Integrand size = 7, antiderivative size = 11 \[ \int \frac {\log (\log (x))}{x} \, dx=-\log (x)+\log (x) \log (\log (x)) \]
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Time = 0.01 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {2601} \[ \int \frac {\log (\log (x))}{x} \, dx=\log (x) \log (\log (x))-\log (x) \]
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Rule 2601
Rubi steps \begin{align*} \text {integral}& = -\log (x)+\log (x) \log (\log (x)) \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.00 \[ \int \frac {\log (\log (x))}{x} \, dx=-\log (x)+\log (x) \log (\log (x)) \]
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Time = 0.03 (sec) , antiderivative size = 12, normalized size of antiderivative = 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 | \(-\ln \left (x \right )+\ln \left (x \right ) \ln \left (\ln \left (x \right )\right )\) | \(12\) |
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none
Time = 0.25 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.00 \[ \int \frac {\log (\log (x))}{x} \, dx=\log \left (x\right ) \log \left (\log \left (x\right )\right ) - \log \left (x\right ) \]
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Time = 0.07 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.91 \[ \int \frac {\log (\log (x))}{x} \, dx=\log {\left (x \right )} \log {\left (\log {\left (x \right )} \right )} - \log {\left (x \right )} \]
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none
Time = 0.19 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.00 \[ \int \frac {\log (\log (x))}{x} \, dx=\log \left (x\right ) \log \left (\log \left (x\right )\right ) - \log \left (x\right ) \]
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none
Time = 0.33 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.00 \[ \int \frac {\log (\log (x))}{x} \, dx=\log \left (x\right ) \log \left (\log \left (x\right )\right ) - \log \left (x\right ) \]
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Time = 0.39 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.73 \[ \int \frac {\log (\log (x))}{x} \, dx=\ln \left (x\right )\,\left (\ln \left (\ln \left (x\right )\right )-1\right ) \]
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