Integrand size = 145, antiderivative size = 22 \[ \int \frac {\left (512+128 x-512 x^2+128 x^4\right ) \log ^7(x)+\left (-640-224 x+1152 x^2-416 x^4\right ) \log ^8(x)}{640000 x^{11}+800000 x^{12}-2800000 x^{13}-3100000 x^{14}+6012500 x^{15}+5400625 x^{16}-8112500 x^{17}-5450000 x^{18}+7403125 x^{19}+3450000 x^{20}-4665000 x^{21}-1393750 x^{22}+2025000 x^{23}+350000 x^{24}-593750 x^{25}-50000 x^{26}+112500 x^{27}+3125 x^{28}-12500 x^{29}+625 x^{31}} \, dx=\frac {16 \log ^8(x)}{625 x^{10} \left (x+\left (-2+x^2\right )^2\right )^4} \]
[Out]
\[ \int \frac {\left (512+128 x-512 x^2+128 x^4\right ) \log ^7(x)+\left (-640-224 x+1152 x^2-416 x^4\right ) \log ^8(x)}{640000 x^{11}+800000 x^{12}-2800000 x^{13}-3100000 x^{14}+6012500 x^{15}+5400625 x^{16}-8112500 x^{17}-5450000 x^{18}+7403125 x^{19}+3450000 x^{20}-4665000 x^{21}-1393750 x^{22}+2025000 x^{23}+350000 x^{24}-593750 x^{25}-50000 x^{26}+112500 x^{27}+3125 x^{28}-12500 x^{29}+625 x^{31}} \, dx=\int \frac {\left (512+128 x-512 x^2+128 x^4\right ) \log ^7(x)+\left (-640-224 x+1152 x^2-416 x^4\right ) \log ^8(x)}{640000 x^{11}+800000 x^{12}-2800000 x^{13}-3100000 x^{14}+6012500 x^{15}+5400625 x^{16}-8112500 x^{17}-5450000 x^{18}+7403125 x^{19}+3450000 x^{20}-4665000 x^{21}-1393750 x^{22}+2025000 x^{23}+350000 x^{24}-593750 x^{25}-50000 x^{26}+112500 x^{27}+3125 x^{28}-12500 x^{29}+625 x^{31}} \, dx \]
[In]
[Out]
Rubi steps \begin{align*} \text {integral}& = \int \frac {32 \log ^7(x) \left (4 \left (4+x-4 x^2+x^4\right )-\left (20+7 x-36 x^2+13 x^4\right ) \log (x)\right )}{625 x^{11} \left (4+x-4 x^2+x^4\right )^5} \, dx \\ & = \frac {32}{625} \int \frac {\log ^7(x) \left (4 \left (4+x-4 x^2+x^4\right )-\left (20+7 x-36 x^2+13 x^4\right ) \log (x)\right )}{x^{11} \left (4+x-4 x^2+x^4\right )^5} \, dx \\ & = \frac {32}{625} \int \left (\frac {4 \log ^7(x)}{x^{11} \left (4+x-4 x^2+x^4\right )^4}-\frac {\left (20+7 x-36 x^2+13 x^4\right ) \log ^8(x)}{x^{11} \left (4+x-4 x^2+x^4\right )^5}\right ) \, dx \\ & = -\left (\frac {32}{625} \int \frac {\left (20+7 x-36 x^2+13 x^4\right ) \log ^8(x)}{x^{11} \left (4+x-4 x^2+x^4\right )^5} \, dx\right )+\frac {128}{625} \int \frac {\log ^7(x)}{x^{11} \left (4+x-4 x^2+x^4\right )^4} \, dx \\ & = -\left (\frac {32}{625} \int \left (\frac {5 \log ^8(x)}{256 x^{11}}-\frac {9 \log ^8(x)}{512 x^{10}}+\frac {37 \log ^8(x)}{512 x^9}-\frac {595 \log ^8(x)}{8192 x^8}+\frac {9897 \log ^8(x)}{65536 x^7}-\frac {10235 \log ^8(x)}{65536 x^6}+\frac {28981 \log ^8(x)}{131072 