Integrand size = 12, antiderivative size = 24 \[ \int \frac {-4+8 x \log (2)}{\log (2)} \, dx=4 \left (-\frac {1}{9}+x^2+\frac {x-x^2}{x \log (2)}\right ) \]
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Time = 0.00 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.58, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.083, Rules used = {9} \[ \int \frac {-4+8 x \log (2)}{\log (2)} \, dx=\frac {(1-2 x \log (2))^2}{\log ^2(2)} \]
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Rule 9
Rubi steps \begin{align*} \text {integral}& = \frac {(1-2 x \log (2))^2}{\log ^2(2)} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.54 \[ \int \frac {-4+8 x \log (2)}{\log (2)} \, dx=4 x^2-\frac {4 x}{\log (2)} \]
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Time = 0.05 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.58
method | result | size |
gosper | \(\frac {4 x \left (x \ln \left (2\right )-1\right )}{\ln \left (2\right )}\) | \(14\) |
norman | \(4 x^{2}-\frac {4 x}{\ln \left (2\right )}\) | \(14\) |
risch | \(4 x^{2}-\frac {4 x}{\ln \left (2\right )}\) | \(14\) |
default | \(\frac {4 x^{2} \ln \left (2\right )-4 x}{\ln \left (2\right )}\) | \(17\) |
parallelrisch | \(\frac {4 x^{2} \ln \left (2\right )-4 x}{\ln \left (2\right )}\) | \(17\) |
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none
Time = 0.24 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.67 \[ \int \frac {-4+8 x \log (2)}{\log (2)} \, dx=\frac {4 \, {\left (x^{2} \log \left (2\right ) - x\right )}}{\log \left (2\right )} \]
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Time = 0.02 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.42 \[ \int \frac {-4+8 x \log (2)}{\log (2)} \, dx=4 x^{2} - \frac {4 x}{\log {\left (2 \right )}} \]
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none
Time = 0.19 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.67 \[ \int \frac {-4+8 x \log (2)}{\log (2)} \, dx=\frac {4 \, {\left (x^{2} \log \left (2\right ) - x\right )}}{\log \left (2\right )} \]
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none
Time = 0.30 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.67 \[ \int \frac {-4+8 x \log (2)}{\log (2)} \, dx=\frac {4 \, {\left (x^{2} \log \left (2\right ) - x\right )}}{\log \left (2\right )} \]
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Time = 0.08 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.62 \[ \int \frac {-4+8 x \log (2)}{\log (2)} \, dx=\frac {{\left (8\,x\,\ln \left (2\right )-4\right )}^2}{16\,{\ln \left (2\right )}^2} \]
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