log}\left (\mathrm {log}\left (2\right )^{2}-x \right )^{2}+148176 \,\mathrm {log}\left (\mathrm {log}\left (2\right )^{2}-x \right )+194481\right )}{\mathrm {log}\left (\mathrm {log}\left (2\right )^{2}-x \right )^{4}+20 \mathrm {log}\left (\mathrm {log}\left (2\right )^{2}-x \right )^{3}+150 \mathrm {log}\left (\mathrm {log}\left (2\right )^{2}-x \right )^{2}+500 \,\mathrm {log}\left (\mathrm {log}\left (2\right )^{2}-x \right )+625} \] Input:
int(((2048*x^7*log(2)^2-2048*x^8)*log(log(2)^2-x)^5+(53248*x^7*log(2)^2-53 248*x^8)*log(log(2)^2-x)^4+(553728*x^7*log(2)^2-553472*x^8)*log(log(2)^2-x )^3+(2878848*x^7*log(2)^2-2874816*x^8)*log(log(2)^2-x)^2+(7482888*x^7*log( 2)^2-7461720*x^8)*log(log(2)^2-x)+7779240*x^7*log(2)^2-7742196*x^8)/((log( 2)^2-x)*log(log(2)^2-x)^5+(25*log(2)^2-25*x)*log(log(2)^2-x)^4+(250*log(2) ^2-250*x)*log(log(2)^2-x)^3+(1250*log(2)^2-1250*x)*log(log(2)^2-x)^2+(3125 *log(2)^2-3125*x)*log(log(2)^2-x)+3125*log(2)^2-3125*x),x)
Output:
(x**8*(256*log(log(2)**2 - x)**4 + 5376*log(log(2)**2 - x)**3 + 42336*log( log(2)**2 - x)**2 + 148176*log(log(2)**2 - x) + 194481))/(log(log(2)**2 - x)**4 + 20*log(log(2)**2 - x)**3 + 150*log(log(2)**2 - x)**2 + 500*log(log (2)**2 - x) + 625)