Integrand size = 184, antiderivative size = 28 \[ \int \frac {72+\left (72-6 x-384 x^3+192 x^4-24 x^5\right ) \log (x)+\left (-6 x+384 x^3-384 x^4+72 x^5\right ) \log ^2(x)+\left (-64 x^4+48 x^5-4104 x^6+5120 x^7-2304 x^8+448 x^9-32 x^{10}\right ) \log ^3(x)}{-27+\left (432 x^3-216 x^4+27 x^5\right ) \log (x)+\left (-2304 x^6+2304 x^7-864 x^8+144 x^9-9 x^{10}\right ) \log ^2(x)+\left (4096 x^9-6144 x^{10}+3840 x^{11}-1280 x^{12}+240 x^{13}-24 x^{14}+x^{15}\right ) \log ^3(x)} \, dx=\left (4+\frac {x}{x (x+(3-x) x)^2-\frac {3}{\log (x)}}\right )^2 \]
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\[ \int \frac {72+\left (72-6 x-384 x^3+192 x^4-24 x^5\right ) \log (x)+\left (-6 x+384 x^3-384 x^4+72 x^5\right ) \log ^2(x)+\left (-64 x^4+48 x^5-4104 x^6+5120 x^7-2304 x^8+448 x^9-32 x^{10}\right ) \log ^3(x)}{-27+\left (432 x^3-216 x^4+27 x^5\right ) \log (x)+\left (-2304 x^6+2304 x^7-864 x^8+144 x^9-9 x^{10}\right ) \log ^2(x)+\left (4096 x^9-6144 x^{10}+3840 x^{11}-1280 x^{12}+240 x^{13}-24 x^{14}+x^{15}\right ) \log ^3(x)} \, dx=\int \frac {72+\left (72-6 x-384 x^3+192 x^4-24 x^5\right ) \log (x)+\left (-6 x+384 x^3-384 x^4+72 x^5\right ) \log ^2(x)+\left (-64 x^4+48 x^5-4104 x^6+5120 x^7-2304 x^8+448 x^9-32 x^{10}\right ) \log ^3(x)}{-27+\left (432 x^3-216 x^4+27 x^5\right ) \log (x)+\left (-2304 x^6+2304 x^7-864 x^8+144 x^9-9 x^{10}\right ) \log ^2(x)+\left (4096 x^9-6144 x^{10}+3840 x^{11}-1280 x^{12}+240 x^{13}-24 x^{14}+x^{15}\right ) \log ^3(x)} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {-72+6 \left (-12+x+64 x^3-32 x^4+4 x^5\right ) \log (x)-6 x \left (-1+64 x^2-64 x^3+12 x^4\right ) \log ^2(x)+8 x^4 \left (8-6 x+513 x^2-640 x^3+288 x^4-56 x^5+4 x^6\right ) \log ^3(x)}{\left (3-(-4+x)^2 x^3 \log (x)\right )^3} \, dx \\ & = \int \left (-\frac {8 \left (-2+x-128 x^2+128 x^3-40 x^4+4 x^5\right )}{(-4+x)^5 x^5}-\frac {18 \left (-36+15 x-64 x^3+48 x^4-12 x^5+x^6\right )}{(-4+x)^5 x^5 \left (-3+16 x^3 \log (x)-8 x^4 \log (x)+x^5 \log (x)\right )^3}-\frac {6 \left (-96+42 x-2304 x^2+2048 x^3-576 x^4-4048 x^5+5121 x^6-2560 x^7+640 x^8-80 x^9+4 x^{10}\right )}{(-4+x)^5 x^5 \left (-3+16 x^3 \log (x)-8 x^4 \log (x)+x^5 \log (x)\right )^2}-\frac {6 \left (-28+13 x-1280 x^2+1216 x^3-368 x^4+36 x^5\right )}{(-4+x)^5 x^5 \left (-3+16 x^3 \log (x)-8 x^4 \log (x)+x^5 \log (x)\right )}\right ) \, dx \\ & = -\left (6 \int \frac {-96+42 x-2304 x^2+2048 x^3-576 x^4-4048 x^5+5121 x^6-2560 x^7+640 x^8-80 x^9+4 x^{10}}{(-4+x)^5 x^5 \left (-3+16 x^3 \log (x)-8 x^4 \log (x)+x^5 \log (x)\right )^2} \, dx\right )-6 \int \frac {-28+13 x-1280 x^2+1216 x^3-368 x^4+36 x^5}{(-4+x)^5 x^5 \left (-3+16 x^3 \log (x)-8 x^4 \log (x)+x^5 \log (x)\right )} \, dx-8 \int \frac {-2+x-128 x^2+128 x^3-40 x^4+4 x^5}{(-4+x)^5 x^5} \, dx-18 \int \frac {-36+15 x-64 x^3+48 x^4-12 x^5+x^6}{(-4+x)^5 x^5 \left (-3+16 x^3 \log (x)-8 x^4 \log (x)+x^5 \log (x)\right )^3} \, dx \\ & = -\left (6 \int \left (\frac {4}{\left (-3+16 x^3 \log (x)-8 x^4 \log (x)+x^5 \log (x)\right )^2}+\frac {9}{128 (-4+x)^5 \left (-3+16 x^3 \log (x)-8 x^4 \log (x)+x^5 \log (x)\right )^2}-\frac {3}{64 (-4+x)^4 \left (-3+16 x^3 \log (x)-8 x^4 \log (x)+x^5 \log (x)\right )^2}+\frac {1551}{1024 (-4+x)^3 \left (-3+16 x^3 \log (x)-8 x^4 \log (x)+x^5 \log (x)\right )^2}-\frac {1}{8 (-4+x)^2 \left (-3+16 x^3 \log (x)-8 x^4 \log (x)+x^5 \log (x)\right )^2}-\frac {5737}{32768 (-4+x) \left (-3+16 x^3 \log (x)-8 x^4 \log (x)+x^5 \log (x)\right )^2}+\frac {3}{32 x^5 \left (-3+16 x^3 \log (x)-8 x^4 \log (x)+x^5 \log (x)\right )^2}+\frac {39}{512 x^4 \left (-3+16 x^3 \log (x)-8 x^4 \log (x)+x^5 \log (x)\right )^2}+\frac {4683}{2048 x^3 \left (-3+16 x^3 \log (x)-8 x^4 \log (x)+x^5 \log (x)\right )^2}+\frac {6761}{8192 x^2 \left (-3+16 x^3 \log (x)-8 x^4 \log (x)+x^5 \log (x)\right )^2}+\frac {5737}{32768 x \left (-3+16 x^3 \log (x)-8 x^4 \log (x)+x^5 \log (x)\right )^2}\right ) \, dx\right )-6 \int \left (\frac {3}{128 (-4+x)^5 \left (-3+16 x^3 \log (x)-8 x^4 \log (x)+x^5 \log (x)\right )}-\frac {17}{1024 (-4+x)^4 \left (-3+16 x^3 \log (x)-8 x^4 \log (x)+x^5 \log (x)\right )}+\frac {4121}{4096 (-4+x)^3 \left (-3+16 x^3 \log (x)-8 x^4 \log (x)+x^5 \log (x)\right )}-\frac {3087}{16384 (-4+x)^2 \left (-3+16 x^3 \log (x)-8 x^4 \log (x)+x^5 \log (x)\right )}-\frac {3107}{65536 (-4+x) \left (-3+16 x^3 \log (x)-8 x^4 \log (x)+x^5 \log (x)\right )}+\frac {7}{256 x^5 \left (-3+16 x^3 \log (x)-8 x^4 \log (x)+x^5 \log (x)\right )}+\frac {11}{512 x^4 \left (-3+16 x^3 \log (x)-8 x^4 \log (x)+x^5 \log (x)\right )}+\frac {645}{512 x^3 \left (-3+16 x^3 \log (x)-8 x^4 \log (x)+x^5 \log (x)\right )}+\frac {3097}{8192 x^2 \left (-3+16 x^3 \log (x)-8 x^4 \log (x)+x^5 \log (x)\right )}+\frac {3107}{65536 x \left (-3+16 x^3 \log (x)-8 x^4 \log (x)+x^5 \log (x)\right )}\right ) \, dx-8 \int \left (\frac {1}{512 (-4+x)^5}-\frac {3}{2048 (-4+x)^4}+\frac {1029}{8192 (-4+x)^3}-\frac {1029}{32768 (-4+x)^2}+\frac {1}{512 x^5}+\frac {3}{2048 x^4}+\frac {1029}{8192 x^3}+\frac {1029}{32768 x^2}\right ) \, dx-18 \int \left (\frac {3}{128 (-4+x)^5 \left (-3+16 x^3 \log (x)-8 x^4 \log (x)+x^5 \log (x)\right )^3}-\frac {15}{1024 (-4+x)^4 \left (-3+16 x^3 \log (x)-8 x^4 \log (x)+x^5 \log (x)\right )^3}+\frac {15}{4096 (-4+x)^3 \left (-3+16 x^3 \log (x)-8 x^4 \log (x)+x^5 \log (x)\right )^3}+\frac {1039}{16384 (-4+x)^2 \left (-3+16 x^3 \log (x)-8 x^4 \log (x)+x^5 \log (x)\right )^3}-\frac {2153}{65536 (-4+x) \left (-3+16 x^3 \log (x)-8 x^4 \log (x)+x^5 \log (x)\right )^3}+\frac {9}{256 x^5 \left (-3+16 x^3 \log (x)-8 x^4 \log (x)+x^5 \log (x)\right )^3}+\frac {15}{512 x^4 \left (-3+16 x^3 \log (x)-8 x^4 \log (x)+x^5 \log (x)\right )^3}+\frac {15}{1024 x^3 \left (-3+16 x^3 \log (x)-8 x^4 \log (x)+x^5 \log (x)\right )^3}+\frac {557}{8192 x^2 \left (-3+16 x^3 \log (x)-8 x^4 \log (x)+x^5 \log (x)\right )^3}+\frac {2153}{65536 x \left (-3+16 x^3 \log (x)-8 x^4 \log (x)+x^5 \log (x)\right )^3}\right ) \, dx \\ & = \text {Too large to display} \\ \end{align*}
Time = 0.08 (sec) , antiderivative size = 41, normalized size of antiderivative = 1.46 \[ \int \frac {72+\left (72-6 x-384 x^3+192 x^4-24 x^5\right ) \log (x)+\left (-6 x+384 x^3-384 x^4+72 x^5\right ) \log ^2(x)+\left (-64 x^4+48 x^5-4104 x^6+5120 x^7-2304 x^8+448 x^9-32 x^{10}\right ) \log ^3(x)}{-27+\left (432 x^3-216 x^4+27 x^5\right ) \log (x)+\left (-2304 x^6+2304 x^7-864 x^8+144 x^9-9 x^{10}\right ) \log ^2(x)+\left (4096 x^9-6144 x^{10}+3840 x^{11}-1280 x^{12}+240 x^{13}-24 x^{14}+x^{15}\right ) \log ^3(x)} \, dx=\frac {x \log (x) \left (-24+\left (x+128 x^3-64 x^4+8 x^5\right ) \log (x)\right )}{\left (-3+(-4+x)^2 x^3 \log (x)\right )^2} \]
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Time = 1.14 (sec) , antiderivative size = 56, normalized size of antiderivative = 2.00
method | result | size |
default | \(\frac {\left (8 x^{5} \ln \left (x \right )-64 x^{4} \ln \left (x \right )+128 x^{3} \ln \left (x \right )+x \ln \left (x \right )-24\right ) x \ln \left (x \right )}{\left (x^{5} \ln \left (x \right )-8 x^{4} \ln \left (x \right )+16 x^{3} \ln \left (x \right )-3\right )^{2}}\) | \(56\) |
