Optimal. Leaf size=11 \[ -\log (x)+\log (x) \log (\log (x)) \]
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Rubi [A]
time = 0.00, antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {2601}
\begin {gather*} \log (x) \log (\log (x))-\log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 2601
Rubi steps
\begin {align*} \int \frac {\log (\log (x))}{x} \, dx &=-\log (x)+\log (x) \log (\log (x))\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 11, normalized size = 1.00 \begin {gather*} -\log (x)+\log (x) \log (\log (x)) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.01, size = 12, normalized size = 1.09
method | result | size |
derivativedivides | \(-\ln \left (x \right )+\ln \left (x \right ) \ln \left (\ln \left (x \right )\right )\) | \(12\) |
default | \(-\ln \left (x \right )+\ln \left (x \right ) \ln \left (\ln \left (x \right )\right )\) | \(12\) |
norman | \(-\ln \left (x \right )+\ln \left (x \right ) \ln \left (\ln \left (x \right )\right )\) | \(12\) |
risch | \(-\ln \left (x \right )+\ln \left (x \right ) \ln \left (\ln \left (x \right )\right )\) | \(12\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 1.59, size = 11, normalized size = 1.00 \begin {gather*} \log \left (x\right ) \log \left (\log \left (x\right )\right ) - \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 1.69, size = 11, normalized size = 1.00 \begin {gather*} \log \left (x\right ) \log \left (\log \left (x\right )\right ) - \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.06, size = 10, normalized size = 0.91 \begin {gather*} \log {\left (x \right )} \log {\left (\log {\left (x \right )} \right )} - \log {\left (x \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 1.00, size = 11, normalized size = 1.00 \begin {gather*} \log \left (x\right ) \log \left (\log \left (x\right )\right ) - \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.32, size = 8, normalized size = 0.73 \begin {gather*} \ln \left (x\right )\,\left (\ln \left (\ln \left (x\right )\right )-1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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