Integrand size = 258, antiderivative size = 21 \[ \int \frac {-80000 x+120000 x^2-60000 x^3+10000 x^4+\left (1024-4096 x+7168 x^2-7168 x^3+4480 x^4-1792 x^5+448 x^6-64 x^7+4 x^8\right ) \log (x)+\left (1024-4096 x+7168 x^2-7168 x^3+4480 x^4-1792 x^5+448 x^6-64 x^7+4 x^8\right ) \log (2 x)}{641601 x-563904 x^2+546832 x^3-326832 x^4+149270 x^5-54208 x^6+13552 x^7-1936 x^8+121 x^9+\left (-25632 x+62528 x^2-69424 x^3+49424 x^4-25890 x^5+9856 x^6-2464 x^7+352 x^8-22 x^9\right ) \log (x) \log (2 x)+\left (256 x-1024 x^2+1792 x^3-1792 x^4+1120 x^5-448 x^6+112 x^7-16 x^8+x^9\right ) \log ^2(x) \log ^2(2 x)} \, dx=\frac {4}{11+\frac {625}{(-2+x)^4}-\log (x) \log (2 x)} \]
Time = 5.14 (sec) , antiderivative size = 41, normalized size of antiderivative = 1.95 \[ \int \frac {-80000 x+120000 x^2-60000 x^3+10000 x^4+\left (1024-4096 x+7168 x^2-7168 x^3+4480 x^4-1792 x^5+448 x^6-64 x^7+4 x^8\right ) \log (x)+\left (1024-4096 x+7168 x^2-7168 x^3+4480 x^4-1792 x^5+448 x^6-64 x^7+4 x^8\right ) \log (2 x)}{641601 x-563904 x^2+546832 x^3-326832 x^4+149270 x^5-54208 x^6+13552 x^7-1936 x^8+121 x^9+\left (-25632 x+62528 x^2-69424 x^3+49424 x^4-25890 x^5+9856 x^6-2464 x^7+352 x^8-22 x^9\right ) \log (x) \log (2 x)+\left (256 x-1024 x^2+1792 x^3-1792 x^4+1120 x^5-448 x^6+112 x^7-16 x^8+x^9\right ) \log ^2(x) \log ^2(2 x)} \, dx=-\frac {4 (-2+x)^4}{-801+352 x-264 x^2+88 x^3-11 x^4+(-2+x)^4 \log (x) \log (2 x)} \]
Integrate[(-80000*x + 120000*x^2 - 60000*x^3 + 10000*x^4 + (1024 - 4096*x + 7168*x^2 - 7168*x^3 + 4480*x^4 - 1792*x^5 + 448*x^6 - 64*x^7 + 4*x^8)*Lo g[x] + (1024 - 4096*x + 7168*x^2 - 7168*x^3 + 4480*x^4 - 1792*x^5 + 448*x^ 6 - 64*x^7 + 4*x^8)*Log[2*x])/(641601*x - 563904*x^2 + 546832*x^3 - 326832 *x^4 + 149270*x^5 - 54208*x^6 + 13552*x^7 - 1936*x^8 + 121*x^9 + (-25632*x + 62528*x^2 - 69424*x^3 + 49424*x^4 - 25890*x^5 + 9856*x^6 - 2464*x^7 + 3 52*x^8 - 22*x^9)*Log[x]*Log[2*x] + (256*x - 1024*x^2 + 1792*x^3 - 1792*x^4 + 1120*x^5 - 448*x^6 + 112*x^7 - 16*x^8 + x^9)*Log[x]^2*Log[2*x]^2),x]
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.
| \(\displaystyle \int \frac {10000 x^4-60000 x^3+120000 x^2+\left (4 x^8-64 x^7+448 x^6-1792 x^5+4480 x^4-7168 x^3+7168 x^2-4096 x+1024\right ) \log (x)+\left (4 x^8-64 x^7+448 x^6-1792 x^5+4480 x^4-7168 x^3+7168 x^2-4096 x+1024\right ) \log (2 x)-80000 x}{121 x^9-1936 x^8+13552 x^7-54208 x^6+149270 x^5-326832 x^4+546832 x^3-563904 x^2+\left (x^9-16 x^8+112 x^7-448 x^6+1120 x^5-1792 x^4+1792 x^3-1024 x^2+256 x\right ) \log ^2(x) \log ^2(2 x)+\left (-22 x^9+352 x^8-2464 x^7+9856 x^6-25890 x^5+49424 x^4-69424 x^3+62528 x^2-25632 x\right ) \log (x) \log (2 x)+641601 x} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {4 (2-x)^3 \left (-2500 x+(x-2)^5 (-\log (x))-(x-2)^5 \log (2 x)\right )}{x \left (11 x^4-88 x^3+264 x^2-352 x+(x-2)^4 (-\log (x)) \log (2 x)+801\right )^2}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 4 \int -\frac {(2-x)^3 \left (-\log (x) (2-x)^5-\log (2 x) (2-x)^5+2500 x\right )}{x \left (-\log (x) \log (2 x) (2-x)^4+11 x^4-88 x^3+264 x^2-352 x+801\right )^2}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -4 \int \frac {(2-x)^3 \left (-\log (x) (2-x)^5-\log (2 x) (2-x)^5+2500 x\right )}{x \left (-\log (x) \log (2 x) (2-x)^4+11 x^4-88 x^3+264 x^2-352 x+801\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (-\frac {(x-2)^4}{x \log (x) \left (\log (x) \log (2 x) x^4-11 x^4-8 \log (x) \log (2 x) x^3+88 x^3+24 \log (x) \log (2 x) x^2-264 x^2-32 \log (x) \log (2 x) x+352 x+16 \log (x) \log (2 x)-801\right )}-\frac {\left (\log ^2(x) x^5+11 x^5-10 \log ^2(x) x^4-110 x^4+40 \log ^2(x) x^3+440 x^3-80 \log ^2(x) x^2-880 x^2+80 \log ^2(x) x+2500 \log (x) x+1505 x-32 \log ^2(x)-1602\right ) (x-2)^3}{x \log (x) \left (\log (x) \log (2 x) x^4-11 x^4-8 \log (x) \log (2 x) x^3+88 x^3+24 \log (x) \log (2 x) x^2-264 x^2-32 \log (x) \log (2 x) x+352 x+16 \log (x) \log (2 x)-801\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {(2-x)^3 \left (\log (x) (x-2)^5+\log (2 x) (x-2)^5+2500 x\right )}{x \left (-\log (x) \log (2 x) (x-2)^4+11 x^4-88 x^3+264 x^2-352 x+801\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (-\frac {(x-2)^4}{x \log (x) \left (\log (x) \log (2 x) x^4-11 x^4-8 \log (x) \log (2 x) x^3+88 x^3+24 \log (x) \log (2 x) x^2-264 x^2-32 \log (x) \log (2 x) x+352 x+16 \log (x) \log (2 x)-801\right )}-\frac {\left (\log ^2(x) x^5+11 x^5-10 \log ^2(x) x^4-110 x^4+40 \log ^2(x) x^3+440 x^3-80 \log ^2(x) x^2-880 x^2+80 \log ^2(x) x+2500 \log (x) x+1505 x-32 \log ^2(x)-1602\right ) (x-2)^3}{x \log (x) \left (\log (x) \log (2 x) x^4-11 x^4-8 \log (x) \log (2 x) x^3+88 x^3+24 \log (x) \log (2 x) x^2-264 x^2-32 \log (x) \log (2 x) x+352 x+16 \log (x) \log (2 x)-801\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {(2-x)^3 \left (\log (x) (x-2)^5+\log (2 x) (x-2)^5+2500 x\right )}{x \left (-\log (x) \log (2 x) (x-2)^4+11 x^4-88 x^3+264 x^2-352 x+801\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (-\frac {(x-2)^4}{x \log (x) \left (\log (x) \log (2 x) x^4-11 x^4-8 \log (x) \log (2 x) x^3+88 x^3+24 \log (x) \log (2 x) x^2-264 x^2-32 \log (x) \log (2 x) x+352 x+16 \log (x) \log (2 x)-801\right )}-\frac {\left (\log ^2(x) x^5+11 x^5-10 \log ^2(x) x^4-110 x^4+40 \log ^2(x) x^3+440 x^3-80 \log ^2(x) x^2-880 x^2+80 \log ^2(x) x+2500 \log (x) x+1505 x-32 \log ^2(x)-1602\right ) (x-2)^3}{x \log (x) \left (\log (x) \log (2 x) x^4-11 x^4-8 \log (x) \log (2 x) x^3+88 x^3+24 \log (x) \log (2 x) x^2-264 x^2-32 \log (x) \log (2 x) x+352 x+16 \log (x) \log (2 x)-801\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {(2-x)^3 \left (\log (x) (x-2)^5+\log (2 x) (x-2)^5+2500 x\right )}{x \left (-\log (x) \log (2 x) (x-2)^4+11 x^4-88 x^3+264 x^2-352 x+801\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (-\frac {(x-2)^4}{x \log (x) \left (\log (x) \log (2 x) x^4-11 x^4-8 \log (x) \log (2 x) x^3+88 x^3+24 \log (x) \log (2 x) x^2-264 x^2-32 \log (x) \log (2 x) x+352 x+16 \log (x) \log (2 x)-801\right )}-\frac {\left (\log ^2(x) x^5+11 x^5-10 \log ^2(x) x^4-110 x^4+40 \log ^2(x) x^3+440 x^3-80 \log ^2(x) x^2-880 x^2+80 \log ^2(x) x+2500 \log (x) x+1505 x-32 \log ^2(x)-1602\right ) (x-2)^3}{x \log (x) \left (\log (x) \log (2 x) x^4-11 x^4-8 \log (x) \log (2 x) x^3+88 x^3+24 \log (x) \log (2 x) x^2-264 x^2-32 \log (x) \log (2 x) x+352 x+16 \log (x) \log (2 x)-801\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {(2-x)^3 \left (\log (x) (x-2)^5+\log (2 x) (x-2)^5+2500 x\right )}{x \left (-\log (x) \log (2 x) (x-2)^4+11 x^4-88 x^3+264 x^2-352 x+801\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (-\frac {(x-2)^4}{x \log (x) \left (\log (x) \log (2 x) x^4-11 x^4-8 \log (x) \log (2 x) x^3+88 x^3+24 \log (x) \log (2 x) x^2-264 x^2-32 \log (x) \log (2 x) x+352 x+16 \log (x) \log (2 x)-801\right )}-\frac {\left (\log ^2(x) x^5+11 x^5-10 \log ^2(x) x^4-110 x^4+40 \log ^2(x) x^3+440 x^3-80 \log ^2(x) x^2-880 x^2+80 \log ^2(x) x+2500 \log (x) x+1505 x-32 \log ^2(x)-1602\right ) (x-2)^3}{x \log (x) \left (\log (x) \log (2 x) x^4-11 x^4-8 \log (x) \log (2 x) x^3+88 x^3+24 \log (x) \log (2 x) x^2-264 x^2-32 \log (x) \log (2 x) x+352 x+16 \log (x) \log (2 x)-801\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {(2-x)^3 \left (\log (x) (x-2)^5+\log (2 x) (x-2)^5+2500 x\right )}{x \left (-\log (x) \log (2 x) (x-2)^4+11 x^4-88 x^3+264 x^2-352 x+801\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (-\frac {(x-2)^4}{x \log (x) \left (\log (x) \log (2 x) x^4-11 x^4-8 \log (x) \log (2 x) x^3+88 x^3+24 \log (x) \log (2 x) x^2-264 x^2-32 \log (x) \log (2 x) x+352 x+16 \log (x) \log (2 x)-801\right )}-\frac {\left (\log ^2(x) x^5+11 x^5-10 \log ^2(x) x^4-110 x^4+40 \log ^2(x) x^3+440 x^3-80 \log ^2(x) x^2-880 x^2+80 \log ^2(x) x+2500 \log (x) x+1505 x-32 \log ^2(x)-1602\right ) (x-2)^3}{x \log (x) \left (\log (x) \log (2 x) x^4-11 x^4-8 \log (x) \log (2 x) x^3+88 x^3+24 \log (x) \log (2 x) x^2-264 x^2-32 \log (x) \log (2 x) x+352 x+16 \log (x) \log (2 x)-801\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {(2-x)^3 \left (\log (x) (x-2)^5+\log (2 x) (x-2)^5+2500 x\right )}{x \left (-\log (x) \log (2 x) (x-2)^4+11 x^4-88 x^3+264 x^2-352 x+801\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (-\frac {(x-2)^4}{x \log (x) \left (\log (x) \log (2 x) x^4-11 x^4-8 \log (x) \log (2 x) x^3+88 x^3+24 \log (x) \log (2 x) x^2-264 x^2-32 \log (x) \log (2 x) x+352 x+16 \log (x) \log (2 x)-801\right )}-\frac {\left (\log ^2(x) x^5+11 x^5-10 \log ^2(x) x^4-110 x^4+40 \log ^2(x) x^3+440 x^3-80 \log ^2(x) x^2-880 x^2+80 \log ^2(x) x+2500 \log (x) x+1505 x-32 \log ^2(x)-1602\right ) (x-2)^3}{x \log (x) \left (\log (x) \log (2 x) x^4-11 x^4-8 \log (x) \log (2 x) x^3+88 x^3+24 \log (x) \log (2 x) x^2-264 x^2-32 \log (x) \log (2 x) x+352 x+16 \log (x) \log (2 x)-801\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {(2-x)^3 \left (\log (x) (x-2)^5+\log (2 x) (x-2)^5+2500 x\right )}{x \left (-\log (x) \log (2 x) (x-2)^4+11 x^4-88 x^3+264 x^2-352 x+801\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (-\frac {(x-2)^4}{x \log (x) \left (\log (x) \log (2 x) x^4-11 x^4-8 \log (x) \log (2 x) x^3+88 x^3+24 \log (x) \log (2 x) x^2-264 x^2-32 \log (x) \log (2 x) x+352 x+16 \log (x) \log (2 x)-801\right )}-\frac {\left (\log ^2(x) x^5+11 x^5-10 \log ^2(x) x^4-110 x^4+40 \log ^2(x) x^3+440 x^3-80 \log ^2(x) x^2-880 x^2+80 \log ^2(x) x+2500 \log (x) x+1505 x-32 \log ^2(x)-1602\right ) (x-2)^3}{x \log (x) \left (\log (x) \log (2 x) x^4-11 x^4-8 \log (x) \log (2 x) x^3+88 x^3+24 \log (x) \log (2 x) x^2-264 x^2-32 \log (x) \log (2 x) x+352 x+16 \log (x) \log (2 x)-801\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {(2-x)^3 \left (\log (x) (x-2)^5+\log (2 x) (x-2)^5+2500 x\right )}{x \left (-\log (x) \log (2 x) (x-2)^4+11 x^4-88 x^3+264 x^2-352 x+801\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (-\frac {(x-2)^4}{x \log (x) \left (\log (x) \log (2 x) x^4-11 x^4-8 \log (x) \log (2 x) x^3+88 x^3+24 \log (x) \log (2 x) x^2-264 x^2-32 \log (x) \log (2 x) x+352 x+16 \log (x) \log (2 x)-801\right )}-\frac {\left (\log ^2(x) x^5+11 x^5-10 \log ^2(x) x^4-110 x^4+40 \log ^2(x) x^3+440 x^3-80 \log ^2(x) x^2-880 x^2+80 \log ^2(x) x+2500 \log (x) x+1505 x-32 \log ^2(x)-1602\right ) (x-2)^3}{x \log (x) \left (\log (x) \log (2 x) x^4-11 x^4-8 \log (x) \log (2 x) x^3+88 x^3+24 \log (x) \log (2 x) x^2-264 x^2-32 \log (x) \log (2 x) x+352 x+16 \log (x) \log (2 x)-801\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {(2-x)^3 \left (\log (x) (x-2)^5+\log (2 x) (x-2)^5+2500 x\right )}{x \left (-\log (x) \log (2 x) (x-2)^4+11 x^4-88 x^3+264 x^2-352 x+801\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (-\frac {(x-2)^4}{x \log (x) \left (\log (x) \log (2 x) x^4-11 x^4-8 \log (x) \log (2 x) x^3+88 x^3+24 \log (x) \log (2 x) x^2-264 x^2-32 \log (x) \log (2 x) x+352 x+16 \log (x) \log (2 x)-801\right )}-\frac {\left (\log ^2(x) x^5+11 x^5-10 \log ^2(x) x^4-110 x^4+40 \log ^2(x) x^3+440 x^3-80 \log ^2(x) x^2-880 x^2+80 \log ^2(x) x+2500 \log (x) x+1505 x-32 \log ^2(x)-1602\right ) (x-2)^3}{x \log (x) \left (\log (x) \log (2 x) x^4-11 x^4-8 \log (x) \log (2 x) x^3+88 x^3+24 \log (x) \log (2 x) x^2-264 x^2-32 \log (x) \log (2 x) x+352 x+16 \log (x) \log (2 x)-801\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {(2-x)^3 \left (\log (x) (x-2)^5+\log (2 x) (x-2)^5+2500 x\right )}{x \left (-\log (x) \log (2 x) (x-2)^4+11 x^4-88 x^3+264 x^2-352 