Integrand size = 145, antiderivative size = 22 \[ \int \frac {\left (512+128 x-512 x^2+128 x^4\right ) \log ^7(x)+\left (-640-224 x+1152 x^2-416 x^4\right ) \log ^8(x)}{640000 x^{11}+800000 x^{12}-2800000 x^{13}-3100000 x^{14}+6012500 x^{15}+5400625 x^{16}-8112500 x^{17}-5450000 x^{18}+7403125 x^{19}+3450000 x^{20}-4665000 x^{21}-1393750 x^{22}+2025000 x^{23}+350000 x^{24}-593750 x^{25}-50000 x^{26}+112500 x^{27}+3125 x^{28}-12500 x^{29}+625 x^{31}} \, dx=\frac {16 \log ^8(x)}{625 x^{10} \left (x+\left (-2+x^2\right )^2\right )^4} \]
Result contains higher order function than in optimal. Order 9 vs. order 3 in optimal.
Time = 72.36 (sec) , antiderivative size = 466003, normalized size of antiderivative = 21181.95 \[ \int \frac {\left (512+128 x-512 x^2+128 x^4\right ) \log ^7(x)+\left (-640-224 x+1152 x^2-416 x^4\right ) \log ^8(x)}{640000 x^{11}+800000 x^{12}-2800000 x^{13}-3100000 x^{14}+6012500 x^{15}+5400625 x^{16}-8112500 x^{17}-5450000 x^{18}+7403125 x^{19}+3450000 x^{20}-4665000 x^{21}-1393750 x^{22}+2025000 x^{23}+350000 x^{24}-593750 x^{25}-50000 x^{26}+112500 x^{27}+3125 x^{28}-12500 x^{29}+625 x^{31}} \, dx=\text {Result too large to show} \]
Integrate[((512 + 128*x - 512*x^2 + 128*x^4)*Log[x]^7 + (-640 - 224*x + 11 52*x^2 - 416*x^4)*Log[x]^8)/(640000*x^11 + 800000*x^12 - 2800000*x^13 - 31 00000*x^14 + 6012500*x^15 + 5400625*x^16 - 8112500*x^17 - 5450000*x^18 + 7 403125*x^19 + 3450000*x^20 - 4665000*x^21 - 1393750*x^22 + 2025000*x^23 + 350000*x^24 - 593750*x^25 - 50000*x^26 + 112500*x^27 + 3125*x^28 - 12500*x ^29 + 625*x^31),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.
| \(\displaystyle \int \frac {\left (-416 x^4+1152 x^2-224 x-640\right ) \log ^8(x)+\left (128 x^4-512 x^2+128 x+512\right ) \log ^7(x)}{625 x^{31}-12500 x^{29}+3125 x^{28}+112500 x^{27}-50000 x^{26}-593750 x^{25}+350000 x^{24}+2025000 x^{23}-1393750 x^{22}-4665000 x^{21}+3450000 x^{20}+7403125 x^{19}-5450000 x^{18}-8112500 x^{17}+5400625 x^{16}+6012500 x^{15}-3100000 x^{14}-2800000 x^{13}+800000 x^{12}+640000 x^{11}} \, dx\) |
| \(\Big \downarrow \) 2026 |
| \(\displaystyle \int \frac {\left (-416 x^4+1152 x^2-224 x-640\right ) \log ^8(x)+\left (128 x^4-512 x^2+128 x+512\right ) \log ^7(x)}{x^{11} \left (625 x^{20}-12500 x^{18}+3125 x^{17}+112500 x^{16}-50000 x^{15}-593750 x^{14}+350000 x^{13}+2025000 x^{12}-1393750 x^{11}-4665000 x^{10}+3450000 x^9+7403125 x^8-5450000 x^7-8112500 x^6+5400625 x^5+6012500 x^4-3100000 x^3-2800000 x^2+800000 x+640000\right )}dx\) |
| \(\Big \downarrow \) 2463 |
| \(\displaystyle \int \left (\frac {3404 \left (\left (-416 x^4+1152 x^2-224 x-640\right ) \log ^8(x)+\left (128 x^4-512 x^2+128 x+512\right ) \log ^7(x)\right )}{244140625 x^{11} (x+1)}-\frac {321 \left (\left (-416 x^4+1152 x^2-224 x-640\right ) \log ^8(x)+\left (128 x^4-512 x^2+128 x+512\right ) \log ^7(x)\right )}{48828125 x^{11} (x+1)^2}+\frac {32 \left (\left (-416 x^4+1152 x^2-224 x-640\right ) \log ^8(x)+\left (128 x^4-512 x^2+128 x+512\right ) \log ^7(x)\right )}{9765625 x^{11} (x+1)^3}-\frac {2 \left (\left (-416 x^4+1152 x^2-224 x-640\right ) \log ^8(x)+\left (128 x^4-512 x^2+128 x+512\right ) \log ^7(x)\right )}{1953125 x^{11} (x+1)^4}+\frac {\left (-416 x^4+1152 x^2-224 x-640\right ) \log ^8(x)+\left (128 x^4-512 x^2+128 x+512\right ) \log ^7(x)}{1953125 x^{11} (x+1)^5}+\frac {\left (-3404 x^2+8413 x-2211\right ) \left (\left (-416 x^4+1152 x^2-224 x-640\right ) \log ^8(x)+\left (128 x^4-512 x^2+128 x+512\right ) \log ^7(x)\right )}{244140625 x^{11} \left (x^3-x^2-3 x+4\right )}-\frac {4 \left (518 x^2-1301 x+427\right ) \left (\left (-416 x^4+1152 x^2-224 x-640\right ) \log ^8(x)+\left (128 x^4-512 x^2+128 x+512\right ) \log ^7(x)\right )}{48828125 x^{11} \left (x^3-x^2-3 x+4\right )^2}+\frac {\left (-1128 x^2+2891 x-1197\right ) \left (\left (-416 x^4+1152 x^2-224 x-640\right ) \log ^8(x)+\left (128 x^4-512 x^2+128 x+512\right ) \log ^7(x)\right )}{9765625 x^{11} \left (x^3-x^2-3 x+4\right )^3}-\frac {2 \left (254 x^2-669 x+359\right ) \left (\left (-416 x^4+1152 x^2-224 x-640\right ) \log ^8(x)+\left (128 x^4-512 x^2+128 x+512\right ) \log ^7(x)\right )}{1953125 x^{11} \left (x^3-x^2-3 x+4\right )^4}+\frac {\left (-756 x^2+2077 x-1539\right ) \left (\left (-416 x^4+1152 x^2-224 x-640\right ) \log ^8(x)+\left (128 x^4-512 x^2+128 x+512\right ) \log ^7(x)\right )}{1953125 x^{11} \left (x^3-x^2-3 x+4\right )^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {32 \log ^7(x) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right )}{625 x^{11} \left (x^4-4 x^2+x+4\right )^5}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {32}{625} \int \frac {\log ^7(x) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right )}{x^{11} \left (x^4-4 x^2+x+4\right )^5}dx\) |
| \(\Big \downarrow \) 2463 |
