Optimal. Leaf size=20 \[ \frac {(-3+\log (2))^4 (4+\log (4))^4}{x^{20} \log ^4(4)} \]
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Rubi [A] time = 0.04, antiderivative size = 22, normalized size of antiderivative = 1.10, number of steps used = 2, number of rules used = 2, integrand size = 146, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.014, Rules used = {12, 30} \begin {gather*} \frac {(3-\log (2))^4 (4+\log (4))^4}{x^{20} \log ^4(4)} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 30
Rubi steps
\begin {gather*} \begin {aligned} \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 {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 20, normalized size = 1.00 \begin {gather*} \frac {(-3+\log (2))^4 (4+\log (4))^4}{x^{20} \log ^4(4)} \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.99, size = 54, normalized size = 2.70 \begin {gather*} \frac {\log \relax (2)^{8} - 4 \, \log \relax (2)^{7} - 18 \, \log \relax (2)^{6} + 68 \, \log \relax (2)^{5} + 145 \, \log \relax (2)^{4} - 408 \, \log \relax (2)^{3} - 648 \, \log \relax (2)^{2} + 864 \, \log \relax (2) + 1296}{x^{20} \log \relax (2)^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.24, size = 141, normalized size = 7.05 \begin {gather*} \frac {{\left (\log \relax (2)^{4} - 12 \, \log \relax (2)^{3} + 54 \, \log \relax (2)^{2} - 108 \, \log \relax (2) + 81\right )} \log \relax (2)^{4} + 8 \, {\left (\log \relax (2)^{4} - 12 \, \log \relax (2)^{3} + 54 \, \log \relax (2)^{2} - 108 \, \log \relax (2) + 81\right )} \log \relax (2)^{3} + 16 \, \log \relax (2)^{4} + 24 \, {\left (\log \relax (2)^{4} - 12 \, \log \relax (2)^{3} + 54 \, \log \relax (2)^{2} - 108 \, \log \relax (2) + 81\right )} \log \relax (2)^{2} - 192 \, \log \relax (2)^{3} + 32 \, {\left (\log \relax (2)^{4} - 12 \, \log \relax (2)^{3} + 54 \, \log \relax (2)^{2} - 108 \, \log \relax (2) + 81\right )} \log \relax (2) + 864 \, \log \relax (2)^{2} - 1728 \, \log \relax (2) + 1296}{x^{20} \log \relax (2)^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.06, size = 55, normalized size = 2.75
method | result | size |
gosper | \(\frac {\ln \relax (2)^{8}-4 \ln \relax (2)^{7}-18 \ln \relax (2)^{6}+68 \ln \relax (2)^{5}+145 \ln \relax (2)^{4}-408 \ln \relax (2)^{3}-648 \ln \relax (2)^{2}+864 \ln \relax (2)+1296}{x^{20} \ln \relax (2)^{4}}\) | \(55\) |
norman | \(\frac {\ln \relax (2)^{8}-4 \ln \relax (2)^{7}-18 \ln \relax (2)^{6}+68 \ln \relax (2)^{5}+145 \ln \relax (2)^{4}-408 \ln \relax (2)^{3}-648 \ln \relax (2)^{2}+864 \ln \relax (2)+1296}{x^{20} \ln \relax (2)^{4}}\) | \(55\) |
risch | \(\frac {\ln \relax (2)^{4}}{x^{20}}-\frac {4 \ln \relax (2)^{3}}{x^{20}}-\frac {18 \ln \relax (2)^{2}}{x^{20}}+\frac {68 \ln \relax (2)}{x^{20}}+\frac {145}{x^{20}}-\frac {408}{x^{20} \ln \relax (2)}-\frac {648}{x^{20} \ln \relax (2)^{2}}+\frac {864}{x^{20} \ln \relax (2)^{3}}+\frac {1296}{x^{20} \ln \relax (2)^{4}}\) | \(76\) |
default | \(-\frac {8 \left (-20 \ln \relax (2)^{4}+240 \ln \relax (2)^{3}-1080 \ln \relax (2)^{2}+2160 \ln \relax (2)-1620\right ) \ln \relax (2)^{4}+4 \left (-320 \ln \relax (2)^{4}+3840 \ln \relax (2)^{3}-17280 \ln \relax (2)^{2}+34560 \ln \relax (2)-25920\right ) \ln \relax (2)^{3}+2 \left (-1920 \ln \relax (2)^{4}+23040 \ln \relax (2)^{3}-103680 \ln \relax (2)^{2}+207360 \ln \relax (2)-155520\right ) \ln \relax (2)^{2}+\left (-5120 \ln \relax (2)^{4}+61440 \ln \relax (2)^{3}-276480 \ln \relax (2)^{2}+552960 \ln \relax (2)-414720\right ) \ln \relax (2)-2560 \ln \relax (2)^{4}+30720 \ln \relax (2)^{3}-138240 \ln \relax (2)^{2}+276480 \ln \relax (2)-207360}{160 \ln \relax (2)^{4} x^{20}}\) | \(151\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.36, size = 141, normalized size = 7.05 \begin {gather*} \frac {{\left (\log \relax (2)^{4} - 12 \, \log \relax (2)^{3} + 54 \, \log \relax (2)^{2} - 108 \, \log \relax (2) + 81\right )} \log \relax (2)^{4} + 8 \, {\left (\log \relax (2)^{4} - 12 \, \log \relax (2)^{3} + 54 \, \log \relax (2)^{2} - 108 \, \log \relax (2) + 81\right )} \log \relax (2)^{3} + 16 \, \log \relax (2)^{4} + 24 \, {\left (\log \relax (2)^{4} - 12 \, \log \relax (2)^{3} + 54 \, \log \relax (2)^{2} - 108 \, \log \relax (2) + 81\right )} \log \relax (2)^{2} - 192 \, \log \relax (2)^{3} + 32 \, {\left (\log \relax (2)^{4} - 12 \, \log \relax (2)^{3} + 54 \, \log \relax (2)^{2} - 108 \, \log \relax (2) + 81\right )} \log \relax (2) + 864 \, \log \relax (2)^{2} - 1728 \, \log \relax (2) + 1296}{x^{20} \log \relax (2)^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.70, size = 20, normalized size = 1.00 \begin {gather*} \frac {{\left (\ln \relax (2)-{\ln \relax (2)}^2+6\right )}^4}{x^{20}\,{\ln \relax (2)}^4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.11, size = 65, normalized size = 3.25 \begin {gather*} - \frac {-25920 - 17280 \log {\relax (2 )} - 2900 \log {\relax (2 )}^{4} - 1360 \log {\relax (2 )}^{5} - 20 \log {\relax (2 )}^{8} + 80 \log {\relax (2 )}^{7} + 360 \log {\relax (2 )}^{6} + 8160 \log {\relax (2 )}^{3} + 12960 \log {\relax (2 )}^{2}}{20 x^{20} \log {\relax (2 )}^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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