Optimal. Leaf size=7 \[ \log (-\log (2 x)) \]
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Rubi [A] time = 0.01, antiderivative size = 5, normalized size of antiderivative = 0.71, number of steps used = 2, number of rules used = 2, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {2302, 29} \begin {gather*} \log (\log (2 x)) \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} \, dx,x,\log (2 x)\right )\\ &=\log (\log (2 x))\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 5, normalized size = 0.71 \begin {gather*} \log (\log (2 x)) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.58, size = 5, normalized size = 0.71 \begin {gather*} \log \left (\log \left (2 \, x\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.12, size = 5, normalized size = 0.71 \begin {gather*} \log \left (\log \left (2 \, x\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 6, normalized size = 0.86
method | result | size |
derivativedivides | \(\ln \left (\ln \left (2 x \right )\right )\) | \(6\) |
default | \(\ln \left (\ln \left (2 x \right )\right )\) | \(6\) |
norman | \(\ln \left (\ln \left (2 x \right )\right )\) | \(6\) |
risch | \(\ln \left (\ln \left (2 x \right )\right )\) | \(6\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.37, size = 5, normalized size = 0.71 \begin {gather*} \log \left (\log \left (2 \, x\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.83, size = 5, normalized size = 0.71 \begin {gather*} \ln \left (\ln \left (2\,x\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 5, normalized size = 0.71 \begin {gather*} \log {\left (\log {\left (2 x \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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