Integrand size = 146, antiderivative size = 20 \[ \int \frac {-414720+552960 \log (2)-276480 \log ^2(2)+61440 \log ^3(2)-5120 \log ^4(2)+\left (-414720+552960 \log (2)-276480 \log ^2(2)+61440 \log ^3(2)-5120 \log ^4(2)\right ) \log (4)+\left (-155520+207360 \log (2)-103680 \log ^2(2)+23040 \log ^3(2)-1920 \log ^4(2)\right ) \log ^2(4)+\left (-25920+34560 \log (2)-17280 \log ^2(2)+3840 \log ^3(2)-320 \log ^4(2)\right ) \log ^3(4)+\left (-1620+2160 \log (2)-1080 \log ^2(2)+240 \log ^3(2)-20 \log ^4(2)\right ) \log ^4(4)}{x^{21} \log ^4(4)} \, dx=\frac {(-3+\log (2))^4 (4+\log (4))^4}{x^{20} \log ^4(4)} \]
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Time = 0.02 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.10, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.014, Rules used = {12, 30} \[ \int \frac {-414720+552960 \log (2)-276480 \log ^2(2)+61440 \log ^3(2)-5120 \log ^4(2)+\left (-414720+552960 \log (2)-276480 \log ^2(2)+61440 \log ^3(2)-5120 \log ^4(2)\right ) \log (4)+\left (-155520+207360 \log (2)-103680 \log ^2(2)+23040 \log ^3(2)-1920 \log ^4(2)\right ) \log ^2(4)+\left (-25920+34560 \log (2)-17280 \log ^2(2)+3840 \log ^3(2)-320 \log ^4(2)\right ) \log ^3(4)+\left (-1620+2160 \log (2)-1080 \log ^2(2)+240 \log ^3(2)-20 \log ^4(2)\right ) \log ^4(4)}{x^{21} \log ^4(4)} \, dx=\frac {(3-\log (2))^4 (4+\log (4))^4}{x^{20} \log ^4(4)} \]
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Rule 12
Rule 30
Rubi steps \begin{align*} \text {integral}& = -\frac {\left (20 (3-\log (2))^4 (4+\log (4))^4\right ) \int \frac {1}{x^{21}} \, dx}{\log ^4(4)} \\ & = \frac {(3-\log (2))^4 (4+\log (4))^4}{x^{20} \log ^4(4)} \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00 \[ \int \frac {-414720+552960 \log (2)-276480 \log ^2(2)+61440 \log ^3(2)-5120 \log ^4(2)+\left (-414720+552960 \log (2)-276480 \log ^2(2)+61440 \log ^3(2)-5120 \log ^4(2)\right ) \log (4)+\left (-155520+207360 \log (2)-103680 \log ^2(2)+23040 \log ^3(2)-1920 \log ^4(2)\right ) \log ^2(4)+\left (-25920+34560 \log (2)-17280 \log ^2(2)+3840 \log ^3(2)-320 \log ^4(2)\right ) \log ^3(4)+\left (-1620+2160 \log (2)-1080 \log ^2(2)+240 \log ^3(2)-20 \log ^4(2)\right ) \log ^4(4)}{x^{21} \log ^4(4)} \, dx=\frac {(-3+\log (2))^4 (4+\log (4))^4}{x^{20} \log ^4(4)} \]
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Leaf count of result is larger than twice the leaf count of optimal. \(54\) vs. \(2(23)=46\).