x+801\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (-\frac {(x-2)^4}{x \log (x) \left (\log (x) \log (2 x) x^4-11 x^4-8 \log (x) \log (2 x) x^3+88 x^3+24 \log (x) \log (2 x) x^2-264 x^2-32 \log (x) \log (2 x) x+352 x+16 \log (x) \log (2 x)-801\right )}-\frac {\left (\log ^2(x) x^5+11 x^5-10 \log ^2(x) x^4-110 x^4+40 \log ^2(x) x^3+440 x^3-80 \log ^2(x) x^2-880 x^2+80 \log ^2(x) x+2500 \log (x) x+1505 x-32 \log ^2(x)-1602\right ) (x-2)^3}{x \log (x) \left (\log (x) \log (2 x) x^4-11 x^4-8 \log (x) \log (2 x) x^3+88 x^3+24 \log (x) \log (2 x) x^2-264 x^2-32 \log (x) \log (2 x) x+352 x+16 \log (x) \log (2 x)-801\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {(2-x)^3 \left (\log (x) (x-2)^5+\log (2 x) (x-2)^5+2500 x\right )}{x \left (-\log (x) \log (2 x) (x-2)^4+11 x^4-88 x^3+264 x^2-352 x+801\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (-\frac {(x-2)^4}{x \log (x) \left (\log (x) \log (2 x) x^4-11 x^4-8 \log (x) \log (2 x) x^3+88 x^3+24 \log (x) \log (2 x) x^2-264 x^2-32 \log (x) \log (2 x) x+352 x+16 \log (x) \log (2 x)-801\right )}-\frac {\left (\log ^2(x) x^5+11 x^5-10 \log ^2(x) x^4-110 x^4+40 \log ^2(x) x^3+440 x^3-80 \log ^2(x) x^2-880 x^2+80 \log ^2(x) x+2500 \log (x) x+1505 x-32 \log ^2(x)-1602\right ) (x-2)^3}{x \log (x) \left (\log (x) \log (2 x) x^4-11 x^4-8 \log (x) \log (2 x) x^3+88 x^3+24 \log (x) \log (2 x) x^2-264 x^2-32 \log (x) \log (2 x) x+352 x+16 \log (x) \log (2 x)-801\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {(2-x)^3 \left (\log (x) (x-2)^5+\log (2 x) (x-2)^5+2500 x\right )}{x \left (-\log (x) \log (2 x) (x-2)^4+11 x^4-88 x^3+264 x^2-352 x+801\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (-\frac {(x-2)^4}{x \log (x) \left (\log (x) \log (2 x) x^4-11 x^4-8 \log (x) \log (2 x) x^3+88 x^3+24 \log (x) \log (2 x) x^2-264 x^2-32 \log (x) \log (2 x) x+352 x+16 \log (x) \log (2 x)-801\right )}-\frac {\left (\log ^2(x) x^5+11 x^5-10 \log ^2(x) x^4-110 x^4+40 \log ^2(x) x^3+440 x^3-80 \log ^2(x) x^2-880 x^2+80 \log ^2(x) x+2500 \log (x) x+1505 x-32 \log ^2(x)-1602\right ) (x-2)^3}{x \log (x) \left (\log (x) \log (2 x) x^4-11 x^4-8 \log (x) \log (2 x) x^3+88 x^3+24 \log (x) \log (2 x) x^2-264 x^2-32 \log (x) \log (2 x) x+352 x+16 \log (x) \log (2 x)-801\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {(2-x)^3 \left (\log (x) (x-2)^5+\log (2 x) (x-2)^5+2500 x\right )}{x \left (-\log (x) \log (2 x) (x-2)^4+11 x^4-88 x^3+264 x^2-352 x+801\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (-\frac {(x-2)^4}{x \log (x) \left (\log (x) \log (2 x) x^4-11 x^4-8 \log (x) \log (2 x) x^3+88 x^3+24 \log (x) \log (2 x) x^2-264 x^2-32 \log (x) \log (2 x) x+352 x+16 \log (x) \log (2 x)-801\right )}-\frac {\left (\log ^2(x) x^5+11 x^5-10 \log ^2(x) x^4-110 x^4+40 \log ^2(x) x^3+440 x^3-80 \log ^2(x) x^2-880 x^2+80 \log ^2(x) x+2500 \log (x) x+1505 x-32 \log ^2(x)-1602\right ) (x-2)^3}{x \log (x) \left (\log (x) \log (2 x) x^4-11 x^4-8 \log (x) \log (2 x) x^3+88 x^3+24 \log (x) \log (2 x) x^2-264 x^2-32 \log (x) \log (2 x) x+352 x+16 \log (x) \log (2 x)-801\right )^2}\right )dx\) |
Int[(-80000*x + 120000*x^2 - 60000*x^3 + 10000*x^4 + (1024 - 4096*x + 7168 *x^2 - 7168*x^3 + 4480*x^4 - 1792*x^5 + 448*x^6 - 64*x^7 + 4*x^8)*Log[x] + (1024 - 4096*x + 7168*x^2 - 7168*x^3 + 4480*x^4 - 1792*x^5 + 448*x^6 - 64 *x^7 + 4*x^8)*Log[2*x])/(641601*x - 563904*x^2 + 546832*x^3 - 326832*x^4 + 149270*x^5 - 54208*x^6 + 13552*x^7 - 1936*x^8 + 121*x^9 + (-25632*x + 625 28*x^2 - 69424*x^3 + 49424*x^4 - 25890*x^5 + 9856*x^6 - 2464*x^7 + 352*x^8 - 22*x^9)*Log[x]*Log[2*x] + (256*x - 1024*x^2 + 1792*x^3 - 1792*x^4 + 112 0*x^5 - 448*x^6 + 112*x^7 - 16*x^8 + x^9)*Log[x]^2*Log[2*x]^2),x]
3.24.99.3.1 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]]
Leaf count of result is larger than twice the leaf count of optimal. \(93\) vs. \(2(21)=42\).
