Integrand size = 132, antiderivative size = 27 \[ \int \frac {-32-32 x+\left (-128-64 x-32 x^2-32 \log (2)\right ) \log \left (\frac {5}{16+8 x+4 x^2+4 \log (2)}\right )}{\left (-8 x-4 x^2-2 x^3-2 x \log (2)\right ) \log \left (\frac {5}{16+8 x+4 x^2+4 \log (2)}\right )+\left (4+2 x+x^2+\log (2)\right ) \log \left (\frac {5}{16+8 x+4 x^2+4 \log (2)}\right ) \log \left (\log \left (\frac {5}{16+8 x+4 x^2+4 \log (2)}\right )\right )} \, dx=16 \log \left (2 x-\log \left (\log \left (\frac {5}{4 \left (4+2 x+x^2+\log (2)\right )}\right )\right )\right ) \]
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Time = 0.16 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.023, Rules used = {6820, 12, 6816} \[ \int \frac {-32-32 x+\left (-128-64 x-32 x^2-32 \log (2)\right ) \log \left (\frac {5}{16+8 x+4 x^2+4 \log (2)}\right )}{\left (-8 x-4 x^2-2 x^3-2 x \log (2)\right ) \log \left (\frac {5}{16+8 x+4 x^2+4 \log (2)}\right )+\left (4+2 x+x^2+\log (2)\right ) \log \left (\frac {5}{16+8 x+4 x^2+4 \log (2)}\right ) \log \left (\log \left (\frac {5}{16+8 x+4 x^2+4 \log (2)}\right )\right )} \, dx=16 \log \left (2 x-\log \left (\log \left (\frac {5}{4 \left (x^2+2 x+4+\log (2)\right )}\right )\right )\right ) \]
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Rule 12
Rule 6816
Rule 6820
Rubi steps \begin{align*} \text {integral}& = \int \frac {32 \left (1+x+\left (4+2 x+x^2+\log (2)\right ) \log \left (\frac {5}{4 \left (4+2 x+x^2+\log (2)\right )}\right )\right )}{\left (4+2 x+x^2+\log (2)\right ) \log \left (\frac {5}{4 \left (4+2 x+x^2+\log (2)\right )}\right ) \left (2 x-\log \left (\log \left (\frac {5}{4 \left (4+2 x+x^2+\log (2)\right )}\right )\right )\right )} \, dx \\ & = 32 \int \frac {1+x+\left (4+2 x+x^2+\log (2)\right ) \log \left (\frac {5}{4 \left (4+2 x+x^2+\log (2)\right )}\right )}{\left (4+2 x+x^2+\log (2)\right ) \log \left (\frac {5}{4 \left (4+2 x+x^2+\log (2)\right )}\right ) \left (2 x-\log \left (\log \left (\frac {5}{4 \left (4+2 x+x^2+\log (2)\right )}\right )\right )\right )} \, dx \\ & = 16 \log \left (2 x-\log \left (\log \left (\frac {5}{4 \left (4+2 x+x^2+\log (2)\right )}\right )\right )\right ) \\ \end{align*}
Time = 0.05 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.00 \[ \int \frac {-32-32 x+\left (-128-64 x-32 x^2-32 \log (2)\right ) \log \left (\frac {5}{16+8 x+4 x^2+4 \log (2)}\right )}{\left (-8 x-4 x^2-2 x^3-2 x \log (2)\right ) \log \left (\frac {5}{16+8 x+4 x^2+4 \log (2)}\right )+\left (4+2 x+x^2+\log (2)\right ) \log \left (\frac {5}{16+8 x+4 x^2+4 \log (2)}\right ) \log \left (\log \left (\frac {5}{16+8 x+4 x^2+4 \log (2)}\right )\right )} \, dx=16 \log \left (2 x-\log \left (\log \left (\frac {5}{4 \left (4+2 x+x^2+\log (2)\right )}\right )\right )\right ) \]
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Time = 2.33 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.89
method | result | size |
parallelrisch | \(16 \ln \left (x -\frac {\ln \left (\ln \left (\frac {5}{4 \left (\ln \left (2\right )+x^{2}+2 x +4\right )}\right )\right )}{2}\right )\) | \(24\) |
