Integrand size = 38, antiderivative size = 17 \[ \int \frac {-7+\left (-2 x-x^2\right ) \log (2)+(1+x) \log (\log (375))}{-7-x^2 \log (2)+x \log (\log (375))} \, dx=x+\log (7+x (x \log (2)-\log (\log (375)))) \]
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Time = 0.02 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.053, Rules used = {1671, 642} \[ \int \frac {-7+\left (-2 x-x^2\right ) \log (2)+(1+x) \log (\log (375))}{-7-x^2 \log (2)+x \log (\log (375))} \, dx=\log \left (x^2 \log (2)-x \log (\log (375))+7\right )+x \]
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Rule 642
Rule 1671
Rubi steps \begin{align*} \text {integral}& = \int \left (1+\frac {-2 x \log (2)+\log (\log (375))}{-7-x^2 \log (2)+x \log (\log (375))}\right ) \, dx \\ & = x+\int \frac {-2 x \log (2)+\log (\log (375))}{-7-x^2 \log (2)+x \log (\log (375))} \, dx \\ & = x+\log \left (7+x^2 \log (2)-x \log (\log (375))\right ) \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.00 \[ \int \frac {-7+\left (-2 x-x^2\right ) \log (2)+(1+x) \log (\log (375))}{-7-x^2 \log (2)+x \log (\log (375))} \, dx=x+\log \left (7+x^2 \log (2)-x \log (\log (375))\right ) \]
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Time = 1.18 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.06
method | result | size |
default | \(x +\ln \left (x^{2} \ln \left (2\right )-x \ln \left (\ln \left (375\right )\right )+7\right )\) | \(18\) |
norman | \(x +\ln \left (x^{2} \ln \left (2\right )-x \ln \left (\ln \left (375\right )\right )+7\right )\) | \(18\) |
risch | \(x +\ln \left (x^{2} \ln \left (2\right )-x \ln \left (\ln \left (3\right )+3 \ln \left (5\right )\right )+7\right )\) | \(23\) |
parallelrisch | \(x +\ln \left (\frac {x^{2} \ln \left (2\right )-x \ln \left (\ln \left (375\right )\right )+7}{\ln \left (2\right )}\right )\) | \(23\) |
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Time = 0.25 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.00 \[ \int \frac {-7+\left (-2 x-x^2\right ) \log (2)+(1+x) \log (\log (375))}{-7-x^2 \log (2)+x \log (\log (375))} \, dx=x + \log \left (x^{2} \log \left (2\right ) - x \log \left (\log \left (375\right )\right ) + 7\right ) \]
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Time = 0.11 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.00 \[ \int \frac {-7+\left (-2 x-x^2\right ) \log (2)+(1+x) \log (\log (375))}{-7-x^2 \log (2)+x \log (\log (375))} \, dx=x + \log {\left (x^{2} \log {\left (2 \right )} - x \log {\left (\log {\left (375 \right )} \right )} + 7 \right )} \]
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Time = 0.19 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.00 \[ \int \frac {-7+\left (-2 x-x^2\right ) \log (2)+(1+x) \log (\log (375))}{-7-x^2 \log (2)+x \log (\log (375))} \, dx=x + \log \left (x^{2} \log \left (2\right ) - x \log \left (\log \left (375\right )\right ) + 7\right ) \]
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Time = 0.26 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.00 \[ \int \frac {-7+\left (-2 x-x^2\right ) \log (2)+(1+x) \log (\log (375))}{-7-x^2 \log (2)+x \log (\log (375))} \, dx=x + \log \left (x^{2} \log \left (2\right ) - x \log \left (\log \left (375\right )\right ) + 7\right ) \]
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Time = 8.22 (sec) , antiderivative size = 17, normalized size of antiderivative = 1.00 \[ \int \frac {-7+\left (-2 x-x^2\right ) \log (2)+(1+x) \log (\log (375))}{-7-x^2 \log (2)+x \log (\log (375))} \, dx=x+\ln \left (\ln \left (2\right )\,x^2-\ln \left (\ln \left (375\right )\right )\,x+7\right ) \]
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