x^5}-\frac {222429 \log ^8(x)}{1048576 x^4}+\frac {3533605 \log ^8(x)}{16777216 x^3}-\frac {4520791 \log ^8(x)}{33554432 x^2}+\frac {2 \log ^8(x)}{625 (1+x)^5}+\frac {63 \log ^8(x)}{3125 (1+x)^4}+\frac {219 \log ^8(x)}{3125 (1+x)^3}+\frac {2144 \log ^8(x)}{15625 (1+x)^2}+\frac {\left (8501009-9580037 x+2589761 x^2\right ) \log ^8(x)}{327680000 \left (4-3 x-x^2+x^3\right )^5}+\frac {\left (314035551-248443403 x+42784119 x^2\right ) \log ^8(x)}{13107200000 \left (4-3 x-x^2+x^3\right )^4}+\frac {\left (171529655-256946579 x+173032851 x^2\right ) \log ^8(x)}{52428800000 \left (4-3 x-x^2+x^3\right )^3}+\frac {\left (-6304985049-662749603 x+2244939789 x^2\right ) \log ^8(x)}{524288000000 \left (4-3 x-x^2+x^3\right )^2}-\frac {3 (660837347+434447611 x) \log ^8(x)}{524288000000 \left (4-3 x-x^2+x^3\right )}\right ) \, dx\right )+\frac {128}{625} \int \left (\frac {\log ^7(x)}{256 x^{11}}-\frac {\log ^7(x)}{256 x^{10}}+\frac {37 \log ^7(x)}{2048 x^9}-\frac {85 \log ^7(x)}{4096 x^8}+\frac {3299 \log ^7(x)}{65536 x^7}-\frac {2047 \log ^7(x)}{32768 x^6}+\frac {28981 \log ^7(x)}{262144 x^5}-\frac {74143 \log ^7(x)}{524288 x^4}+\frac {3533605 \log ^7(x)}{16777216 x^3}-\frac {4520791 \log ^7(x)}{16777216 x^2}+\frac {48823151 \log ^7(x)}{134217728 x}-\frac {\log ^7(x)}{625 (1+x)^4}-\frac {47 \log ^7(x)}{3125 (1+x)^3}-\frac {266 \log ^7(x)}{3125 (1+x)^2}-\frac {5618 \log ^7(x)}{15625 (1+x)}+\frac {\left (-3216893+1908449 x-108397 x^2\right ) \log ^7(x)}{2621440000 \left (4-3 x-x^2+x^3\right )^4}+\frac {\left (-50053763+19088719 x-18513767 x^2\right ) \log ^7(x)}{52428800000 \left (4-3 x-x^2+x^3\right )^3}+\frac {\left (403919387-50753335 x-204251131 x^2\right ) \log ^7(x)}{104857600000 \left (4-3 x-x^2+x^3\right )^2}+\frac {\left (23762938581-1600204193 x-8826538471 x^2\right ) \log ^7(x)}{2097152000000 \left (4-3 x-x^2+x^3\right )}\right ) \, dx \\ & = \frac {\int \frac {\left (23762938581-1600204193 x-8826538471 x^2\right ) \log ^7(x)}{4-3 x-x^2+x^3} \, dx}{10240000000000}-\frac {\int \frac {\left (-6304985049-662749603 x+2244939789 x^2\right ) \log ^8(x)}{\left (4-3 x-x^2+x^3\right )^2} \, dx}{10240000000000}+\frac {3 \int \frac {(660837347+434447611 x) \log ^8(x)}{4-3 x-x^2+x^3} \, dx}{10240000000000}-\frac {\int \frac {\left (171529655-256946579 x+173032851 x^2\right ) \log ^8(x)}{\left (4-3 x-x^2+x^3\right )^3} \, dx}{1024000000000}+\frac {\int \frac {\left (403919387-50753335 x-204251131 x^2\right ) \log ^7(x)}{\left (4-3 x-x^2+x^3\right )^2} \, dx}{512000000000}+\frac {\int \frac {\left (-50053763+19088719 x-18513767 x^2\right ) \log ^7(x)}{\left (4-3 x-x^2+x^3\right )^3} \, dx}{256000000000}-\frac {\int \frac {\left (314035551-248443403 x+42784119 x^2\right ) \log ^8(x)}{\left (4-3 x-x^2+x^3\right )^4} \, dx}{256000000000}+\frac {\int \frac {\left (-3216893+1908449 x-108397 x^2\right ) \log ^7(x)}{\left (4-3 x-x^2+x^3\right )^4} \, dx}{12800000000}-\frac {\int \frac {\left (8501009-9580037 x+2589761 x^2\right ) \log ^8(x)}{\left (4-3 x-x^2+x^3\right )^5} \, dx}{6400000000}-\frac {64 \int \frac {\log ^8(x)}{(1+x)^5} \, dx}{390625}-\frac {128 \int \frac {\log ^7(x)}{(1+x)^4} \, dx}{390625}+\frac {\int \frac {\log ^7(x)}{x^{11}} \, dx}{1250}-\frac {\int \frac {\log ^7(x)}{x^{10}} \, dx}{1250}+\frac {9 \int \frac {\log ^8(x)}{x^{10}} \, dx}{10000}-\frac {\int \frac {\log ^8(x)}{x^{11}} \, dx}{1000}-\frac {2016 \int \frac {\log ^8(x)}{(1+x)^4} \, dx}{1953125}-\frac {6016 \int \frac {\log ^7(x)}{(1+x)^3} \, dx}{1953125}-\frac {7008 \int \frac {\log ^8(x)}{(1+x)^3} \, dx}{1953125}+\frac {37 \int \frac {\log ^7(x)}{x^9} \, dx}{10000}-\frac {37 \int \frac {\log ^8(x)}{x^9} \, dx}{10000}+\frac {119 \int \frac {\log ^8(x)}{x^8} \, dx}{32000}-\frac {17 \int \frac {\log ^7(x)}{x^8} \, dx}{4000}+\frac {4520791 \int \frac {\log ^8(x)}{x^2} \, dx}{655360000}-\frac {68608 \int \frac {\log ^8(x)}{(1+x)^2} \, dx}{9765625}-\frac {9897 \int \frac {\log ^8(x)}{x^7} \, dx}{1280000}+\frac {2047 \int \frac {\log ^8(x)}{x^6} \, dx}{256000}+\frac {3299 \int \frac {\log ^7(x)}{x^7} \, dx}{320000}-\frac {706721 \int \frac {\log ^8(x)}{x^3} \, dx}{65536000}+\frac {222429 \int \frac {\log ^8(x)}{x^4} \, dx}{20480000}-\frac {28981 \int \frac {\log ^8(x)}{x^5} \, dx}{2560000}-\frac {2047 \int \frac {\log ^7(x)}{x^6} \, dx}{160000}-\frac {34048 \int \frac {\log ^7(x)}{(1+x)^2} \, dx}{1953125}+\frac {28981 \int \frac {\log ^7(x)}{x^5} \, dx}{1280000}-\frac {74143 \int \frac {\log ^7(x)}{x^4} \, dx}{2560000}+\frac {706721 \int \frac {\log ^7(x)}{x^3} \, dx}{16384000}-\frac {4520791 \int \frac {\log ^7(x)}{x^2} \, dx}{81920000}-\frac {719104 \int \frac {\log ^7(x)}{1+x} \, dx}{9765625}+\frac {48823151 \int \frac {\log ^7(x)}{x} \, dx}{655360000} \\ & = \text {Too large to display} \\ \end{align*}