parallelrisch | \(\frac {6144 x^{6} \ln \left (x \right )^{2}+98304 x^{4} \ln \left (x \right )^{2}-18432 x \ln \left (x \right )-49152 x^{5} \ln \left (x \right )^{2}+768 x^{2} \ln \left (x \right )^{2}}{768 x^{10} \ln \left (x \right )^{2}-12288 x^{9} \ln \left (x \right )^{2}+73728 x^{8} \ln \left (x \right )^{2}-196608 x^{7} \ln \left (x \right )^{2}+196608 x^{6} \ln \left (x \right )^{2}-4608 x^{5} \ln \left (x \right )+36864 x^{4} \ln \left (x \right )-73728 x^{3} \ln \left (x \right )+6912}\) | \(114\) |
risch | \(\frac {8 x^{4}-64 x^{3}+128 x^{2}+1}{\left (x^{4}-16 x^{3}+96 x^{2}-256 x +256\right ) x^{4}}+\frac {24 x^{9} \ln \left (x \right )-384 x^{8} \ln \left (x \right )+2304 x^{7} \ln \left (x \right )-6144 x^{6} \ln \left (x \right )+6150 x^{5} \ln \left (x \right )-48 x^{4} \ln \left (x \right )-72 x^{4}+96 x^{3} \ln \left (x \right )+576 x^{3}-1152 x^{2}-9}{\left (x -4\right ) \left (x^{3}-12 x^{2}+48 x -64\right ) \left (x^{5} \ln \left (x \right )-8 x^{4} \ln \left (x \right )+16 x^{3} \ln \left (x \right )-3\right )^{2} x^{4}}\) | \(158\) |
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Leaf count of result is larger than twice the leaf count of optimal. 82 vs. \(2 (28) = 56\).
Time = 0.26 (sec) , antiderivative size = 82, normalized size of antiderivative = 2.93 \[ \int \frac {72+\left (72-6 x-384 x^3+192 x^4-24 x^5\right ) \log (x)+\left (-6 x+384 x^3-384 x^4+72 x^5\right ) \log ^2(x)+\left (-64 x^4+48 x^5-4104 x^6+5120 x^7-2304 x^8+448 x^9-32 x^{10}\right ) \log ^3(x)}{-27+\left (432 x^3-216 x^4+27 x^5\right ) \log (x)+\left (-2304 x^6+2304 x^7-864 x^8+144 x^9-9 x^{10}\right ) \log ^2(x)+\left (4096 x^9-6144 x^{10}+3840 x^{11}-1280 x^{12}+240 x^{13}-24 x^{14}+x^{15}\right ) \log ^3(x)} \, dx=\frac {{\left (8 \, x^{6} - 64 \, x^{5} + 128 \, x^{4} + x^{2}\right )} \log \left (x\right )^{2} - 24 \, x \log \left (x\right )}{{\left (x^{10} - 16 \, x^{9} + 96 \, x^{8} - 256 \, x^{7} + 256 \, x^{6}\right )} \log \left (x\right )^{2} - 6 \, {\left (x^{5} - 8 \, x^{4} + 16 \, x^{3}\right )} \log \left (x\right ) + 9} \]
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Leaf count of result is larger than twice the leaf count of optimal. 209 vs. \(2 (19) = 38\).