Time = 0.10 (sec) , antiderivative size = 55, normalized size of antiderivative = 2.75
method | result | size |
gosper | \(\frac {\ln \left (2\right )^{8}-4 \ln \left (2\right )^{7}-18 \ln \left (2\right )^{6}+68 \ln \left (2\right )^{5}+145 \ln \left (2\right )^{4}-408 \ln \left (2\right )^{3}-648 \ln \left (2\right )^{2}+864 \ln \left (2\right )+1296}{x^{20} \ln \left (2\right )^{4}}\) | \(55\) |
norman | \(\frac {\ln \left (2\right )^{8}-4 \ln \left (2\right )^{7}-18 \ln \left (2\right )^{6}+68 \ln \left (2\right )^{5}+145 \ln \left (2\right )^{4}-408 \ln \left (2\right )^{3}-648 \ln \left (2\right )^{2}+864 \ln \left (2\right )+1296}{x^{20} \ln \left (2\right )^{4}}\) | \(55\) |
risch | \(\frac {\ln \left (2\right )^{4}}{x^{20}}-\frac {4 \ln \left (2\right )^{3}}{x^{20}}-\frac {18 \ln \left (2\right )^{2}}{x^{20}}+\frac {68 \ln \left (2\right )}{x^{20}}+\frac {145}{x^{20}}-\frac {408}{x^{20} \ln \left (2\right )}-\frac {648}{x^{20} \ln \left (2\right )^{2}}+\frac {864}{x^{20} \ln \left (2\right )^{3}}+\frac {1296}{x^{20} \ln \left (2\right )^{4}}\) | \(76\) |
default | \(-\frac {8 \left (-20 \ln \left (2\right )^{4}+240 \ln \left (2\right )^{3}-1080 \ln \left (2\right )^{2}+2160 \ln \left (2\right )-1620\right ) \ln \left (2\right )^{4}+4 \left (-320 \ln \left (2\right )^{4}+3840 \ln \left (2\right )^{3}-17280 \ln \left (2\right )^{2}+34560 \ln \left (2\right )-25920\right ) \ln \left (2\right )^{3}+2 \left (-1920 \ln \left (2\right )^{4}+23040 \ln \left (2\right )^{3}-103680 \ln \left (2\right )^{2}+207360 \ln \left (2\right )-155520\right ) \ln \left (2\right )^{2}+\left (-5120 \ln \left (2\right )^{4}+61440 \ln \left (2\right )^{3}-276480 \ln \left (2\right )^{2}+552960 \ln \left (2\right )-414720\right ) \ln \left (2\right )-2560 \ln \left (2\right )^{4}+30720 \ln \left (2\right )^{3}-138240 \ln \left (2\right )^{2}+276480 \ln \left (2\right )-207360}{160 \ln \left (2\right )^{4} x^{20}}\) | \(151\) |
parallelrisch | \(-\frac {16 \left (-20 \ln \left (2\right )^{4}+240 \ln \left (2\right )^{3}-1080 \ln \left (2\right )^{2}+2160 \ln \left (2\right )-1620\right ) \ln \left (2\right )^{4}+8 \left (-320 \ln \left (2\right )^{4}+3840 \ln \left (2\right )^{3}-17280 \ln \left (2\right )^{2}+34560 \ln \left (2\right )-25920\right ) \ln \left (2\right )^{3}+4 \left (-1920 \ln \left (2\right )^{4}+23040 \ln \left (2\right )^{3}-103680 \ln \left (2\right )^{2}+207360 \ln \left (2\right )-155520\right ) \ln \left (2\right )^{2}+2 \left (-5120 \ln \left (2\right )^{4}+61440 \ln \left (2\right )^{3}-276480 \ln \left (2\right )^{2}+552960 \ln \left (2\right )-414720\right ) \ln \left (2\right )-5120 \ln \left (2\right )^{4}+61440 \ln \left (2\right )^{3}-276480 \ln \left (2\right )^{2}+552960 \ln \left (2\right )-414720}{320 x^{20} \ln \left (2\right )^{4}}\) | \(152\) |
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Leaf count of result is larger than twice the leaf count of optimal. 54 vs. \(2 (20) = 40\).
