Integrand size = 72, antiderivative size = 18 \[ \int \frac {9765625 x^{15} \left (30-35 x+5 x \log \left (x^2\right )\right )}{\left (2 x-3 x^2+x^2 \log \left (x^2\right )\right ) \left (4-12 x+9 x^2+\left (4 x-6 x^2\right ) \log \left (x^2\right )+x^2 \log ^2\left (x^2\right )\right )^5} \, dx=\frac {9765625 x^5}{\left (-3+\frac {2}{x}+\log \left (x^2\right )\right )^{10}} \]
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\[ \int \frac {9765625 x^{15} \left (30-35 x+5 x \log \left (x^2\right )\right )}{\left (2 x-3 x^2+x^2 \log \left (x^2\right )\right ) \left (4-12 x+9 x^2+\left (4 x-6 x^2\right ) \log \left (x^2\right )+x^2 \log ^2\left (x^2\right )\right )^5} \, dx=\int \frac {9765625 x^{15} \left (30-35 x+5 x \log \left (x^2\right )\right )}{\left (2 x-3 x^2+x^2 \log \left (x^2\right )\right ) \left (4-12 x+9 x^2+\left (4 x-6 x^2\right ) \log \left (x^2\right )+x^2 \log ^2\left (x^2\right )\right )^5} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = 9765625 \int \frac {x^{15} \left (30-35 x+5 x \log \left (x^2\right )\right )}{\left (2 x-3 x^2+x^2 \log \left (x^2\right )\right ) \left (4-12 x+9 x^2+\left (4 x-6 x^2\right ) \log \left (x^2\right )+x^2 \log ^2\left (x^2\right )\right )^5} \, dx \\ & = 9765625 \int \frac {5 x^{14} \left (6-7 x+x \log \left (x^2\right )\right )}{\left (2-3 x+x \log \left (x^2\right )\right )^{11}} \, dx \\ & = 48828125 \int \frac {x^{14} \left (6-7 x+x \log \left (x^2\right )\right )}{\left (2-3 x+x \log \left (x^2\right )\right )^{11}} \, dx \\ & = 48828125 \int \left (-\frac {4 (-1+x) x^{14}}{\left (2-3 x+x \log \left (x^2\right )\right )^{11}}+\frac {x^{14}}{\left (2-3 x+x \log \left (x^2\right )\right )^{10}}\right ) \, dx \\ & = 48828125 \int \frac {x^{14}}{\left (2-3 x+x \log \left (x^2\right )\right )^{10}} \, dx-195312500 \int \frac {(-1+x) x^{14}}{\left (2-3 x+x \log \left (x^2\right )\right )^{11}} \, dx \\ & = 48828125 \int \frac {x^{14}}{\left (2-3 x+x \log \left (x^2\right )\right )^{10}} \, dx-195312500 \int \left (-\frac {x^{14}}{\left (2-3 x+x \log \left (x^2\right )\right )^{11}}+\frac {x^{15}}{\left (2-3 x+x \log \left (x^2\right )\right )^{11}}\right ) \, dx \\ & = 48828125 \int \frac {x^{14}}{\left (2-3 x+x \log \left (x^2\right )\right )^{10}} \, dx+195312500 \int \frac {x^{14}}{\left (2-3 x+x \log \left (x^2\right )\right )^{11}} \, dx-195312500 \int \frac {x^{15}}{\left (2-3 x+x \log \left (x^2\right )\right )^{11}} \, dx \\ \end{align*}
Time = 1.36 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00 \[ \int \frac {9765625 x^{15} \left (30-35 x+5 x \log \left (x^2\right )\right )}{\left (2 x-3 x^2+x^2 \log \left (x^2\right )\right ) \left (4-12 x+9 x^2+\left (4 x-6 x^2\right ) \log \left (x^2\right )+x^2 \log ^2\left (x^2\right )\right )^5} \, dx=\frac {9765625 x^{15}}{\left (2-3 x+x \log \left (x^2\right )\right )^{10}} \]
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Time = 0.96 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.06
method | result | size |
risch | \(\frac {9765625 x^{15}}{{\left (x \ln \left (x^{2}\right )-3 x +2\right )}^{10}}\) | \(19\) |
parallelrisch | \(\frac {9765625 x^{15}}{\left (x^{2} \ln \left (x^{2}\right )^{2}-6 x^{2} \ln \left (x^{2}\right )+4 x \ln \left (x^{2}\right )+9 x^{2}-12 x +4\right )^{4} {\left (x \ln \left (x^{2}\right )-3 x +2\right )}^{2}}\) | \(57\) |
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Leaf count of result is larger than twice the leaf count of optimal. 414 vs. \(2 (18) = 36\).