Time = 0.33 (sec) , antiderivative size = 209, normalized size of antiderivative = 7.46 \[ \int \frac {72+\left (72-6 x-384 x^3+192 x^4-24 x^5\right ) \log (x)+\left (-6 x+384 x^3-384 x^4+72 x^5\right ) \log ^2(x)+\left (-64 x^4+48 x^5-4104 x^6+5120 x^7-2304 x^8+448 x^9-32 x^{10}\right ) \log ^3(x)}{-27+\left (432 x^3-216 x^4+27 x^5\right ) \log (x)+\left (-2304 x^6+2304 x^7-864 x^8+144 x^9-9 x^{10}\right ) \log ^2(x)+\left (4096 x^9-6144 x^{10}+3840 x^{11}-1280 x^{12}+240 x^{13}-24 x^{14}+x^{15}\right ) \log ^3(x)} \, dx=- \frac {- 8 x^{4} + 64 x^{3} - 128 x^{2} - 1}{x^{8} - 16 x^{7} + 96 x^{6} - 256 x^{5} + 256 x^{4}} + \frac {- 72 x^{4} + 576 x^{3} - 1152 x^{2} + \left (24 x^{9} - 384 x^{8} + 2304 x^{7} - 6144 x^{6} + 6150 x^{5} - 48 x^{4} + 96 x^{3}\right ) \log {\left (x \right )} - 9}{9 x^{8} - 144 x^{7} + 864 x^{6} - 2304 x^{5} + 2304 x^{4} + \left (- 6 x^{13} + 144 x^{12} - 1440 x^{11} + 7680 x^{10} - 23040 x^{9} + 36864 x^{8} - 24576 x^{7}\right ) \log {\left (x \right )} + \left (x^{18} - 32 x^{17} + 448 x^{16} - 3584 x^{15} + 17920 x^{14} - 57344 x^{13} + 114688 x^{12} - 131072 x^{11} + 65536 x^{10}\right ) \log {\left (x \right )}^{2}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 82 vs. \(2 (28) = 56\).
Time = 0.25 (sec) , antiderivative size = 82, normalized size of antiderivative = 2.93 \[ \int \frac {72+\left (72-6 x-384 x^3+192 x^4-24 x^5\right ) \log (x)+\left (-6 x+384 x^3-384 x^4+72 x^5\right ) \log ^2(x)+\left (-64 x^4+48 x^5-4104 x^6+5120 x^7-2304 x^8+448 x^9-32 x^{10}\right ) \log ^3(x)}{-27+\left (432 x^3-216 x^4+27 x^5\right ) \log (x)+\left (-2304 x^6+2304 x^7-864 x^8+144 x^9-9 x^{10}\right ) \log ^2(x)+\left (4096 x^9-6144 x^{10}+3840 x^{11}-1280 x^{12}+240 x^{13}-24 x^{14}+x^{15}\right ) \log ^3(x)} \, dx=\frac {{\left (8 \, x^{6} - 64 \, x^{5} + 128 \, x^{4} + x^{2}\right )} \log \left (x\right )^{2} - 24 \, x \log \left (x\right )}{{\left (x^{10} - 16 \, x^{9} + 96 \, x^{8} - 256 \, x^{7} + 256 \, x^{6}\right )} \log \left (x\right )^{2} - 6 \, {\left (x^{5} - 8 \, x^{4} + 16 \, x^{3}\right )} \log \left (x\right ) + 9} \]
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Leaf count of result is larger than twice the leaf count of optimal. 283 vs. \(2 (28) = 56\).