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 \[ \int \frac {\left (512+128 x-512 x^2+128 x^4\right ) \log ^7(x)+\left (-640-224 x+1152 x^2-416 x^4\right ) \log ^8(x)}{640000 x^{11}+800000 x^{12}-2800000 x^{13}-3100000 x^{14}+6012500 x^{15}+5400625 x^{16}-8112500 x^{17}-5450000 x^{18}+7403125 x^{19}+3450000 x^{20}-4665000 x^{21}-1393750 x^{22}+2025000 x^{23}+350000 x^{24}-593750 x^{25}-50000 x^{26}+112500 x^{27}+3125 x^{28}-12500 x^{29}+625 x^{31}} \, dx=\text {Result too large to show} \]
[In]
[Out]
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 | \(\frac {16 \ln \left (x \right )^{8}}{625 x^{10} \left (x^{16}-16 x^{14}+4 x^{13}+112 x^{12}-48 x^{11}-442 x^{10}+240 x^{9}+1072 x^{8}-636 x^{7}-1648 x^{6}+944 x^{5}+1601 x^{4}-752 x^{3}-928 x^{2}+256 x +256\right )}\) | \(85\) |
[In]
[Out]
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 \[ \int \frac {\left (512+128 x-512 x^2+128 x^4\right ) \log ^7(x)+\left (-640-224 x+1152 x^2-416 x^4\right ) \log ^8(x)}{640000 x^{11}+800000 x^{12}-2800000 x^{13}-3100000 x^{14}+6012500 x^{15}+5400625 x^{16}-8112500 x^{17}-5450000 x^{18}+7403125 x^{19}+3450000 x^{20}-4665000 x^{21}-1393750 x^{22}+2025000 x^{23}+350000 x^{24}-593750 x^{25}-50000 x^{26}+112500 x^{27}+3125 x^{28}-12500 x^{29}+625 x^{31}} \, dx=\frac {16 \, \log \left (x\right )^{8}}{625 \, {\left (x^{26} - 16 \, x^{24} + 4 \, x^{23} + 112 \, x^{22} - 48 \, x^{21} - 442 \, x^{20} + 240 \, x^{19} + 1072 \, x^{18} - 636 \, x^{17} - 1648 \, x^{16} + 944 \, x^{15} + 1601 \, x^{14} - 752 \, x^{13} - 928 \, x^{12} + 256 \, x^{11} + 256 \, x^{10}\right )}} \]
[In]
[Out]
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 \[ \int \frac {\left (512+128 x-512 x^2+128 x^4\right ) \log ^7(x)+\left (-640-224 x+1152 x^2-416 x^4\right ) \log ^8(x)}{640000 x^{11}+800000 x^{12}-2800000 x^{13}-3100000 x^{14}+6012500 x^{15}+5400625 x^{16}-8112500 x^{17}-5450000 x^{18}+7403125 x^{19}+3450000 x^{20}-4665000 x^{21}-1393750 x^{22}+2025000 x^{23}+350000 x^{24}-593750 x^{25}-50000 x^{26}+112500 x^{27}+3125 x^{28}-12500 x^{29}+625 x^{31}} \, dx=\frac {16 \log {\left (x \right )}^{8}}{625 x^{26} - 10000 x^{24} + 2500 x^{23} + 70000 x^{22} - 30000 x^{21} - 276250 x^{20} + 150000 x^{19} + 670000 x^{18} - 397500 x^{17} - 1030000 x^{16} + 590000 x^{15} + 1000625 x^{14} - 470000 x^{13} - 580000 x^{12} + 160000 x^{11} + 160000 x^{10}} \]
[In]
[Out]