| \(\displaystyle \frac {32}{625} \int \left (\frac {3404 \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{390625 x^{11} (x+1)}+\frac {\left (-3404 x^2+8413 x-2211\right ) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{390625 x^{11} \left (x^3-x^2-3 x+4\right )}-\frac {321 \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{78125 x^{11} (x+1)^2}-\frac {4 \left (518 x^2-1301 x+427\right ) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{78125 x^{11} \left (x^3-x^2-3 x+4\right )^2}+\frac {32 \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{15625 x^{11} (x+1)^3}+\frac {\left (-1128 x^2+2891 x-1197\right ) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{15625 x^{11} \left (x^3-x^2-3 x+4\right )^3}-\frac {2 \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{3125 x^{11} (x+1)^4}-\frac {2 \left (254 x^2-669 x+359\right ) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{3125 x^{11} \left (x^3-x^2-3 x+4\right )^4}+\frac {\left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{3125 x^{11} (x+1)^5}+\frac {\left (-756 x^2+2077 x-1539\right ) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{3125 x^{11} \left (x^3-x^2-3 x+4\right )^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {32}{625} \int \frac {\log ^7(x) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right )}{x^{11} \left (x^4-4 x^2+x+4\right )^5}dx\) |
| \(\Big \downarrow \) 2463 |
| \(\displaystyle \frac {32}{625} \int \left (\frac {3404 \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{390625 x^{11} (x+1)}+\frac {\left (-3404 x^2+8413 x-2211\right ) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{390625 x^{11} \left (x^3-x^2-3 x+4\right )}-\frac {321 \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{78125 x^{11} (x+1)^2}-\frac {4 \left (518 x^2-1301 x+427\right ) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{78125 x^{11} \left (x^3-x^2-3 x+4\right )^2}+\frac {32 \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{15625 x^{11} (x+1)^3}+\frac {\left (-1128 x^2+2891 x-1197\right ) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{15625 x^{11} \left (x^3-x^2-3 x+4\right )^3}-\frac {2 \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{3125 x^{11} (x+1)^4}-\frac {2 \left (254 x^2-669 x+359\right ) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{3125 x^{11} \left (x^3-x^2-3 x+4\right )^4}+\frac {\left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{3125 x^{11} (x+1)^5}+\frac {\left (-756 x^2+2077 x-1539\right ) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{3125 x^{11} \left (x^3-x^2-3 x+4\right )^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {32}{625} \int \frac {\log ^7(x) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right )}{x^{11} \left (x^4-4 x^2+x+4\right )^5}dx\) |
| \(\Big \downarrow \) 2463 |
| \(\displaystyle \frac {32}{625} \int \left (\frac {3404 \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{390625 x^{11} (x+1)}+\frac {\left (-3404 x^2+8413 x-2211\right ) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{390625 x^{11} \left (x^3-x^2-3 x+4\right )}-\frac {321 \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{78125 x^{11} (x+1)^2}-\frac {4 \left (518 x^2-1301 x+427\right ) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{78125 x^{11} \left (x^3-x^2-3 x+4\right )^2}+\frac {32 \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{15625 x^{11} (x+1)^3}+\frac {\left (-1128 x^2+2891 x-1197\right ) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{15625 x^{11} \left (x^3-x^2-3 x+4\right )^3}-\frac {2 \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{3125 x^{11} (x+1)^4}-\frac {2 \left (254 x^2-669 x+359\right ) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{3125 x^{11} \left (x^3-x^2-3 x+4\right )^4}+\frac {\left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{3125 x^{11} (x+1)^5}+\frac {\left (-756 x^2+2077 x-1539\right ) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{3125 x^{11} \left (x^3-x^2-3 x+4\right )^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {32}{625} \int \frac {\log ^7(x) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right )}{x^{11} \left (x^4-4 x^2+x+4\right )^5}dx\) |
| \(\Big \downarrow \) 2463 |