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Time = 0.24 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.85 \[ \int \frac {-32-32 x+\left (-128-64 x-32 x^2-32 \log (2)\right ) \log \left (\frac {5}{16+8 x+4 x^2+4 \log (2)}\right )}{\left (-8 x-4 x^2-2 x^3-2 x \log (2)\right ) \log \left (\frac {5}{16+8 x+4 x^2+4 \log (2)}\right )+\left (4+2 x+x^2+\log (2)\right ) \log \left (\frac {5}{16+8 x+4 x^2+4 \log (2)}\right ) \log \left (\log \left (\frac {5}{16+8 x+4 x^2+4 \log (2)}\right )\right )} \, dx=16 \, \log \left (-2 \, x + \log \left (\log \left (\frac {5}{4 \, {\left (x^{2} + 2 \, x + \log \left (2\right ) + 4\right )}}\right )\right )\right ) \]
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Time = 0.37 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.96 \[ \int \frac {-32-32 x+\left (-128-64 x-32 x^2-32 \log (2)\right ) \log \left (\frac {5}{16+8 x+4 x^2+4 \log (2)}\right )}{\left (-8 x-4 x^2-2 x^3-2 x \log (2)\right ) \log \left (\frac {5}{16+8 x+4 x^2+4 \log (2)}\right )+\left (4+2 x+x^2+\log (2)\right ) \log \left (\frac {5}{16+8 x+4 x^2+4 \log (2)}\right ) \log \left (\log \left (\frac {5}{16+8 x+4 x^2+4 \log (2)}\right )\right )} \, dx=16 \log {\left (- 2 x + \log {\left (\log {\left (\frac {5}{4 x^{2} + 8 x + 4 \log {\left (2 \right )} + 16} \right )} \right )} \right )} \]
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Time = 0.33 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.04 \[ \int \frac {-32-32 x+\left (-128-64 x-32 x^2-32 \log (2)\right ) \log \left (\frac {5}{16+8 x+4 x^2+4 \log (2)}\right )}{\left (-8 x-4 x^2-2 x^3-2 x \log (2)\right ) \log \left (\frac {5}{16+8 x+4 x^2+4 \log (2)}\right )+\left (4+2 x+x^2+\log (2)\right ) \log \left (\frac {5}{16+8 x+4 x^2+4 \log (2)}\right ) \log \left (\log \left (\frac {5}{16+8 x+4 x^2+4 \log (2)}\right )\right )} \, dx=16 \, \log \left (-2 \, x + \log \left (\log \left (5\right ) - 2 \, \log \left (2\right ) - \log \left (x^{2} + 2 \, x + \log \left (2\right ) + 4\right )\right )\right ) \]
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Time = 0.46 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.11 \[ \int \frac {-32-32 x+\left (-128-64 x-32 x^2-32 \log (2)\right ) \log \left (\frac {5}{16+8 x+4 x^2+4 \log (2)}\right )}{\left (-8 x-4 x^2-2 x^3-2 x \log (2)\right ) \log \left (\frac {5}{16+8 x+4 x^2+4 \log (2)}\right )+\left (4+2 x+x^2+\log (2)\right ) \log \left (\frac {5}{16+8 x+4 x^2+4 \log (2)}\right ) \log \left (\log \left (\frac {5}{16+8 x+4 x^2+4 \log (2)}\right )\right )} \, dx=16 \, \log \left (2 \, x - \log \left (\log \left (5\right ) - 2 \, \log \left (2\right ) - \log \left (x^{2} + 2 \, x + \log \left (2\right ) + 4\right )\right )\right ) \]
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Timed out. \[ \int \frac {-32-32 x+\left (-128-64 x-32 x^2-32 \log (2)\right ) \log \left (\frac {5}{16+8 x+4 x^2+4 \log (2)}\right )}{\left (-8 x-4 x^2-2 x^3-2 x \log (2)\right ) \log \left (\frac {5}{16+8 x+4 x^2+4 \log (2)}\right )+\left (4+2 x+x^2+\log (2)\right ) \log \left (\frac {5}{16+8 x+4 x^2+4 \log (2)}\right ) \log \left (\log \left (\frac {5}{16+8 x+4 x^2+4 \log (2)}\right )\right )} \, dx=\text {Hanged} \]
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