Optimal. Leaf size=13 \[ \log \left (\frac {3 \log \left (\frac {3}{\log (x)}\right )}{e^3}\right ) \]
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Rubi [A] time = 0.05, antiderivative size = 8, normalized size of antiderivative = 0.62, number of steps used = 3, number of rules used = 2, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {2302, 29} \begin {gather*} \log \left (\log \left (\frac {3}{\log (x)}\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 29
Rule 2302
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\operatorname {Subst}\left (\int \frac {1}{x \log \left (\frac {3}{x}\right )} \, dx,x,\log (x)\right )\\ &=\operatorname {Subst}\left (\int \frac {1}{x} \, dx,x,\log \left (\frac {3}{\log (x)}\right )\right )\\ &=\log \left (\log \left (\frac {3}{\log (x)}\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 8, normalized size = 0.62 \begin {gather*} \log \left (\log \left (\frac {3}{\log (x)}\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.44, size = 8, normalized size = 0.62 \begin {gather*} \log \left (\log \left (\frac {3}{\log \relax (x)}\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.12, size = 27, normalized size = 2.08 \begin {gather*} \frac {1}{2} \, \log \left (\frac {1}{4} \, \pi ^{2} {\left (\mathrm {sgn}\left (\log \relax (x)\right ) - 1\right )}^{2} + {\left (\log \relax (3) - \log \left ({\left | \log \relax (x) \right |}\right )\right )}^{2}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 9, normalized size = 0.69
method | result | size |
derivativedivides | \(\ln \left (\ln \left (\frac {3}{\ln \relax (x )}\right )\right )\) | \(9\) |
default | \(\ln \left (\ln \left (\frac {3}{\ln \relax (x )}\right )\right )\) | \(9\) |
norman | \(\ln \left (\ln \left (\frac {3}{\ln \relax (x )}\right )\right )\) | \(9\) |
risch | \(\ln \left (\ln \left (\ln \relax (x )\right )-\ln \relax (3)\right )\) | \(10\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.37, size = 8, normalized size = 0.62 \begin {gather*} \log \left (\log \left (\frac {3}{\log \relax (x)}\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 7.04, size = 8, normalized size = 0.62 \begin {gather*} \ln \left (\ln \left (\frac {3}{\ln \relax (x)}\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.24, size = 7, normalized size = 0.54 \begin {gather*} \log {\left (\log {\left (\frac {3}{\log {\relax (x )}} \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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