| \(\displaystyle \frac {32}{625} \int \left (\frac {3404 \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{390625 x^{11} (x+1)}+\frac {\left (-3404 x^2+8413 x-2211\right ) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{390625 x^{11} \left (x^3-x^2-3 x+4\right )}-\frac {321 \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{78125 x^{11} (x+1)^2}-\frac {4 \left (518 x^2-1301 x+427\right ) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{78125 x^{11} \left (x^3-x^2-3 x+4\right )^2}+\frac {32 \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{15625 x^{11} (x+1)^3}+\frac {\left (-1128 x^2+2891 x-1197\right ) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{15625 x^{11} \left (x^3-x^2-3 x+4\right )^3}-\frac {2 \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{3125 x^{11} (x+1)^4}-\frac {2 \left (254 x^2-669 x+359\right ) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{3125 x^{11} \left (x^3-x^2-3 x+4\right )^4}+\frac {\left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{3125 x^{11} (x+1)^5}+\frac {\left (-756 x^2+2077 x-1539\right ) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{3125 x^{11} \left (x^3-x^2-3 x+4\right )^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {32}{625} \int \frac {\log ^7(x) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right )}{x^{11} \left (x^4-4 x^2+x+4\right )^5}dx\) |
| \(\Big \downarrow \) 2463 |
| \(\displaystyle \frac {32}{625} \int \left (\frac {3404 \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{390625 x^{11} (x+1)}+\frac {\left (-3404 x^2+8413 x-2211\right ) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{390625 x^{11} \left (x^3-x^2-3 x+4\right )}-\frac {321 \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{78125 x^{11} (x+1)^2}-\frac {4 \left (518 x^2-1301 x+427\right ) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{78125 x^{11} \left (x^3-x^2-3 x+4\right )^2}+\frac {32 \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{15625 x^{11} (x+1)^3}+\frac {\left (-1128 x^2+2891 x-1197\right ) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{15625 x^{11} \left (x^3-x^2-3 x+4\right )^3}-\frac {2 \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{3125 x^{11} (x+1)^4}-\frac {2 \left (254 x^2-669 x+359\right ) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{3125 x^{11} \left (x^3-x^2-3 x+4\right )^4}+\frac {\left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{3125 x^{11} (x+1)^5}+\frac {\left (-756 x^2+2077 x-1539\right ) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{3125 x^{11} \left (x^3-x^2-3 x+4\right )^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {32}{625} \int \frac {\log ^7(x) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right )}{x^{11} \left (x^4-4 x^2+x+4\right )^5}dx\) |
| \(\Big \downarrow \) 2463 |
| \(\displaystyle \frac {32}{625} \int \left (\frac {3404 \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{390625 x^{11} (x+1)}+\frac {\left (-3404 x^2+8413 x-2211\right ) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{390625 x^{11} \left (x^3-x^2-3 x+4\right )}-\frac {321 \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{78125 x^{11} (x+1)^2}-\frac {4 \left (518 x^2-1301 x+427\right ) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{78125 x^{11} \left (x^3-x^2-3 x+4\right )^2}+\frac {32 \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{15625 x^{11} (x+1)^3}+\frac {\left (-1128 x^2+2891 x-1197\right ) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{15625 x^{11} \left (x^3-x^2-3 x+4\right )^3}-\frac {2 \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{3125 x^{11} (x+1)^4}-\frac {2 \left (254 x^2-669 x+359\right ) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{3125 x^{11} \left (x^3-x^2-3 x+4\right )^4}+\frac {\left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{3125 x^{11} (x+1)^5}+\frac {\left (-756 x^2+2077 x-1539\right ) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{3125 x^{11} \left (x^3-x^2-3 x+4\right )^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {32}{625} \int \frac {\log ^7(x) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right )}{x^{11} \left (x^4-4 x^2+x+4\right )^5}dx\) |
| \(\Big \downarrow \) 2463 |
| \(\displaystyle \frac {32}{625} \int \left (\frac {3404 \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{390625 x^{11} (x+1)}+\frac {\left (-3404 x^2+8413 x-2211\right ) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{390625 x^{11} \left (x^3-x^2-3 x+4\right )}-\frac {321 \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{78125 x^{11} (x+1)^2}-\frac {4 \left (518 x^2-1301 x+427\right ) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{78125 x^{11} \left (x^3-x^2-3 x+4\right )^2}+\frac {32 \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{15625 x^{11} (x+1)^3}+\frac {\left (-1128 x^2+2891 x-1197\right ) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{15625 x^{11} \left (x^3-x^2-3 x+4\right )^3}-\frac {2 \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{3125 x^{11} (x+1)^4}-\frac {2 \left (254 x^2-669 x+359\right ) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{3125 x^{11} \left (x^3-x^2-3 x+4\right )^4}+\frac {\left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{3125 x^{11} (x+1)^5}+\frac {\left (-756 x^2+2077 x-1539\right ) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{3125 x^{11} \left (x^3-x^2-3 x+4\right )^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {32}{625} \int \frac {\log ^7(x) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right )}{x^{11} \left (x^4-4 x^2+x+4\right )^5}dx\) |
