Optimal. Leaf size=10 \[ 25 \log (6) \log ^2(2 x) \]
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Rubi [A]
time = 0.01, antiderivative size = 10, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {12, 2338}
\begin {gather*} 25 \log (6) \log ^2(2 x) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2338
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=(50 \log (6)) \int \frac {\log (2 x)}{x} \, dx\\ &=25 \log (6) \log ^2(2 x)\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 10, normalized size = 1.00 \begin {gather*} 25 \log (6) \log ^2(2 x) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.04, size = 11, normalized size = 1.10
method | result | size |
derivativedivides | \(25 \ln \left (2 x \right )^{2} \ln \left (6\right )\) | \(11\) |
default | \(25 \ln \left (2 x \right )^{2} \ln \left (6\right )\) | \(11\) |
norman | \(25 \ln \left (2 x \right )^{2} \ln \left (6\right )\) | \(11\) |
risch | \(25 \ln \left (2 x \right )^{2} \ln \left (2\right )+25 \ln \left (2 x \right )^{2} \ln \left (3\right )\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 10, normalized size = 1.00 \begin {gather*} 25 \, \log \left (6\right ) \log \left (2 \, x\right )^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.33, size = 10, normalized size = 1.00 \begin {gather*} 25 \, \log \left (6\right ) \log \left (2 \, x\right )^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 10, normalized size = 1.00 \begin {gather*} 25 \log {\left (6 \right )} \log {\left (2 x \right )}^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 10, normalized size = 1.00 \begin {gather*} 25 \, \log \left (6\right ) \log \left (2 \, x\right )^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.03, size = 10, normalized size = 1.00 \begin {gather*} 25\,{\ln \left (2\,x\right )}^2\,\ln \left (6\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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