Integrand size = 20, antiderivative size = 10 \[ \int \frac {2}{(4+x) \log (4+x) \log (\log (4+x))} \, dx=\log \left (2304 \log ^2(\log (4+x))\right ) \]
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Time = 0.03 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.80, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {12, 6816} \[ \int \frac {2}{(4+x) \log (4+x) \log (\log (4+x))} \, dx=2 \log (\log (\log (x+4))) \]
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Rule 12
Rule 6816
Rubi steps \begin{align*} \text {integral}& = 2 \int \frac {1}{(4+x) \log (4+x) \log (\log (4+x))} \, dx \\ & = 2 \log (\log (\log (4+x))) \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.80 \[ \int \frac {2}{(4+x) \log (4+x) \log (\log (4+x))} \, dx=2 \log (\log (\log (4+x))) \]
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Time = 1.00 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.90
method | result | size |
derivativedivides | \(2 \ln \left (\ln \left (\ln \left (4+x \right )\right )\right )\) | \(9\) |
default | \(2 \ln \left (\ln \left (\ln \left (4+x \right )\right )\right )\) | \(9\) |
norman | \(2 \ln \left (\ln \left (\ln \left (4+x \right )\right )\right )\) | \(9\) |
risch | \(2 \ln \left (\ln \left (\ln \left (4+x \right )\right )\right )\) | \(9\) |
parallelrisch | \(2 \ln \left (\ln \left (\ln \left (4+x \right )\right )\right )\) | \(9\) |
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none
Time = 0.26 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.80 \[ \int \frac {2}{(4+x) \log (4+x) \log (\log (4+x))} \, dx=2 \, \log \left (\log \left (\log \left (x + 4\right )\right )\right ) \]
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Time = 0.08 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.80 \[ \int \frac {2}{(4+x) \log (4+x) \log (\log (4+x))} \, dx=2 \log {\left (\log {\left (\log {\left (x + 4 \right )} \right )} \right )} \]
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none
Time = 0.19 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.80 \[ \int \frac {2}{(4+x) \log (4+x) \log (\log (4+x))} \, dx=2 \, \log \left (\log \left (\log \left (x + 4\right )\right )\right ) \]
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none
Time = 0.26 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.80 \[ \int \frac {2}{(4+x) \log (4+x) \log (\log (4+x))} \, dx=2 \, \log \left (\log \left (\log \left (x + 4\right )\right )\right ) \]
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Time = 9.41 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.80 \[ \int \frac {2}{(4+x) \log (4+x) \log (\log (4+x))} \, dx=2\,\ln \left (\ln \left (\ln \left (x+4\right )\right )\right ) \]
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