Optimal. Leaf size=18 \[ \log ^2\left (9+3 x-\frac {\log (x \log (4))}{x^2}\right ) \]
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Rubi [A]
time = 0.32, antiderivative size = 25, normalized size of antiderivative = 1.39, number of steps
used = 1, number of rules used = 5, integrand size = 58, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.086, Rules used = {6873, 12, 6874,
6816, 6818} \begin {gather*} \log ^2\left (\frac {3 x^3+9 x^2-\log (x \log (4))}{x^2}\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6816
Rule 6818
Rule 6873
Rule 6874
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\log ^2\left (\frac {9 x^2+3 x^3-\log (x \log (4))}{x^2}\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.04, size = 18, normalized size = 1.00 \begin {gather*} \log ^2\left (9+3 x-\frac {\log (x \log (4))}{x^2}\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [F]
time = 1.52, size = 0, normalized size = 0.00 \[\int \frac {\left (-4 \ln \left (2 x \ln \left (2\right )\right )-6 x^{3}+2\right ) \ln \left (\frac {-\ln \left (2 x \ln \left (2\right )\right )+3 x^{3}+9 x^{2}}{x^{2}}\right )}{x \ln \left (2 x \ln \left (2\right )\right )-3 x^{4}-9 x^{3}}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 103 vs.
\(2 (19) = 38\).
time = 0.52, size = 103, normalized size = 5.72 \begin {gather*} -\log \left (-3 \, x^{3} - 9 \, x^{2} + \log \left (2\right ) + \log \left (x\right ) + \log \left (\log \left (2\right )\right )\right )^{2} + 4 \, \log \left (-3 \, x^{3} - 9 \, x^{2} + \log \left (2\right ) + \log \left (x\right ) + \log \left (\log \left (2\right )\right )\right ) \log \left (x\right ) - 4 \, \log \left (x\right )^{2} + 2 \, {\left (\log \left (-3 \, x^{3} - 9 \, x^{2} + \log \left (2\right ) + \log \left (x\right ) + \log \left (\log \left (2\right )\right )\right ) - 2 \, \log \left (x\right )\right )} \log \left (\frac {3 \, x^{3} + 9 \, x^{2} - \log \left (2 \, x \log \left (2\right )\right )}{x^{2}}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.49, size = 26, normalized size = 1.44 \begin {gather*} \log \left (\frac {3 \, x^{3} + 9 \, x^{2} - \log \left (2 \, x \log \left (2\right )\right )}{x^{2}}\right )^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.17, size = 24, normalized size = 1.33 \begin {gather*} \log {\left (\frac {3 x^{3} + 9 x^{2} - \log {\left (2 x \log {\left (2 \right )} \right )}}{x^{2}} \right )}^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 79 vs.
\(2 (19) = 38\).
time = 0.43, size = 79, normalized size = 4.39 \begin {gather*} 2 \, {\left (\log \left (-3 \, x^{3} - 9 \, x^{2} + \log \left (2\right ) + \log \left (x\right ) + \log \left (\log \left (2\right )\right )\right ) - 2 \, \log \left (x\right )\right )} \log \left (3 \, x^{3} + 9 \, x^{2} - \log \left (2\right ) - \log \left (x \log \left (2\right )\right )\right ) - \log \left (-3 \, x^{3} - 9 \, x^{2} + \log \left (2\right ) + \log \left (x\right ) + \log \left (\log \left (2\right )\right )\right )^{2} + 4 \, \log \left (x\right )^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 8.00, size = 26, normalized size = 1.44 \begin {gather*} {\ln \left (\frac {9\,x^2-\ln \left (2\,x\,\ln \left (2\right )\right )+3\,x^3}{x^2}\right )}^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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