Time = 0.25 (sec) , antiderivative size = 414, normalized size of antiderivative = 23.00 \[ \int \frac {9765625 x^{15} \left (30-35 x+5 x \log \left (x^2\right )\right )}{\left (2 x-3 x^2+x^2 \log \left (x^2\right )\right ) \left (4-12 x+9 x^2+\left (4 x-6 x^2\right ) \log \left (x^2\right )+x^2 \log ^2\left (x^2\right )\right )^5} \, dx=\frac {9765625 \, x^{15}}{x^{10} \log \left (x^{2}\right )^{10} + 59049 \, x^{10} - 10 \, {\left (3 \, x^{10} - 2 \, x^{9}\right )} \log \left (x^{2}\right )^{9} - 393660 \, x^{9} + 45 \, {\left (9 \, x^{10} - 12 \, x^{9} + 4 \, x^{8}\right )} \log \left (x^{2}\right )^{8} + 1180980 \, x^{8} - 120 \, {\left (27 \, x^{10} - 54 \, x^{9} + 36 \, x^{8} - 8 \, x^{7}\right )} \log \left (x^{2}\right )^{7} - 2099520 \, x^{7} + 210 \, {\left (81 \, x^{10} - 216 \, x^{9} + 216 \, x^{8} - 96 \, x^{7} + 16 \, x^{6}\right )} \log \left (x^{2}\right )^{6} + 2449440 \, x^{6} - 252 \, {\left (243 \, x^{10} - 810 \, x^{9} + 1080 \, x^{8} - 720 \, x^{7} + 240 \, x^{6} - 32 \, x^{5}\right )} \log \left (x^{2}\right )^{5} - 1959552 \, x^{5} + 210 \, {\left (729 \, x^{10} - 2916 \, x^{9} + 4860 \, x^{8} - 4320 \, x^{7} + 2160 \, x^{6} - 576 \, x^{5} + 64 \, x^{4}\right )} \log \left (x^{2}\right )^{4} + 1088640 \, x^{4} - 120 \, {\left (2187 \, x^{10} - 10206 \, x^{9} + 20412 \, x^{8} - 22680 \, x^{7} + 15120 \, x^{6} - 6048 \, x^{5} + 1344 \, x^{4} - 128 \, x^{3}\right )} \log \left (x^{2}\right )^{3} - 414720 \, x^{3} + 45 \, {\left (6561 \, x^{10} - 34992 \, x^{9} + 81648 \, x^{8} - 108864 \, x^{7} + 90720 \, x^{6} - 48384 \, x^{5} + 16128 \, x^{4} - 3072 \, x^{3} + 256 \, x^{2}\right )} \log \left (x^{2}\right )^{2} + 103680 \, x^{2} - 10 \, {\left (19683 \, x^{10} - 118098 \, x^{9} + 314928 \, x^{8} - 489888 \, x^{7} + 489888 \, x^{6} - 326592 \, x^{5} + 145152 \, x^{4} - 41472 \, x^{3} + 6912 \, x^{2} - 512 \, x\right )} \log \left (x^{2}\right ) - 15360 \, x + 1024} \]
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Leaf count of result is larger than twice the leaf count of optimal. 398 vs. \(2 (15) = 30\).