Time = 11.06 (sec) , antiderivative size = 94, normalized size of antiderivative = 4.48
| method | result | size |
| parallelrisch | \(\frac {-6307840 x^{4}+50462720 x^{3}-151388160 x^{2}+201850880 x -100925440}{1576960 \ln \left (x \right ) \ln \left (2 x \right ) x^{4}-12615680 \ln \left (x \right ) \ln \left (2 x \right ) x^{3}+37847040 x^{2} \ln \left (x \right ) \ln \left (2 x \right )-17346560 x^{4}-50462720 x \ln \left (x \right ) \ln \left (2 x \right )+138772480 x^{3}+25231360 \ln \left (x \right ) \ln \left (2 x \right )-416317440 x^{2}+555089920 x -1263144960}\) | \(94\) |
| risch | \(-\frac {8 \left (x^{4}-8 x^{3}+24 x^{2}-32 x +16\right )}{-1602+704 x +32 \ln \left (2\right ) \ln \left (x \right )+2 x^{4} \ln \left (x \right )^{2}-64 x \ln \left (x \right )^{2}-16 x^{3} \ln \left (x \right )^{2}+48 x^{2} \ln \left (x \right )^{2}-64 x \ln \left (2\right ) \ln \left (x \right )+48 x^{2} \ln \left (2\right ) \ln \left (x \right )+32 \ln \left (x \right )^{2}-22 x^{4}+176 x^{3}-528 x^{2}-16 \ln \left (2\right ) \ln \left (x \right ) x^{3}+2 \ln \left (2\right ) \ln \left (x \right ) x^{4}}\) | \(123\) |
| default | \(-\frac {4}{\ln \left (2\right ) \ln \left (x \right )+\ln \left (x \right )^{2}-11}-\frac {2500}{\left (\ln \left (2\right ) \ln \left (x \right )+\ln \left (x \right )^{2}-11\right ) \left (\ln \left (2\right ) \ln \left (x \right ) x^{4}+x^{4} \ln \left (x \right )^{2}-8 \ln \left (2\right ) \ln \left (x \right ) x^{3}-8 x^{3} \ln \left (x \right )^{2}+24 x^{2} \ln \left (2\right ) \ln \left (x \right )-11 x^{4}+24 x^{2} \ln \left (x \right )^{2}-32 x \ln \left (2\right ) \ln \left (x \right )+88 x^{3}-32 x \ln \left (x \right )^{2}+16 \ln \left (2\right ) \ln \left (x \right )-264 x^{2}+16 \ln \left (x \right )^{2}+352 x -801\right )}\) | \(132\) |
int(((4*x^8-64*x^7+448*x^6-1792*x^5+4480*x^4-7168*x^3+7168*x^2-4096*x+1024 )*ln(2*x)+(4*x^8-64*x^7+448*x^6-1792*x^5+4480*x^4-7168*x^3+7168*x^2-4096*x +1024)*ln(x)+10000*x^4-60000*x^3+120000*x^2-80000*x)/((x^9-16*x^8+112*x^7- 448*x^6+1120*x^5-1792*x^4+1792*x^3-1024*x^2+256*x)*ln(x)^2*ln(2*x)^2+(-22* x^9+352*x^8-2464*x^7+9856*x^6-25890*x^5+49424*x^4-69424*x^3+62528*x^2-2563 2*x)*ln(x)*ln(2*x)+121*x^9-1936*x^8+13552*x^7-54208*x^6+149270*x^5-326832* x^4+546832*x^3-563904*x^2+641601*x),x,method=_RETURNVERBOSE)
1/1576960*(-6307840*x^4+50462720*x^3-151388160*x^2+201850880*x-100925440)/ (ln(x)*ln(2*x)*x^4-8*ln(x)*ln(2*x)*x^3+24*x^2*ln(x)*ln(2*x)-11*x^4-32*x*ln (x)*ln(2*x)+88*x^3+16*ln(x)*ln(2*x)-264*x^2+352*x-801)
Leaf count of result is larger than twice the leaf count of optimal. 90 vs. \(2 (20) = 40\).