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 \[ \int \frac {\left (512+128 x-512 x^2+128 x^4\right ) \log ^7(x)+\left (-640-224 x+1152 x^2-416 x^4\right ) \log ^8(x)}{640000 x^{11}+800000 x^{12}-2800000 x^{13}-3100000 x^{14}+6012500 x^{15}+5400625 x^{16}-8112500 x^{17}-5450000 x^{18}+7403125 x^{19}+3450000 x^{20}-4665000 x^{21}-1393750 x^{22}+2025000 x^{23}+350000 x^{24}-593750 x^{25}-50000 x^{26}+112500 x^{27}+3125 x^{28}-12500 x^{29}+625 x^{31}} \, dx=\frac {16 \, \log \left (x\right )^{8}}{625 \, {\left (x^{26} - 16 \, x^{24} + 4 \, x^{23} + 112 \, x^{22} - 48 \, x^{21} - 442 \, x^{20} + 240 \, x^{19} + 1072 \, x^{18} - 636 \, x^{17} - 1648 \, x^{16} + 944 \, x^{15} + 1601 \, x^{14} - 752 \, x^{13} - 928 \, x^{12} + 256 \, x^{11} + 256 \, x^{10}\right )}} \]
[In]
[Out]
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 \[ \int \frac {\left (512+128 x-512 x^2+128 x^4\right ) \log ^7(x)+\left (-640-224 x+1152 x^2-416 x^4\right ) \log ^8(x)}{640000 x^{11}+800000 x^{12}-2800000 x^{13}-3100000 x^{14}+6012500 x^{15}+5400625 x^{16}-8112500 x^{17}-5450000 x^{18}+7403125 x^{19}+3450000 x^{20}-4665000 x^{21}-1393750 x^{22}+2025000 x^{23}+350000 x^{24}-593750 x^{25}-50000 x^{26}+112500 x^{27}+3125 x^{28}-12500 x^{29}+625 x^{31}} \, dx=\frac {1}{655360000} \, {\left (\frac {4520791 \, x^{15} - 3533605 \, x^{14} - 69960080 \, x^{13} + 72766060 \, x^{12} + 455281020 \, x^{11} - 574439424 \, x^{10} - 1586688070 \, x^{9} + 2342625650 \, x^{8} + 3147073760 \, x^{7} - 5412734100 \, x^{6} - 3490610724 \, x^{5} + 7169196160 \, x^{4} + 1960274855 \, x^{3} - 5125415925 \, x^{2} - 405863120 \, x + 1562340832}{x^{16} - 16 \, x^{14} + 4 \, x^{13} + 112 \, x^{12} - 48 \, x^{11} - 442 \, x^{10} + 240 \, x^{9} + 1072 \, x^{8} - 636 \, x^{7} - 1648 \, x^{6} + 944 \, x^{5} + 1601 \, x^{4} - 752 \, x^{3} - 928 \, x^{2} + 256 \, x + 256} - \frac {4520791 \, x^{9} - 3533605 \, x^{8} + 2372576 \, x^{7} - 1854784 \, x^{6} + 1048064 \, x^{5} - 844544 \, x^{4} + 348160 \, x^{3} - 303104 \, x^{2} + 65536 \, x - 65536}{x^{10}}\right )} \log \left (x\right )^{8} \]
[In]
[Out]
Time = 13.27 (sec) , antiderivative size = 89, normalized size of antiderivative = 4.05 \[ \int \frac {\left (512+128 x-512 x^2+128 x^4\right ) \log ^7(x)+\left (-640-224 x+1152 x^2-416 x^4\right ) \log ^8(x)}{640000 x^{11}+800000 x^{12}-2800000 x^{13}-3100000 x^{14}+6012500 x^{15}+5400625 x^{16}-8112500 x^{17}-5450000 x^{18}+7403125 x^{19}+3450000 x^{20}-4665000 x^{21}-1393750 x^{22}+2025000 x^{23}+350000 x^{24}-593750 x^{25}-50000 x^{26}+112500 x^{27}+3125 x^{28}-12500 x^{29}+625 x^{31}} \, dx=\frac {16\,{\ln \left (x\right )}^8}{625\,\left (x^{26}-16\,x^{24}+4\,x^{23}+112\,x^{22}-48\,x^{21}-442\,x^{20}+240\,x^{19}+1072\,x^{18}-636\,x^{17}-1648\,x^{16}+944\,x^{15}+1601\,x^{14}-752\,x^{13}-928\,x^{12}+256\,x^{11}+256\,x^{10}\right )} \]
[In]
[Out]