Optimal. Leaf size=3 \[ \log (\log (x)) \]
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Rubi [A]
time = 0.01, antiderivative size = 3, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 8, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, Rules used = {2339, 29}
\begin {gather*} \log (\log (x)) \end {gather*}
Antiderivative was successfully verified.
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Rule 29
Rule 2339
Rubi steps
\begin {align*} \int \frac {1}{x \log (x)} \, dx &=\text {Subst}\left (\int \frac {1}{x} \, dx,x,\log (x)\right )\\ &=\log (\log (x))\\ \end {align*}
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Mathematica [A]
time = 0.00, size = 3, normalized size = 1.00 \begin {gather*} \log (\log (x)) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.00, size = 4, normalized size = 1.33
method | result | size |
derivativedivides | \(\ln \left (\ln \left (x \right )\right )\) | \(4\) |
default | \(\ln \left (\ln \left (x \right )\right )\) | \(4\) |
norman | \(\ln \left (\ln \left (x \right )\right )\) | \(4\) |
risch | \(\ln \left (\ln \left (x \right )\right )\) | \(4\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 1.84, size = 3, normalized size = 1.00 \begin {gather*} \log \left (\log \left (x\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.92, size = 3, normalized size = 1.00 \begin {gather*} \log \left (\log \left (x\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 3, normalized size = 1.00 \begin {gather*} \log {\left (\log {\left (x \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.80, size = 4, normalized size = 1.33 \begin {gather*} \log \left ({\left | \log \left (x\right ) \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.18, size = 3, normalized size = 1.00 \begin {gather*} \ln \left (\ln \left (x\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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