Optimal. Leaf size=14 \[ 1+\frac {2 \log ^2(x)}{-1+\log (2)} \]
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Rubi [A]
time = 0.01, antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 3, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.214, Rules used = {6, 12, 2338}
\begin {gather*} -\frac {2 \log ^2(x)}{1-\log (2)} \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rule 12
Rule 2338
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {4 \log (x)}{x (-1+\log (2))} \, dx\\ &=-\frac {4 \int \frac {\log (x)}{x} \, dx}{1-\log (2)}\\ &=-\frac {2 \log ^2(x)}{1-\log (2)}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 14, normalized size = 1.00 \begin {gather*} -\frac {4 \log ^2(x)}{2-\log (4)} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 6.44, size = 13, normalized size = 0.93
method | result | size |
default | \(\frac {2 \ln \left (x \right )^{2}}{\ln \left (2\right )-1}\) | \(13\) |
norman | \(\frac {2 \ln \left (x \right )^{2}}{\ln \left (2\right )-1}\) | \(13\) |
risch | \(\frac {2 \ln \left (x \right )^{2}}{\ln \left (2\right )-1}\) | \(13\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.49, size = 12, normalized size = 0.86 \begin {gather*} \frac {2 \, \log \left (x\right )^{2}}{\log \left (2\right ) - 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 12, normalized size = 0.86 \begin {gather*} \frac {2 \, \log \left (x\right )^{2}}{\log \left (2\right ) - 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 10, normalized size = 0.71 \begin {gather*} \frac {2 \log {\left (x \right )}^{2}}{-1 + \log {\left (2 \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 12, normalized size = 0.86 \begin {gather*} \frac {2 \, \log \left (x\right )^{2}}{\log \left (2\right ) - 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.25, size = 12, normalized size = 0.86 \begin {gather*} \frac {2\,{\ln \left (x\right )}^2}{\ln \left (2\right )-1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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