| \(\Big \downarrow \) 2463 |
| \(\displaystyle \frac {32}{625} \int \left (\frac {3404 \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{390625 x^{11} (x+1)}+\frac {\left (-3404 x^2+8413 x-2211\right ) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{390625 x^{11} \left (x^3-x^2-3 x+4\right )}-\frac {321 \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{78125 x^{11} (x+1)^2}-\frac {4 \left (518 x^2-1301 x+427\right ) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{78125 x^{11} \left (x^3-x^2-3 x+4\right )^2}+\frac {32 \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{15625 x^{11} (x+1)^3}+\frac {\left (-1128 x^2+2891 x-1197\right ) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{15625 x^{11} \left (x^3-x^2-3 x+4\right )^3}-\frac {2 \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{3125 x^{11} (x+1)^4}-\frac {2 \left (254 x^2-669 x+359\right ) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{3125 x^{11} \left (x^3-x^2-3 x+4\right )^4}+\frac {\left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{3125 x^{11} (x+1)^5}+\frac {\left (-756 x^2+2077 x-1539\right ) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{3125 x^{11} \left (x^3-x^2-3 x+4\right )^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {32}{625} \int \frac {\log ^7(x) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right )}{x^{11} \left (x^4-4 x^2+x+4\right )^5}dx\) |
| \(\Big \downarrow \) 2463 |
| \(\displaystyle \frac {32}{625} \int \left (\frac {3404 \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{390625 x^{11} (x+1)}+\frac {\left (-3404 x^2+8413 x-2211\right ) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{390625 x^{11} \left (x^3-x^2-3 x+4\right )}-\frac {321 \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{78125 x^{11} (x+1)^2}-\frac {4 \left (518 x^2-1301 x+427\right ) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{78125 x^{11} \left (x^3-x^2-3 x+4\right )^2}+\frac {32 \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{15625 x^{11} (x+1)^3}+\frac {\left (-1128 x^2+2891 x-1197\right ) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{15625 x^{11} \left (x^3-x^2-3 x+4\right )^3}-\frac {2 \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{3125 x^{11} (x+1)^4}-\frac {2 \left (254 x^2-669 x+359\right ) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{3125 x^{11} \left (x^3-x^2-3 x+4\right )^4}+\frac {\left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{3125 x^{11} (x+1)^5}+\frac {\left (-756 x^2+2077 x-1539\right ) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{3125 x^{11} \left (x^3-x^2-3 x+4\right )^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {32}{625} \int \frac {\log ^7(x) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right )}{x^{11} \left (x^4-4 x^2+x+4\right )^5}dx\) |
| \(\Big \downarrow \) 2463 |
| \(\displaystyle \frac {32}{625} \int \left (\frac {3404 \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{390625 x^{11} (x+1)}+\frac {\left (-3404 x^2+8413 x-2211\right ) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{390625 x^{11} \left (x^3-x^2-3 x+4\right )}-\frac {321 \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{78125 x^{11} (x+1)^2}-\frac {4 \left (518 x^2-1301 x+427\right ) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{78125 x^{11} \left (x^3-x^2-3 x+4\right )^2}+\frac {32 \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{15625 x^{11} (x+1)^3}+\frac {\left (-1128 x^2+2891 x-1197\right ) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{15625 x^{11} \left (x^3-x^2-3 x+4\right )^3}-\frac {2 \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{3125 x^{11} (x+1)^4}-\frac {2 \left (254 x^2-669 x+359\right ) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{3125 x^{11} \left (x^3-x^2-3 x+4\right )^4}+\frac {\left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{3125 x^{11} (x+1)^5}+\frac {\left (-756 x^2+2077 x-1539\right ) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{3125 x^{11} \left (x^3-x^2-3 x+4\right )^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {32}{625} \int \frac {\log ^7(x) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right )}{x^{11} \left (x^4-4 x^2+x+4\right )^5}dx\) |
| \(\Big \downarrow \) 2463 |
