Integrand size = 9, antiderivative size = 15 \[ \int -\frac {8 \log ^2(2)}{x} \, dx=-3+4 \log ^2(2) \log \left (\frac {\log (3)}{x^2}\right ) \]
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Time = 0.00 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.53, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {12, 29} \[ \int -\frac {8 \log ^2(2)}{x} \, dx=-8 \log ^2(2) \log (x) \]
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Rule 12
Rule 29
Rubi steps \begin{align*} \text {integral}& = -\left (\left (8 \log ^2(2)\right ) \int \frac {1}{x} \, dx\right ) \\ & = -8 \log ^2(2) \log (x) \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.53 \[ \int -\frac {8 \log ^2(2)}{x} \, dx=-8 \log ^2(2) \log (x) \]
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Time = 0.07 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.60
method | result | size |
default | \(-8 \ln \left (x \right ) \ln \left (2\right )^{2}\) | \(9\) |
norman | \(-8 \ln \left (x \right ) \ln \left (2\right )^{2}\) | \(9\) |
risch | \(-8 \ln \left (x \right ) \ln \left (2\right )^{2}\) | \(9\) |
parallelrisch | \(-8 \ln \left (x \right ) \ln \left (2\right )^{2}\) | \(9\) |
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none
Time = 0.24 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.53 \[ \int -\frac {8 \log ^2(2)}{x} \, dx=-8 \, \log \left (2\right )^{2} \log \left (x\right ) \]
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Time = 0.02 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.67 \[ \int -\frac {8 \log ^2(2)}{x} \, dx=- 8 \log {\left (2 \right )}^{2} \log {\left (x \right )} \]
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none
Time = 0.20 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.53 \[ \int -\frac {8 \log ^2(2)}{x} \, dx=-8 \, \log \left (2\right )^{2} \log \left (x\right ) \]
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none
Time = 0.25 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.60 \[ \int -\frac {8 \log ^2(2)}{x} \, dx=-8 \, \log \left (2\right )^{2} \log \left ({\left | x \right |}\right ) \]
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Time = 0.05 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.53 \[ \int -\frac {8 \log ^2(2)}{x} \, dx=-8\,{\ln \left (2\right )}^2\,\ln \left (x\right ) \]
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