Time = 0.26 (sec) , antiderivative size = 90, normalized size of antiderivative = 4.29 \[ \int \frac {-80000 x+120000 x^2-60000 x^3+10000 x^4+\left (1024-4096 x+7168 x^2-7168 x^3+4480 x^4-1792 x^5+448 x^6-64 x^7+4 x^8\right ) \log (x)+\left (1024-4096 x+7168 x^2-7168 x^3+4480 x^4-1792 x^5+448 x^6-64 x^7+4 x^8\right ) \log (2 x)}{641601 x-563904 x^2+546832 x^3-326832 x^4+149270 x^5-54208 x^6+13552 x^7-1936 x^8+121 x^9+\left (-25632 x+62528 x^2-69424 x^3+49424 x^4-25890 x^5+9856 x^6-2464 x^7+352 x^8-22 x^9\right ) \log (x) \log (2 x)+\left (256 x-1024 x^2+1792 x^3-1792 x^4+1120 x^5-448 x^6+112 x^7-16 x^8+x^9\right ) \log ^2(x) \log ^2(2 x)} \, dx=\frac {4 \, {\left (x^{4} - 8 \, x^{3} + 24 \, x^{2} - 32 \, x + 16\right )}}{11 \, x^{4} - 88 \, x^{3} - {\left (x^{4} - 8 \, x^{3} + 24 \, x^{2} - 32 \, x + 16\right )} \log \left (2\right ) \log \left (x\right ) - {\left (x^{4} - 8 \, x^{3} + 24 \, x^{2} - 32 \, x + 16\right )} \log \left (x\right )^{2} + 264 \, x^{2} - 352 \, x + 801} \]
integrate(((4*x^8-64*x^7+448*x^6-1792*x^5+4480*x^4-7168*x^3+7168*x^2-4096* x+1024)*log(2*x)+(4*x^8-64*x^7+448*x^6-1792*x^5+4480*x^4-7168*x^3+7168*x^2 -4096*x+1024)*log(x)+10000*x^4-60000*x^3+120000*x^2-80000*x)/((x^9-16*x^8+ 112*x^7-448*x^6+1120*x^5-1792*x^4+1792*x^3-1024*x^2+256*x)*log(x)^2*log(2* x)^2+(-22*x^9+352*x^8-2464*x^7+9856*x^6-25890*x^5+49424*x^4-69424*x^3+6252 8*x^2-25632*x)*log(x)*log(2*x)+121*x^9-1936*x^8+13552*x^7-54208*x^6+149270 *x^5-326832*x^4+546832*x^3-563904*x^2+641601*x),x, algorithm=\
4*(x^4 - 8*x^3 + 24*x^2 - 32*x + 16)/(11*x^4 - 88*x^3 - (x^4 - 8*x^3 + 24* x^2 - 32*x + 16)*log(2)*log(x) - (x^4 - 8*x^3 + 24*x^2 - 32*x + 16)*log(x) ^2 + 264*x^2 - 352*x + 801)
Leaf count of result is larger than twice the leaf count of optimal. 102 vs. \(2 (17) = 34\).
Time = 0.53 (sec) , antiderivative size = 102, normalized size of antiderivative = 4.86 \[ \int \frac {-80000 x+120000 x^2-60000 x^3+10000 x^4+\left (1024-4096 x+7168 x^2-7168 x^3+4480 x^4-1792 x^5+448 x^6-64 x^7+4 x^8\right ) \log (x)+\left (1024-4096 x+7168 x^2-7168 x^3+4480 x^4-1792 x^5+448 x^6-64 x^7+4 x^8\right ) \log (2 x)}{641601 x-563904 x^2+546832 x^3-326832 x^4+149270 x^5-54208 x^6+13552 x^7-1936 x^8+121 x^9+\left (-25632 x+62528 x^2-69424 x^3+49424 x^4-25890 x^5+9856 x^6-2464 x^7+352 x^8-22 x^9\right ) \log (x) \log (2 x)+\left (256 x-1024 x^2+1792 x^3-1792 x^4+1120 x^5-448 x^6+112 x^7-16 x^8+x^9\right ) \log ^2(x) \log ^2(2 x)} \, dx=\frac {- 4 x^{4} + 32 x^{3} - 96 x^{2} + 128 x - 64}{- 11 x^{4} + 88 x^{3} - 264 x^{2} + 352 x + \left (x^{4} - 8 x^{3} + 24 x^{2} - 32 x + 16\right ) \log {\left (x \right )}^{2} + \left (x^{4} \log {\left (2 \right )} - 8 x^{3} \log {\left (2 \right )} + 24 x^{2} \log {\left (2 \right )} - 32 x \log {\left (2 \right )} + 16 \log {\left (2 \right )}\right ) \log {\left (x \right )} - 801} \]
integrate(((4*x**8-64*x**7+448*x**6-1792*x**5+4480*x**4-7168*x**3+7168*x** 2-4096*x+1024)*ln(2*x)+(4*x**8-64*x**7+448*x**6-1792*x**5+4480*x**4-7168*x **3+7168*x**2-4096*x+1024)*ln(x)+10000*x**4-60000*x**3+120000*x**2-80000*x )/((x**9-16*x**8+112*x**7-448*x**6+1120*x**5-1792*x**4+1792*x**3-1024*x**2 +256*x)*ln(x)**2*ln(2*x)**2+(-22*x**9+352*x**8-2464*x**7+9856*x**6-25890*x **5+49424*x**4-69424*x**3+62528*x**2-25632*x)*ln(x)*ln(2*x)+121*x**9-1936* x**8+13552*x**7-54208*x**6+149270*x**5-326832*x**4+546832*x**3-563904*x**2 +641601*x),x)
(-4*x**4 + 32*x**3 - 96*x**2 + 128*x - 64)/(-11*x**4 + 88*x**3 - 264*x**2 + 352*x + (x**4 - 8*x**3 + 24*x**2 - 32*x + 16)*log(x)**2 + (x**4*log(2) - 8*x**3*log(2) + 24*x**2*log(2) - 32*x*log(2) + 16*log(2))*log(x) - 801)
Leaf count of result is larger than twice the leaf count of optimal. 100 vs. \(2 (20) = 40\).