| \(\displaystyle \frac {32}{625} \int \left (\frac {3404 \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{390625 x^{11} (x+1)}+\frac {\left (-3404 x^2+8413 x-2211\right ) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{390625 x^{11} \left (x^3-x^2-3 x+4\right )}-\frac {321 \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{78125 x^{11} (x+1)^2}-\frac {4 \left (518 x^2-1301 x+427\right ) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{78125 x^{11} \left (x^3-x^2-3 x+4\right )^2}+\frac {32 \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{15625 x^{11} (x+1)^3}+\frac {\left (-1128 x^2+2891 x-1197\right ) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{15625 x^{11} \left (x^3-x^2-3 x+4\right )^3}-\frac {2 \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{3125 x^{11} (x+1)^4}-\frac {2 \left (254 x^2-669 x+359\right ) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{3125 x^{11} \left (x^3-x^2-3 x+4\right )^4}+\frac {\left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{3125 x^{11} (x+1)^5}+\frac {\left (-756 x^2+2077 x-1539\right ) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{3125 x^{11} \left (x^3-x^2-3 x+4\right )^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {32}{625} \int \frac {\log ^7(x) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right )}{x^{11} \left (x^4-4 x^2+x+4\right )^5}dx\) |
| \(\Big \downarrow \) 2463 |
| \(\displaystyle \frac {32}{625} \int \left (\frac {3404 \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{390625 x^{11} (x+1)}+\frac {\left (-3404 x^2+8413 x-2211\right ) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{390625 x^{11} \left (x^3-x^2-3 x+4\right )}-\frac {321 \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{78125 x^{11} (x+1)^2}-\frac {4 \left (518 x^2-1301 x+427\right ) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{78125 x^{11} \left (x^3-x^2-3 x+4\right )^2}+\frac {32 \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{15625 x^{11} (x+1)^3}+\frac {\left (-1128 x^2+2891 x-1197\right ) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{15625 x^{11} \left (x^3-x^2-3 x+4\right )^3}-\frac {2 \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{3125 x^{11} (x+1)^4}-\frac {2 \left (254 x^2-669 x+359\right ) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{3125 x^{11} \left (x^3-x^2-3 x+4\right )^4}+\frac {\left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{3125 x^{11} (x+1)^5}+\frac {\left (-756 x^2+2077 x-1539\right ) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{3125 x^{11} \left (x^3-x^2-3 x+4\right )^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {32}{625} \int \frac {\log ^7(x) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right )}{x^{11} \left (x^4-4 x^2+x+4\right )^5}dx\) |
| \(\Big \downarrow \) 2463 |
| \(\displaystyle \frac {32}{625} \int \left (\frac {3404 \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{390625 x^{11} (x+1)}+\frac {\left (-3404 x^2+8413 x-2211\right ) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{390625 x^{11} \left (x^3-x^2-3 x+4\right )}-\frac {321 \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{78125 x^{11} (x+1)^2}-\frac {4 \left (518 x^2-1301 x+427\right ) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{78125 x^{11} \left (x^3-x^2-3 x+4\right )^2}+\frac {32 \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{15625 x^{11} (x+1)^3}+\frac {\left (-1128 x^2+2891 x-1197\right ) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{15625 x^{11} \left (x^3-x^2-3 x+4\right )^3}-\frac {2 \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{3125 x^{11} (x+1)^4}-\frac {2 \left (254 x^2-669 x+359\right ) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{3125 x^{11} \left (x^3-x^2-3 x+4\right )^4}+\frac {\left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{3125 x^{11} (x+1)^5}+\frac {\left (-756 x^2+2077 x-1539\right ) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right ) \log ^7(x)}{3125 x^{11} \left (x^3-x^2-3 x+4\right )^5}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {32}{625} \int \frac {\log ^7(x) \left (4 \left (x^4-4 x^2+x+4\right )-\left (13 x^4-36 x^2+7 x+20\right ) \log (x)\right )}{x^{11} \left (x^4-4 x^2+x+4\right )^5}dx\) |
Int[((512 + 128*x - 512*x^2 + 128*x^4)*Log[x]^7 + (-640 - 224*x + 1152*x^2 - 416*x^4)*Log[x]^8)/(640000*x^11 + 800000*x^12 - 2800000*x^13 - 3100000* x^14 + 6012500*x^15 + 5400625*x^16 - 8112500*x^17 - 5450000*x^18 + 7403125 *x^19 + 3450000*x^20 - 4665000*x^21 - 1393750*x^22 + 2025000*x^23 + 350000 *x^24 - 593750*x^25 - 50000*x^26 + 112500*x^27 + 3125*x^28 - 12500*x^29 + 625*x^31),x]
3.18.38.3.1 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[(Fx_.)*(Px_)^(p_.), x_Symbol] :> With[{r = Expon[Px, x, Min]}, Int[x^(p *r)*ExpandToSum[Px/x^r, x]^p*Fx, x] /; IGtQ[r, 0]] /; PolyQ[Px, x] && Integ erQ[p] && !MonomialQ[Px, x] && (ILtQ[p, 0] || !PolyQ[u, x])
Int[(u_.)*(Px_)^(p_), x_Symbol] :> With[{Qx = Factor[Px]}, Int[ExpandIntegr and[u, Qx^p, x], x] /; !SumQ[NonfreeFactors[Qx, x]]] /; PolyQ[Px, x] && Gt Q[Expon[Px, x], 2] && !BinomialQ[Px, x] && !TrinomialQ[Px, x] && ILtQ[p, 0]
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. \(84\) vs. \(2(20)=40\).
