Optimal. Leaf size=9 \[ \log (x)+\log (2) \log (\log (x)) \]
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Rubi [A]
time = 0.02, antiderivative size = 18, normalized size of antiderivative = 2.00, number of steps
used = 2, number of rules used = 4, integrand size = 12, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.333, Rules used = {2339, 29, 2413,
2601} \begin {gather*} -\log (\log (x)) \log (x)+\log (x)+\log (2 x) \log (\log (x)) \end {gather*}
Antiderivative was successfully verified.
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Rule 29
Rule 2339
Rule 2413
Rule 2601
Rubi steps
\begin {gather*} \begin {aligned} \text {Integral} &=\log (2 x) \log (\log (x))-\int \frac {\log (\log (x))}{x} \, dx\\ &=\log (x)-\log (x) \log (\log (x))+\log (2 x) \log (\log (x))\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 9, normalized size = 1.00 \begin {gather*} \log (x)+\log (2) \log (\log (x)) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.03, size = 10, normalized size = 1.11
method | result | size |
default | \(\ln \left (x \right )+\ln \left (2\right ) \ln \left (\ln \left (x \right )\right )\) | \(10\) |
risch | \(\ln \left (x \right )+\ln \left (2\right ) \ln \left (\ln \left (x \right )\right )\) | \(10\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.34, size = 18, normalized size = 2.00 \begin {gather*} \log \left (2 \, x\right ) \log \left (\log \left (x\right )\right ) - \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 = 0.59, size = 9, normalized size = 1.00 \begin {gather*} \log \left (2\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 = 0.04, size = 10, normalized size = 1.11 \begin {gather*} \log {\left (x \right )} + \log {\left (2 \right )} \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 = 0.46, size = 10, normalized size = 1.11 \begin {gather*} \log \left (2\right ) \log \left ({\left | \log \left (x\right ) \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 = 0.14, size = 9, normalized size = 1.00 \begin {gather*} \ln \left (x\right )+\ln \left (\ln \left (x\right )\right )\,\ln \left (2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Chatgpt [F] Failed to verify
time = 1.00, size = 9, normalized size = 1.00 \begin {gather*} \hyperbolicCosineIntegral \left (2 x \right )-\hyperbolicCosineIntegral \left (x \right ) \end {gather*}
Warning: Unable to verify antiderivative.
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