Time = 0.22 (sec) , antiderivative size = 54, normalized size of antiderivative = 2.70 \[ \int \frac {-414720+552960 \log (2)-276480 \log ^2(2)+61440 \log ^3(2)-5120 \log ^4(2)+\left (-414720+552960 \log (2)-276480 \log ^2(2)+61440 \log ^3(2)-5120 \log ^4(2)\right ) \log (4)+\left (-155520+207360 \log (2)-103680 \log ^2(2)+23040 \log ^3(2)-1920 \log ^4(2)\right ) \log ^2(4)+\left (-25920+34560 \log (2)-17280 \log ^2(2)+3840 \log ^3(2)-320 \log ^4(2)\right ) \log ^3(4)+\left (-1620+2160 \log (2)-1080 \log ^2(2)+240 \log ^3(2)-20 \log ^4(2)\right ) \log ^4(4)}{x^{21} \log ^4(4)} \, dx=\frac {\log \left (2\right )^{8} - 4 \, \log \left (2\right )^{7} - 18 \, \log \left (2\right )^{6} + 68 \, \log \left (2\right )^{5} + 145 \, \log \left (2\right )^{4} - 408 \, \log \left (2\right )^{3} - 648 \, \log \left (2\right )^{2} + 864 \, \log \left (2\right ) + 1296}{x^{20} \log \left (2\right )^{4}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 65 vs. \(2 (24) = 48\).
Time = 0.06 (sec) , antiderivative size = 65, normalized size of antiderivative = 3.25 \[ \int \frac {-414720+552960 \log (2)-276480 \log ^2(2)+61440 \log ^3(2)-5120 \log ^4(2)+\left (-414720+552960 \log (2)-276480 \log ^2(2)+61440 \log ^3(2)-5120 \log ^4(2)\right ) \log (4)+\left (-155520+207360 \log (2)-103680 \log ^2(2)+23040 \log ^3(2)-1920 \log ^4(2)\right ) \log ^2(4)+\left (-25920+34560 \log (2)-17280 \log ^2(2)+3840 \log ^3(2)-320 \log ^4(2)\right ) \log ^3(4)+\left (-1620+2160 \log (2)-1080 \log ^2(2)+240 \log ^3(2)-20 \log ^4(2)\right ) \log ^4(4)}{x^{21} \log ^4(4)} \, dx=- \frac {-25920 - 17280 \log {\left (2 \right )} - 2900 \log {\left (2 \right )}^{4} - 1360 \log {\left (2 \right )}^{5} - 20 \log {\left (2 \right )}^{8} + 80 \log {\left (2 \right )}^{7} + 360 \log {\left (2 \right )}^{6} + 8160 \log {\left (2 \right )}^{3} + 12960 \log {\left (2 \right )}^{2}}{20 x^{20} \log {\left (2 \right )}^{4}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 141 vs. \(2 (20) = 40\).
Time = 0.22 (sec) , antiderivative size = 141, normalized size of antiderivative = 7.05 \[ \int \frac {-414720+552960 \log (2)-276480 \log ^2(2)+61440 \log ^3(2)-5120 \log ^4(2)+\left (-414720+552960 \log (2)-276480 \log ^2(2)+61440 \log ^3(2)-5120 \log ^4(2)\right ) \log (4)+\left (-155520+207360 \log (2)-103680 \log ^2(2)+23040 \log ^3(2)-1920 \log ^4(2)\right ) \log ^2(4)+\left (-25920+34560 \log (2)-17280 \log ^2(2)+3840 \log ^3(2)-320 \log ^4(2)\right ) \log ^3(4)+\left (-1620+2160 \log (2)-1080 \log ^2(2)+240 \log ^3(2)-20 \log ^4(2)\right ) \log ^4(4)}{x^{21} \log ^4(4)} \, dx=\frac {{\left (\log \left (2\right )^{4} - 12 \, \log \left (2\right )^{3} + 54 \, \log \left (2\right )^{2} - 108 \, \log \left (2\right ) + 81\right )} \log \left (2\right )^{4} + 8 \, {\left (\log \left (2\right )^{4} - 12 \, \log \left (2\right )^{3} + 54 \, \log \left (2\right )^{2} - 108 \, \log \left (2\right ) + 81\right )} \log \left (2\right )^{3} + 16 \, \log \left (2\right )^{4} + 24 \, {\left (\log \left (2\right )^{4} - 12 \, \log \left (2\right )^{3} + 54 \, \log \left (2\right )^{2} - 108 \, \log \left (2\right ) + 81\right )} \log \left (2\right )^{2} - 192 \, \log \left (2\right )^{3} + 32 \, {\left (\log \left (2\right )^{4} - 12 \, \log \left (2\right )^{3} + 54 \, \log \left (2\right )^{2} - 108 \, \log \left (2\right ) + 81\right )} \log \left (2\right ) + 864 \, \log \left (2\right )^{2} - 1728 \, \log \left (2\right ) + 1296}{x^{20} \log \left (2\right )^{4}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 141 vs. \(2 (20) = 40\).
