Integrand size = 14, antiderivative size = 15 \[ \int -\frac {1}{4-4 x+4 \log (\log (4))} \, dx=\frac {1}{4} (-5+\log (-1+x-\log (\log (4)))) \]
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Time = 0.00 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.87, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.071, Rules used = {31} \[ \int -\frac {1}{4-4 x+4 \log (\log (4))} \, dx=\frac {1}{4} \log (-x+1+\log (\log (4))) \]
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Rule 31
Rubi steps \begin{align*} \text {integral}& = \frac {1}{4} \log (1-x+\log (\log (4))) \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.00 \[ \int -\frac {1}{4-4 x+4 \log (\log (4))} \, dx=\frac {1}{4} \log (4-4 x+4 \log (\log (4))) \]
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Time = 0.15 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.93
method | result | size |
default | \(\frac {\ln \left (\ln \left (2 \ln \left (2\right )\right )-x +1\right )}{4}\) | \(14\) |
parallelrisch | \(\frac {\ln \left (x -1-\ln \left (2 \ln \left (2\right )\right )\right )}{4}\) | \(14\) |
norman | \(\frac {\ln \left (4 \ln \left (2 \ln \left (2\right )\right )-4 x +4\right )}{4}\) | \(16\) |
risch | \(\frac {\ln \left (-\ln \left (2\right )-\ln \left (\ln \left (2\right )\right )+x -1\right )}{4}\) | \(16\) |
meijerg | \(-\frac {\left (-\ln \left (2\right )-\ln \left (\ln \left (2\right )\right )-1\right ) \ln \left (1-\frac {x}{\ln \left (2\right )+\ln \left (\ln \left (2\right )\right )+1}\right )}{4 \ln \left (2 \ln \left (2\right )\right )+4}\) | \(40\) |
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none
Time = 0.24 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.87 \[ \int -\frac {1}{4-4 x+4 \log (\log (4))} \, dx=\frac {1}{4} \, \log \left (x - \log \left (2 \, \log \left (2\right )\right ) - 1\right ) \]
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Time = 0.03 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.27 \[ \int -\frac {1}{4-4 x+4 \log (\log (4))} \, dx=\frac {\log {\left (4 x - 4 - 4 \log {\left (2 \right )} - 4 \log {\left (\log {\left (2 \right )} \right )} \right )}}{4} \]
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none
Time = 0.18 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.87 \[ \int -\frac {1}{4-4 x+4 \log (\log (4))} \, dx=\frac {1}{4} \, \log \left (x - \log \left (2 \, \log \left (2\right )\right ) - 1\right ) \]
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none
Time = 0.27 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.93 \[ \int -\frac {1}{4-4 x+4 \log (\log (4))} \, dx=\frac {1}{4} \, \log \left ({\left | x - \log \left (2 \, \log \left (2\right )\right ) - 1 \right |}\right ) \]
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Time = 0.21 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.87 \[ \int -\frac {1}{4-4 x+4 \log (\log (4))} \, dx=\frac {\ln \left (x-\ln \left (2\,\ln \left (2\right )\right )-1\right )}{4} \]
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