Time = 6.47 (sec) , antiderivative size = 85, normalized size of antiderivative = 3.86
| method | result | size |
| risch | \(\frac {16 \ln \left (x \right )^{8}}{625 x^{10} \left (x^{16}-16 x^{14}+4 x^{13}+112 x^{12}-48 x^{11}-442 x^{10}+240 x^{9}+1072 x^{8}-636 x^{7}-1648 x^{6}+944 x^{5}+1601 x^{4}-752 x^{3}-928 x^{2}+256 x +256\right )}\) | \(85\) |
| parallelrisch | \(\frac {16 \ln \left (x \right )^{8}}{625 x^{10} \left (x^{16}-16 x^{14}+4 x^{13}+112 x^{12}-48 x^{11}-442 x^{10}+240 x^{9}+1072 x^{8}-636 x^{7}-1648 x^{6}+944 x^{5}+1601 x^{4}-752 x^{3}-928 x^{2}+256 x +256\right )}\) | \(85\) |
int(((-416*x^4+1152*x^2-224*x-640)*ln(x)^8+(128*x^4-512*x^2+128*x+512)*ln( x)^7)/(625*x^31-12500*x^29+3125*x^28+112500*x^27-50000*x^26-593750*x^25+35 0000*x^24+2025000*x^23-1393750*x^22-4665000*x^21+3450000*x^20+7403125*x^19 -5450000*x^18-8112500*x^17+5400625*x^16+6012500*x^15-3100000*x^14-2800000* x^13+800000*x^12+640000*x^11),x,method=_RETURNVERBOSE)
16/625/x^10/(x^16-16*x^14+4*x^13+112*x^12-48*x^11-442*x^10+240*x^9+1072*x^ 8-636*x^7-1648*x^6+944*x^5+1601*x^4-752*x^3-928*x^2+256*x+256)*ln(x)^8
Leaf count of result is larger than twice the leaf count of optimal. 87 vs. \(2 (20) = 40\).
Time = 0.35 (sec) , antiderivative size = 87, normalized size of antiderivative = 3.95 \[ \int \frac {\left (512+128 x-512 x^2+128 x^4\right ) \log ^7(x)+\left (-640-224 x+1152 x^2-416 x^4\right ) \log ^8(x)}{640000 x^{11}+800000 x^{12}-2800000 x^{13}-3100000 x^{14}+6012500 x^{15}+5400625 x^{16}-8112500 x^{17}-5450000 x^{18}+7403125 x^{19}+3450000 x^{20}-4665000 x^{21}-1393750 x^{22}+2025000 x^{23}+350000 x^{24}-593750 x^{25}-50000 x^{26}+112500 x^{27}+3125 x^{28}-12500 x^{29}+625 x^{31}} \, dx=\frac {16 \, \log \left (x\right )^{8}}{625 \, {\left (x^{26} - 16 \, x^{24} + 4 \, x^{23} + 112 \, x^{22} - 48 \, x^{21} - 442 \, x^{20} + 240 \, x^{19} + 1072 \, x^{18} - 636 \, x^{17} - 1648 \, x^{16} + 944 \, x^{15} + 1601 \, x^{14} - 752 \, x^{13} - 928 \, x^{12} + 256 \, x^{11} + 256 \, x^{10}\right )}} \]
integrate(((-416*x^4+1152*x^2-224*x-640)*log(x)^8+(128*x^4-512*x^2+128*x+5 12)*log(x)^7)/(625*x^31-12500*x^29+3125*x^28+112500*x^27-50000*x^26-593750 *x^25+350000*x^24+2025000*x^23-1393750*x^22-4665000*x^21+3450000*x^20+7403 125*x^19-5450000*x^18-8112500*x^17+5400625*x^16+6012500*x^15-3100000*x^14- 2800000*x^13+800000*x^12+640000*x^11),x, algorithm=\
16/625*log(x)^8/(x^26 - 16*x^24 + 4*x^23 + 112*x^22 - 48*x^21 - 442*x^20 + 240*x^19 + 1072*x^18 - 636*x^17 - 1648*x^16 + 944*x^15 + 1601*x^14 - 752* x^13 - 928*x^12 + 256*x^11 + 256*x^10)
Leaf count of result is larger than twice the leaf count of optimal. 87 vs. \(2 (20) = 40\).