Time = 0.34 (sec) , antiderivative size = 283, normalized size of antiderivative = 10.11 \[ \int \frac {72+\left (72-6 x-384 x^3+192 x^4-24 x^5\right ) \log (x)+\left (-6 x+384 x^3-384 x^4+72 x^5\right ) \log ^2(x)+\left (-64 x^4+48 x^5-4104 x^6+5120 x^7-2304 x^8+448 x^9-32 x^{10}\right ) \log ^3(x)}{-27+\left (432 x^3-216 x^4+27 x^5\right ) \log (x)+\left (-2304 x^6+2304 x^7-864 x^8+144 x^9-9 x^{10}\right ) \log ^2(x)+\left (4096 x^9-6144 x^{10}+3840 x^{11}-1280 x^{12}+240 x^{13}-24 x^{14}+x^{15}\right ) \log ^3(x)} \, dx=\frac {3 \, {\left (8 \, x^{9} \log \left (x\right ) - 128 \, x^{8} \log \left (x\right ) + 768 \, x^{7} \log \left (x\right ) - 2048 \, x^{6} \log \left (x\right ) + 2050 \, x^{5} \log \left (x\right ) - 16 \, x^{4} \log \left (x\right ) - 24 \, x^{4} + 32 \, x^{3} \log \left (x\right ) + 192 \, x^{3} - 384 \, x^{2} - 3\right )}}{x^{18} \log \left (x\right )^{2} - 32 \, x^{17} \log \left (x\right )^{2} + 448 \, x^{16} \log \left (x\right )^{2} - 3584 \, x^{15} \log \left (x\right )^{2} + 17920 \, x^{14} \log \left (x\right )^{2} - 57344 \, x^{13} \log \left (x\right )^{2} - 6 \, x^{13} \log \left (x\right ) + 114688 \, x^{12} \log \left (x\right )^{2} + 144 \, x^{12} \log \left (x\right ) - 131072 \, x^{11} \log \left (x\right )^{2} - 1440 \, x^{11} \log \left (x\right ) + 65536 \, x^{10} \log \left (x\right )^{2} + 7680 \, x^{10} \log \left (x\right ) - 23040 \, x^{9} \log \left (x\right ) + 36864 \, x^{8} \log \left (x\right ) + 9 \, x^{8} - 24576 \, x^{7} \log \left (x\right ) - 144 \, x^{7} + 864 \, x^{6} - 2304 \, x^{5} + 2304 \, x^{4}} - \frac {1029 \, x^{3} - 14406 \, x^{2} + 65872 \, x - 98864}{4096 \, {\left (x^{4} - 16 \, x^{3} + 96 \, x^{2} - 256 \, x + 256\right )}} + \frac {1029 \, x^{3} + 2058 \, x^{2} + 16 \, x + 16}{4096 \, x^{4}} \]
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Timed out. \[ \int \frac {72+\left (72-6 x-384 x^3+192 x^4-24 x^5\right ) \log (x)+\left (-6 x+384 x^3-384 x^4+72 x^5\right ) \log ^2(x)+\left (-64 x^4+48 x^5-4104 x^6+5120 x^7-2304 x^8+448 x^9-32 x^{10}\right ) \log ^3(x)}{-27+\left (432 x^3-216 x^4+27 x^5\right ) \log (x)+\left (-2304 x^6+2304 x^7-864 x^8+144 x^9-9 x^{10}\right ) \log ^2(x)+\left (4096 x^9-6144 x^{10}+3840 x^{11}-1280 x^{12}+240 x^{13}-24 x^{14}+x^{15}\right ) \log ^3(x)} \, dx=-\int -\frac {\left (32\,x^{10}-448\,x^9+2304\,x^8-5120\,x^7+4104\,x^6-48\,x^5+64\,x^4\right )\,{\ln \left (x\right )}^3+\left (-72\,x^5+384\,x^4-384\,x^3+6\,x\right )\,{\ln \left (x\right )}^2+\left (24\,x^5-192\,x^4+384\,x^3+6\,x-72\right )\,\ln \left (x\right )-72}{\left (-x^{15}+24\,x^{14}-240\,x^{13}+1280\,x^{12}-3840\,x^{11}+6144\,x^{10}-4096\,x^9\right )\,{\ln \left (x\right )}^3+\left (9\,x^{10}-144\,x^9+864\,x^8-2304\,x^7+2304\,x^6\right )\,{\ln \left (x\right )}^2+\left (-27\,x^5+216\,x^4-432\,x^3\right )\,\ln \left (x\right )+27} \,d x \]
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