Time = 0.37 (sec) , antiderivative size = 100, normalized size of antiderivative = 4.76 \[ \int \frac {-80000 x+120000 x^2-60000 x^3+10000 x^4+\left (1024-4096 x+7168 x^2-7168 x^3+4480 x^4-1792 x^5+448 x^6-64 x^7+4 x^8\right ) \log (x)+\left (1024-4096 x+7168 x^2-7168 x^3+4480 x^4-1792 x^5+448 x^6-64 x^7+4 x^8\right ) \log (2 x)}{641601 x-563904 x^2+546832 x^3-326832 x^4+149270 x^5-54208 x^6+13552 x^7-1936 x^8+121 x^9+\left (-25632 x+62528 x^2-69424 x^3+49424 x^4-25890 x^5+9856 x^6-2464 x^7+352 x^8-22 x^9\right ) \log (x) \log (2 x)+\left (256 x-1024 x^2+1792 x^3-1792 x^4+1120 x^5-448 x^6+112 x^7-16 x^8+x^9\right ) \log ^2(x) \log ^2(2 x)} \, dx=\frac {4 \, {\left (x^{4} - 8 \, x^{3} + 24 \, x^{2} - 32 \, x + 16\right )}}{11 \, x^{4} - 88 \, x^{3} - {\left (x^{4} - 8 \, x^{3} + 24 \, x^{2} - 32 \, x + 16\right )} \log \left (x\right )^{2} + 264 \, x^{2} - {\left (x^{4} \log \left (2\right ) - 8 \, x^{3} \log \left (2\right ) + 24 \, x^{2} \log \left (2\right ) - 32 \, x \log \left (2\right ) + 16 \, \log \left (2\right )\right )} \log \left (x\right ) - 352 \, x + 801} \]
integrate(((4*x^8-64*x^7+448*x^6-1792*x^5+4480*x^4-7168*x^3+7168*x^2-4096* x+1024)*log(2*x)+(4*x^8-64*x^7+448*x^6-1792*x^5+4480*x^4-7168*x^3+7168*x^2 -4096*x+1024)*log(x)+10000*x^4-60000*x^3+120000*x^2-80000*x)/((x^9-16*x^8+ 112*x^7-448*x^6+1120*x^5-1792*x^4+1792*x^3-1024*x^2+256*x)*log(x)^2*log(2* x)^2+(-22*x^9+352*x^8-2464*x^7+9856*x^6-25890*x^5+49424*x^4-69424*x^3+6252 8*x^2-25632*x)*log(x)*log(2*x)+121*x^9-1936*x^8+13552*x^7-54208*x^6+149270 *x^5-326832*x^4+546832*x^3-563904*x^2+641601*x),x, algorithm=\
4*(x^4 - 8*x^3 + 24*x^2 - 32*x + 16)/(11*x^4 - 88*x^3 - (x^4 - 8*x^3 + 24* x^2 - 32*x + 16)*log(x)^2 + 264*x^2 - (x^4*log(2) - 8*x^3*log(2) + 24*x^2* log(2) - 32*x*log(2) + 16*log(2))*log(x) - 352*x + 801)
Leaf count of result is larger than twice the leaf count of optimal. 120 vs. \(2 (20) = 40\).
Time = 0.44 (sec) , antiderivative size = 120, normalized size of antiderivative = 5.71 \[ \int \frac {-80000 x+120000 x^2-60000 x^3+10000 x^4+\left (1024-4096 x+7168 x^2-7168 x^3+4480 x^4-1792 x^5+448 x^6-64 x^7+4 x^8\right ) \log (x)+\left (1024-4096 x+7168 x^2-7168 x^3+4480 x^4-1792 x^5+448 x^6-64 x^7+4 x^8\right ) \log (2 x)}{641601 x-563904 x^2+546832 x^3-326832 x^4+149270 x^5-54208 x^6+13552 x^7-1936 x^8+121 x^9+\left (-25632 x+62528 x^2-69424 x^3+49424 x^4-25890 x^5+9856 x^6-2464 x^7+352 x^8-22 x^9\right ) \log (x) \log (2 x)+\left (256 x-1024 x^2+1792 x^3-1792 x^4+1120 x^5-448 x^6+112 x^7-16 x^8+x^9\right ) \log ^2(x) \log ^2(2 x)} \, dx=-\frac {4 \, {\left (x^{4} - 8 \, x^{3} + 24 \, x^{2} - 32 \, x + 16\right )}}{x^{4} \log \left (2\right ) \log \left (x\right ) + x^{4} \log \left (x\right )^{2} - 8 \, x^{3} \log \left (2\right ) \log \left (x\right ) - 8 \, x^{3} \log \left (x\right )^{2} - 11 \, x^{4} + 24 \, x^{2} \log \left (2\right ) \log \left (x\right ) + 24 \, x^{2} \log \left (x\right )^{2} + 88 \, x^{3} - 32 \, x \log \left (2\right ) \log \left (x\right ) - 32 \, x \log \left (x\right )^{2} - 264 \, x^{2} + 16 \, \log \left (2\right ) \log \left (x\right ) + 16 \, \log \left (x\right )^{2} + 352 \, x - 801} \]