Time = 1.39 (sec) , antiderivative size = 398, normalized size of antiderivative = 22.11 \[ \int \frac {9765625 x^{15} \left (30-35 x+5 x \log \left (x^2\right )\right )}{\left (2 x-3 x^2+x^2 \log \left (x^2\right )\right ) \left (4-12 x+9 x^2+\left (4 x-6 x^2\right ) \log \left (x^2\right )+x^2 \log ^2\left (x^2\right )\right )^5} \, dx=\frac {9765625 x^{15}}{x^{10} \log {\left (x^{2} \right )}^{10} + 59049 x^{10} - 393660 x^{9} + 1180980 x^{8} - 2099520 x^{7} + 2449440 x^{6} - 1959552 x^{5} + 1088640 x^{4} - 414720 x^{3} + 103680 x^{2} - 15360 x + \left (- 30 x^{10} + 20 x^{9}\right ) \log {\left (x^{2} \right )}^{9} + \left (405 x^{10} - 540 x^{9} + 180 x^{8}\right ) \log {\left (x^{2} \right )}^{8} + \left (- 3240 x^{10} + 6480 x^{9} - 4320 x^{8} + 960 x^{7}\right ) \log {\left (x^{2} \right )}^{7} + \left (17010 x^{10} - 45360 x^{9} + 45360 x^{8} - 20160 x^{7} + 3360 x^{6}\right ) \log {\left (x^{2} \right )}^{6} + \left (- 61236 x^{10} + 204120 x^{9} - 272160 x^{8} + 181440 x^{7} - 60480 x^{6} + 8064 x^{5}\right ) \log {\left (x^{2} \right )}^{5} + \left (153090 x^{10} - 612360 x^{9} + 1020600 x^{8} - 907200 x^{7} + 453600 x^{6} - 120960 x^{5} + 13440 x^{4}\right ) \log {\left (x^{2} \right )}^{4} + \left (- 262440 x^{10} + 1224720 x^{9} - 2449440 x^{8} + 2721600 x^{7} - 1814400 x^{6} + 725760 x^{5} - 161280 x^{4} + 15360 x^{3}\right ) \log {\left (x^{2} \right )}^{3} + \left (295245 x^{10} - 1574640 x^{9} + 3674160 x^{8} - 4898880 x^{7} + 4082400 x^{6} - 2177280 x^{5} + 725760 x^{4} - 138240 x^{3} + 11520 x^{2}\right ) \log {\left (x^{2} \right )}^{2} + \left (- 196830 x^{10} + 1180980 x^{9} - 3149280 x^{8} + 4898880 x^{7} - 4898880 x^{6} + 3265920 x^{5} - 1451520 x^{4} + 414720 x^{3} - 69120 x^{2} + 5120 x\right ) \log {\left (x^{2} \right )} + 1024} \]
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Leaf count of result is larger than twice the leaf count of optimal. 395 vs. \(2 (18) = 36\).
Time = 0.46 (sec) , antiderivative size = 395, normalized size of antiderivative = 21.94 \[ \int \frac {9765625 x^{15} \left (30-35 x+5 x \log \left (x^2\right )\right )}{\left (2 x-3 x^2+x^2 \log \left (x^2\right )\right ) \left (4-12 x+9 x^2+\left (4 x-6 x^2\right ) \log \left (x^2\right )+x^2 \log ^2\left (x^2\right )\right )^5} \, dx=\frac {9765625 \, x^{15}}{1024 \, x^{10} \log \left (x\right )^{10} + 59049 \, x^{10} - 5120 \, {\left (3 \, x^{10} - 2 \, x^{9}\right )} \log \left (x\right )^{9} - 393660 \, x^{9} + 11520 \, {\left (9 \, x^{10} - 12 \, x^{9} + 4 \, x^{8}\right )} \log \left (x\right )^{8} + 1180980 \, x^{8} - 15360 \, {\left (27 \, x^{10} - 54 \, x^{9} + 36 \, x^{8} - 8 \, x^{7}\right )} \log \left (x\right )^{7} - 2099520 \, x^{7} + 13440 \, {\left (81 \, x^{10} - 216 \, x^{9} + 216 \, x^{8} - 