Time = 0.26 (sec) , antiderivative size = 141, normalized size of antiderivative = 7.05 \[ \int \frac {-414720+552960 \log (2)-276480 \log ^2(2)+61440 \log ^3(2)-5120 \log ^4(2)+\left (-414720+552960 \log (2)-276480 \log ^2(2)+61440 \log ^3(2)-5120 \log ^4(2)\right ) \log (4)+\left (-155520+207360 \log (2)-103680 \log ^2(2)+23040 \log ^3(2)-1920 \log ^4(2)\right ) \log ^2(4)+\left (-25920+34560 \log (2)-17280 \log ^2(2)+3840 \log ^3(2)-320 \log ^4(2)\right ) \log ^3(4)+\left (-1620+2160 \log (2)-1080 \log ^2(2)+240 \log ^3(2)-20 \log ^4(2)\right ) \log ^4(4)}{x^{21} \log ^4(4)} \, dx=\frac {{\left (\log \left (2\right )^{4} - 12 \, \log \left (2\right )^{3} + 54 \, \log \left (2\right )^{2} - 108 \, \log \left (2\right ) + 81\right )} \log \left (2\right )^{4} + 8 \, {\left (\log \left (2\right )^{4} - 12 \, \log \left (2\right )^{3} + 54 \, \log \left (2\right )^{2} - 108 \, \log \left (2\right ) + 81\right )} \log \left (2\right )^{3} + 16 \, \log \left (2\right )^{4} + 24 \, {\left (\log \left (2\right )^{4} - 12 \, \log \left (2\right )^{3} + 54 \, \log \left (2\right )^{2} - 108 \, \log \left (2\right ) + 81\right )} \log \left (2\right )^{2} - 192 \, \log \left (2\right )^{3} + 32 \, {\left (\log \left (2\right )^{4} - 12 \, \log \left (2\right )^{3} + 54 \, \log \left (2\right )^{2} - 108 \, \log \left (2\right ) + 81\right )} \log \left (2\right ) + 864 \, \log \left (2\right )^{2} - 1728 \, \log \left (2\right ) + 1296}{x^{20} \log \left (2\right )^{4}} \]
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Time = 9.00 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00 \[ \int \frac {-414720+552960 \log (2)-276480 \log ^2(2)+61440 \log ^3(2)-5120 \log ^4(2)+\left (-414720+552960 \log (2)-276480 \log ^2(2)+61440 \log ^3(2)-5120 \log ^4(2)\right ) \log (4)+\left (-155520+207360 \log (2)-103680 \log ^2(2)+23040 \log ^3(2)-1920 \log ^4(2)\right ) \log ^2(4)+\left (-25920+34560 \log (2)-17280 \log ^2(2)+3840 \log ^3(2)-320 \log ^4(2)\right ) \log ^3(4)+\left (-1620+2160 \log (2)-1080 \log ^2(2)+240 \log ^3(2)-20 \log ^4(2)\right ) \log ^4(4)}{x^{21} \log ^4(4)} \, dx=\frac {{\left (\ln \left (2\right )-{\ln \left (2\right )}^2+6\right )}^4}{x^{20}\,{\ln \left (2\right )}^4} \]
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