integrate(((4*x^8-64*x^7+448*x^6-1792*x^5+4480*x^4-7168*x^3+7168*x^2-4096* x+1024)*log(2*x)+(4*x^8-64*x^7+448*x^6-1792*x^5+4480*x^4-7168*x^3+7168*x^2 -4096*x+1024)*log(x)+10000*x^4-60000*x^3+120000*x^2-80000*x)/((x^9-16*x^8+ 112*x^7-448*x^6+1120*x^5-1792*x^4+1792*x^3-1024*x^2+256*x)*log(x)^2*log(2* x)^2+(-22*x^9+352*x^8-2464*x^7+9856*x^6-25890*x^5+49424*x^4-69424*x^3+6252 8*x^2-25632*x)*log(x)*log(2*x)+121*x^9-1936*x^8+13552*x^7-54208*x^6+149270 *x^5-326832*x^4+546832*x^3-563904*x^2+641601*x),x, algorithm=\
-4*(x^4 - 8*x^3 + 24*x^2 - 32*x + 16)/(x^4*log(2)*log(x) + x^4*log(x)^2 - 8*x^3*log(2)*log(x) - 8*x^3*log(x)^2 - 11*x^4 + 24*x^2*log(2)*log(x) + 24* x^2*log(x)^2 + 88*x^3 - 32*x*log(2)*log(x) - 32*x*log(x)^2 - 264*x^2 + 16* log(2)*log(x) + 16*log(x)^2 + 352*x - 801)
Timed out. \[ \int \frac {-80000 x+120000 x^2-60000 x^3+10000 x^4+\left (1024-4096 x+7168 x^2-7168 x^3+4480 x^4-1792 x^5+448 x^6-64 x^7+4 x^8\right ) \log (x)+\left (1024-4096 x+7168 x^2-7168 x^3+4480 x^4-1792 x^5+448 x^6-64 x^7+4 x^8\right ) \log (2 x)}{641601 x-563904 x^2+546832 x^3-326832 x^4+149270 x^5-54208 x^6+13552 x^7-1936 x^8+121 x^9+\left (-25632 x+62528 x^2-69424 x^3+49424 x^4-25890 x^5+9856 x^6-2464 x^7+352 x^8-22 x^9\right ) \log (x) \log (2 x)+\left (256 x-1024 x^2+1792 x^3-1792 x^4+1120 x^5-448 x^6+112 x^7-16 x^8+x^9\right ) \log ^2(x) \log ^2(2 x)} \, dx=\int \frac {\ln \left (2\,x\right )\,\left (4\,x^8-64\,x^7+448\,x^6-1792\,x^5+4480\,x^4-7168\,x^3+7168\,x^2-4096\,x+1024\right )-80000\,x+120000\,x^2-60000\,x^3+10000\,x^4+\ln \left (x\right )\,\left (4\,x^8-64\,x^7+448\,x^6-1792\,x^5+4480\,x^4-7168\,x^3+7168\,x^2-4096\,x+1024\right )}{641601\,x-563904\,x^2+546832\,x^3-326832\,x^4+149270\,x^5-54208\,x^6+13552\,x^7-1936\,x^8+121\,x^9-\ln \left (2\,x\right )\,\ln \left (x\right )\,\left (22\,x^9-352\,x^8+2464\,x^7-9856\,x^6+25890\,x^5-49424\,x^4+69424\,x^3-62528\,x^2+25632\,x\right )+{\ln \left (2\,x\right )}^2\,{\ln \left (x\right )}^2\,\left (x^9-16\,x^8+112\,x^7-448\,x^6+1120\,x^5-1792\,x^4+1792\,x^3-1024\,x^2+256\,x\right )} \,d x \]
int((log(2*x)*(7168*x^2 - 4096*x - 7168*x^3 + 4480*x^4 - 1792*x^5 + 448*x^ 6 - 64*x^7 + 4*x^8 + 1024) - 80000*x + 120000*x^2 - 60000*x^3 + 10000*x^4 + log(x)*(7168*x^2 - 4096*x - 7168*x^3 + 4480*x^4 - 1792*x^5 + 448*x^6 - 6 4*x^7 + 4*x^8 + 1024))/(641601*x - 563904*x^2 + 546832*x^3 - 326832*x^4 + 149270*x^5 - 54208*x^6 + 13552*x^7 - 1936*x^8 + 121*x^9 - log(2*x)*log(x)* (25632*x - 62528*x^2 + 69424*x^3 - 49424*x^4 + 25890*x^5 - 9856*x^6 + 2464 *x^7 - 352*x^8 + 22*x^9) + log(2*x)^2*log(x)^2*(256*x - 1024*x^2 + 1792*x^ 3 - 1792*x^4 + 1120*x^5 - 448*x^6 + 112*x^7 - 16*x^8 + x^9)),x)
int((log(2*x)*(7168*x^2 - 4096*x - 7168*x^3 + 4480*x^4 - 1792*x^5 + 448*x^ 6 - 64*x^7 + 4*x^8 + 1024) - 80000*x + 120000*x^2 - 60000*x^3 + 10000*x^4 + log(x)*(7168*x^2 - 4096*x - 7168*x^3 + 4480*x^4 - 1792*x^5 + 448*x^6 - 6 4*x^7 + 4*x^8 + 1024))/(641601*x - 563904*x^2 + 546832*x^3 - 326832*x^4 + 149270*x^5 - 54208*x^6 + 13552*x^7 - 1936*x^8 + 121*x^9 - log(2*x)*log(x)* (25632*x - 62528*x^2 + 69424*x^3 - 49424*x^4 + 25890*x^5 - 9856*x^6 + 2464 *x^7 - 352*x^8 + 22*x^9) + log(2*x)^2*log(x)^2*(256*x - 1024*x^2 + 1792*x^ 3 - 1792*x^4 + 1120*x^5 - 448*x^6 + 112*x^7 - 16*x^8 + x^9)), x)