Time = 0.23 (sec) , antiderivative size = 87, normalized size of antiderivative = 3.95 \[ \int \frac {\left (512+128 x-512 x^2+128 x^4\right ) \log ^7(x)+\left (-640-224 x+1152 x^2-416 x^4\right ) \log ^8(x)}{640000 x^{11}+800000 x^{12}-2800000 x^{13}-3100000 x^{14}+6012500 x^{15}+5400625 x^{16}-8112500 x^{17}-5450000 x^{18}+7403125 x^{19}+3450000 x^{20}-4665000 x^{21}-1393750 x^{22}+2025000 x^{23}+350000 x^{24}-593750 x^{25}-50000 x^{26}+112500 x^{27}+3125 x^{28}-12500 x^{29}+625 x^{31}} \, dx=\frac {16 \log {\left (x \right )}^{8}}{625 x^{26} - 10000 x^{24} + 2500 x^{23} + 70000 x^{22} - 30000 x^{21} - 276250 x^{20} + 150000 x^{19} + 670000 x^{18} - 397500 x^{17} - 1030000 x^{16} + 590000 x^{15} + 1000625 x^{14} - 470000 x^{13} - 580000 x^{12} + 160000 x^{11} + 160000 x^{10}} \]
integrate(((-416*x**4+1152*x**2-224*x-640)*ln(x)**8+(128*x**4-512*x**2+128 *x+512)*ln(x)**7)/(625*x**31-12500*x**29+3125*x**28+112500*x**27-50000*x** 26-593750*x**25+350000*x**24+2025000*x**23-1393750*x**22-4665000*x**21+345 0000*x**20+7403125*x**19-5450000*x**18-8112500*x**17+5400625*x**16+6012500 *x**15-3100000*x**14-2800000*x**13+800000*x**12+640000*x**11),x)
16*log(x)**8/(625*x**26 - 10000*x**24 + 2500*x**23 + 70000*x**22 - 30000*x **21 - 276250*x**20 + 150000*x**19 + 670000*x**18 - 397500*x**17 - 1030000 *x**16 + 590000*x**15 + 1000625*x**14 - 470000*x**13 - 580000*x**12 + 1600 00*x**11 + 160000*x**10)
Leaf count of result is larger than twice the leaf count of optimal. 87 vs. \(2 (20) = 40\).
Time = 0.30 (sec) , antiderivative size = 87, normalized size of antiderivative = 3.95 \[ \int \frac {\left (512+128 x-512 x^2+128 x^4\right ) \log ^7(x)+\left (-640-224 x+1152 x^2-416 x^4\right ) \log ^8(x)}{640000 x^{11}+800000 x^{12}-2800000 x^{13}-3100000 x^{14}+6012500 x^{15}+5400625 x^{16}-8112500 x^{17}-5450000 x^{18}+7403125 x^{19}+3450000 x^{20}-4665000 x^{21}-1393750 x^{22}+2025000 x^{23}+350000 x^{24}-593750 x^{25}-50000 x^{26}+112500 x^{27}+3125 x^{28}-12500 x^{29}+625 x^{31}} \, dx=\frac {16 \, \log \left (x\right )^{8}}{625 \, {\left (x^{26} - 16 \, x^{24} + 4 \, x^{23} + 112 \, x^{22} - 48 \, x^{21} - 442 \, x^{20} + 240 \, x^{19} + 1072 \, x^{18} - 636 \, x^{17} - 1648 \, x^{16} + 944 \, x^{15} + 1601 \, x^{14} - 752 \, x^{13} - 928 \, x^{12} + 256 \, x^{11} + 256 \, x^{10}\right )}} \]
integrate(((-416*x^4+1152*x^2-224*x-640)*log(x)^8+(128*x^4-512*x^2+128*x+5 12)*log(x)^7)/(625*x^31-12500*x^29+3125*x^28+112500*x^27-50000*x^26-593750 *x^25+350000*x^24+2025000*x^23-1393750*x^22-4665000*x^21+3450000*x^20+7403 125*x^19-5450000*x^18-8112500*x^17+5400625*x^16+6012500*x^15-3100000*x^14- 2800000*x^13+800000*x^12+640000*x^11),x, algorithm=\
16/625*log(x)^8/(x^26 - 16*x^24 + 4*x^23 + 112*x^22 - 48*x^21 - 442*x^20 + 240*x^19 + 1072*x^18 - 636*x^17 - 1648*x^16 + 944*x^15 + 1601*x^14 - 752* x^13 - 928*x^12 + 256*x^11 + 256*x^10)
Leaf count of result is larger than twice the leaf count of optimal. 208 vs. \(2 (20) = 40\).
