Integrand size = 14, antiderivative size = 14 \[ \int \frac {4 \log (x)}{-x+x \log (2)} \, dx=1+\frac {2 \log ^2(x)}{-1+\log (2)} \]
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Time = 0.01 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.214, Rules used = {6, 12, 2338} \[ \int \frac {4 \log (x)}{-x+x \log (2)} \, dx=-\frac {2 \log ^2(x)}{1-\log (2)} \]
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Rule 6
Rule 12
Rule 2338
Rubi steps \begin{align*} \text {integral}& = \int \frac {4 \log (x)}{x (-1+\log (2))} \, dx \\ & = -\frac {4 \int \frac {\log (x)}{x} \, dx}{1-\log (2)} \\ & = -\frac {2 \log ^2(x)}{1-\log (2)} \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.00 \[ \int \frac {4 \log (x)}{-x+x \log (2)} \, dx=-\frac {4 \log ^2(x)}{2-\log (4)} \]
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Time = 0.15 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.93
method | result | size |
default | \(\frac {2 \ln \left (x \right )^{2}}{\ln \left (2\right )-1}\) | \(13\) |
norman | \(\frac {2 \ln \left (x \right )^{2}}{\ln \left (2\right )-1}\) | \(13\) |
risch | \(\frac {2 \ln \left (x \right )^{2}}{\ln \left (2\right )-1}\) | \(13\) |
parts | \(\frac {2 \ln \left (x \right )^{2}}{\ln \left (2\right )-1}\) | \(13\) |
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none
Time = 0.25 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.86 \[ \int \frac {4 \log (x)}{-x+x \log (2)} \, dx=\frac {2 \, \log \left (x\right )^{2}}{\log \left (2\right ) - 1} \]
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Time = 0.05 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.71 \[ \int \frac {4 \log (x)}{-x+x \log (2)} \, dx=\frac {2 \log {\left (x \right )}^{2}}{-1 + \log {\left (2 \right )}} \]
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none
Time = 0.27 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.86 \[ \int \frac {4 \log (x)}{-x+x \log (2)} \, dx=\frac {2 \, \log \left (x\right )^{2}}{\log \left (2\right ) - 1} \]
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none
Time = 0.28 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.86 \[ \int \frac {4 \log (x)}{-x+x \log (2)} \, dx=\frac {2 \, \log \left (x\right )^{2}}{\log \left (2\right ) - 1} \]
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Time = 12.42 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.86 \[ \int \frac {4 \log (x)}{-x+x \log (2)} \, dx=\frac {2\,{\ln \left (x\right )}^2}{\ln \left (2\right )-1} \]
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