96 \, x^{7} + 16 \, x^{6}\right )} \log \left (x\right )^{6} + 2449440 \, x^{6} - 8064 \, {\left (243 \, x^{10} - 810 \, x^{9} + 1080 \, x^{8} - 720 \, x^{7} + 240 \, x^{6} - 32 \, x^{5}\right )} \log \left (x\right )^{5} - 1959552 \, x^{5} + 3360 \, {\left (729 \, x^{10} - 2916 \, x^{9} + 4860 \, x^{8} - 4320 \, x^{7} + 2160 \, x^{6} - 576 \, x^{5} + 64 \, x^{4}\right )} \log \left (x\right )^{4} + 1088640 \, x^{4} - 960 \, {\left (2187 \, x^{10} - 10206 \, x^{9} + 20412 \, x^{8} - 22680 \, x^{7} + 15120 \, x^{6} - 6048 \, x^{5} + 1344 \, x^{4} - 128 \, x^{3}\right )} \log \left (x\right )^{3} - 414720 \, x^{3} + 180 \, {\left (6561 \, x^{10} - 34992 \, x^{9} + 81648 \, x^{8} - 108864 \, x^{7} + 90720 \, x^{6} - 48384 \, x^{5} + 16128 \, x^{4} - 3072 \, x^{3} + 256 \, x^{2}\right )} \log \left (x\right )^{2} + 103680 \, x^{2} - 20 \, {\left (19683 \, x^{10} - 118098 \, x^{9} + 314928 \, x^{8} - 489888 \, x^{7} + 489888 \, x^{6} - 326592 \, x^{5} + 145152 \, x^{4} - 41472 \, x^{3} + 6912 \, x^{2} - 512 \, x\right )} \log \left (x\right ) - 15360 \, x + 1024} \]
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Leaf count of result is larger than twice the leaf count of optimal. 758 vs. \(2 (18) = 36\).
Time = 0.36 (sec) , antiderivative size = 758, normalized size of antiderivative = 42.11 \[ \int \frac {9765625 x^{15} \left (30-35 x+5 x \log \left (x^2\right )\right )}{\left (2 x-3 x^2+x^2 \log \left (x^2\right )\right ) \left (4-12 x+9 x^2+\left (4 x-6 x^2\right ) \log \left (x^2\right )+x^2 \log ^2\left (x^2\right )\right )^5} \, dx=\text {Too large to display} \]
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Time = 10.71 (sec) , antiderivative size = 192, normalized size of antiderivative = 10.67 \[ \int \frac {9765625 x^{15} \left (30-35 x+5 x \log \left (x^2\right )\right )}{\left (2 x-3 x^2+x^2 \log \left (x^2\right )\right ) \left (4-12 x+9 x^2+\left (4 x-6 x^2\right ) \log \left (x^2\right )+x^2 \log ^2\left (x^2\right )\right )^5} \, dx=-\frac {9765625\,\left (x^{15}-x^{16}\right )}{\left (x-1\right )\,\left ({\left (3\,x-2\right )}^{10}+x^{10}\,{\ln \left (x^2\right )}^{10}-10\,x^9\,{\ln \left (x^2\right )}^9\,\left (3\,x-2\right )+45\,x^2\,{\ln \left (x^2\right )}^2\,{\left (3\,x-2\right )}^8-120\,x^3\,{\ln \left (x^2\right )}^3\,{\left (3\,x-2\right )}^7+210\,x^4\,{\ln \left (x^2\right )}^4\,{\left (3\,x-2\right )}^6-252\,x^5\,{\ln \left (x^2\right )}^5\,{\left (3\,x-2\right )}^5+210\,x^6\,{\ln \left (x^2\right )}^6\,{\left (3\,x-2\right )}^4-120\,x^7\,{\ln \left (x^2\right )}^7\,{\left (3\,x-2\right )}^3+45\,x^8\,{\ln \left (x^2\right )}^8\,{\left (3\,x-2\right )}^2-10\,x\,\ln \left (x^2\right )\,{\left (3\,x-2\right )}^9\right )} \]
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