Time = 0.30 (sec) , antiderivative size = 208, normalized size of antiderivative = 9.45 \[ \int \frac {\left (512+128 x-512 x^2+128 x^4\right ) \log ^7(x)+\left (-640-224 x+1152 x^2-416 x^4\right ) \log ^8(x)}{640000 x^{11}+800000 x^{12}-2800000 x^{13}-3100000 x^{14}+6012500 x^{15}+5400625 x^{16}-8112500 x^{17}-5450000 x^{18}+7403125 x^{19}+3450000 x^{20}-4665000 x^{21}-1393750 x^{22}+2025000 x^{23}+350000 x^{24}-593750 x^{25}-50000 x^{26}+112500 x^{27}+3125 x^{28}-12500 x^{29}+625 x^{31}} \, dx=\frac {1}{655360000} \, {\left (\frac {4520791 \, x^{15} - 3533605 \, x^{14} - 69960080 \, x^{13} + 72766060 \, x^{12} + 455281020 \, x^{11} - 574439424 \, x^{10} - 1586688070 \, x^{9} + 2342625650 \, x^{8} + 3147073760 \, x^{7} - 5412734100 \, x^{6} - 3490610724 \, x^{5} + 7169196160 \, x^{4} + 1960274855 \, x^{3} - 5125415925 \, x^{2} - 405863120 \, x + 1562340832}{x^{16} - 16 \, x^{14} + 4 \, x^{13} + 112 \, x^{12} - 48 \, x^{11} - 442 \, x^{10} + 240 \, x^{9} + 1072 \, x^{8} - 636 \, x^{7} - 1648 \, x^{6} + 944 \, x^{5} + 1601 \, x^{4} - 752 \, x^{3} - 928 \, x^{2} + 256 \, x + 256} - \frac {4520791 \, x^{9} - 3533605 \, x^{8} + 2372576 \, x^{7} - 1854784 \, x^{6} + 1048064 \, x^{5} - 844544 \, x^{4} + 348160 \, x^{3} - 303104 \, x^{2} + 65536 \, x - 65536}{x^{10}}\right )} \log \left (x\right )^{8} \]
integrate(((-416*x^4+1152*x^2-224*x-640)*log(x)^8+(128*x^4-512*x^2+128*x+5 12)*log(x)^7)/(625*x^31-12500*x^29+3125*x^28+112500*x^27-50000*x^26-593750 *x^25+350000*x^24+2025000*x^23-1393750*x^22-4665000*x^21+3450000*x^20+7403 125*x^19-5450000*x^18-8112500*x^17+5400625*x^16+6012500*x^15-3100000*x^14- 2800000*x^13+800000*x^12+640000*x^11),x, algorithm=\
1/655360000*((4520791*x^15 - 3533605*x^14 - 69960080*x^13 + 72766060*x^12 + 455281020*x^11 - 574439424*x^10 - 1586688070*x^9 + 2342625650*x^8 + 3147 073760*x^7 - 5412734100*x^6 - 3490610724*x^5 + 7169196160*x^4 + 1960274855 *x^3 - 5125415925*x^2 - 405863120*x + 1562340832)/(x^16 - 16*x^14 + 4*x^13 + 112*x^12 - 48*x^11 - 442*x^10 + 240*x^9 + 1072*x^8 - 636*x^7 - 1648*x^6 + 944*x^5 + 1601*x^4 - 752*x^3 - 928*x^2 + 256*x + 256) - (4520791*x^9 - 3533605*x^8 + 2372576*x^7 - 1854784*x^6 + 1048064*x^5 - 844544*x^4 + 34816 0*x^3 - 303104*x^2 + 65536*x - 65536)/x^10)*log(x)^8
Time = 13.27 (sec) , antiderivative size = 89, normalized size of antiderivative = 4.05 \[ \int \frac {\left (512+128 x-512 x^2+128 x^4\right ) \log ^7(x)+\left (-640-224 x+1152 x^2-416 x^4\right ) \log ^8(x)}{640000 x^{11}+800000 x^{12}-2800000 x^{13}-3100000 x^{14}+6012500 x^{15}+5400625 x^{16}-8112500 x^{17}-5450000 x^{18}+7403125 x^{19}+3450000 x^{20}-4665000 x^{21}-1393750 x^{22}+2025000 x^{23}+350000 x^{24}-593750 x^{25}-50000 x^{26}+112500 x^{27}+3125 x^{28}-12500 x^{29}+625 x^{31}} \, dx=\frac {16\,{\ln \left (x\right )}^8}{625\,\left (x^{26}-16\,x^{24}+4\,x^{23}+112\,x^{22}-48\,x^{21}-442\,x^{20}+240\,x^{19}+1072\,x^{18}-636\,x^{17}-1648\,x^{16}+944\,x^{15}+1601\,x^{14}-752\,x^{13}-928\,x^{12}+256\,x^{11}+256\,x^{10}\right )} \]
int((log(x)^7*(128*x - 512*x^2 + 128*x^4 + 512) - log(x)^8*(224*x - 1152*x ^2 + 416*x^4 + 640))/(640000*x^11 + 800000*x^12 - 2800000*x^13 - 3100000*x ^14 + 6012500*x^15 + 5400625*x^16 - 8112500*x^17 - 5450000*x^18 + 7403125* x^19 + 3450000*x^20 - 4665000*x^21 - 1393750*x^22 + 2025000*x^23 + 350000* x^24 - 593750*x^25 - 50000*x^26 + 112500*x^27 + 3125*x^28 - 12500*x^29 + 6 25*x^31),x)