Integrand size = 112, antiderivative size = 18 \[ \int \frac {-2-x+\log (48)+(-3-x+\log (48)) \log \left (-\frac {5}{-3-x+\log (48)}\right )}{-3 x-x^2+x \log (48)+\left (-3 x-x^2+x \log (48)\right ) \log \left (-\frac {5}{-3-x+\log (48)}\right )+\left (-3-x+\log (48)+(-3-x+\log (48)) \log \left (-\frac {5}{-3-x+\log (48)}\right )\right ) \log \left (1+\log \left (-\frac {5}{-3-x+\log (48)}\right )\right )} \, dx=\log \left (x+\log \left (1+\log \left (\frac {5}{3+x-\log (48)}\right )\right )\right ) \]
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Time = 0.16 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.027, Rules used = {6, 6820, 6816} \[ \int \frac {-2-x+\log (48)+(-3-x+\log (48)) \log \left (-\frac {5}{-3-x+\log (48)}\right )}{-3 x-x^2+x \log (48)+\left (-3 x-x^2+x \log (48)\right ) \log \left (-\frac {5}{-3-x+\log (48)}\right )+\left (-3-x+\log (48)+(-3-x+\log (48)) \log \left (-\frac {5}{-3-x+\log (48)}\right )\right ) \log \left (1+\log \left (-\frac {5}{-3-x+\log (48)}\right )\right )} \, dx=\log \left (x+\log \left (\log \left (\frac {5}{x+3-\log (48)}\right )+1\right )\right ) \]
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Rule 6
Rule 6816
Rule 6820
Rubi steps \begin{align*} \text {integral}& = \int \frac {-2-x+\log (48)+(-3-x+\log (48)) \log \left (-\frac {5}{-3-x+\log (48)}\right )}{-x^2+x (-3+\log (48))+\left (-3 x-x^2+x \log (48)\right ) \log \left (-\frac {5}{-3-x+\log (48)}\right )+\left (-3-x+\log (48)+(-3-x+\log (48)) \log \left (-\frac {5}{-3-x+\log (48)}\right )\right ) \log \left (1+\log \left (-\frac {5}{-3-x+\log (48)}\right )\right )} \, dx \\ & = \int \frac {x+2 \left (1-\frac {\log (48)}{2}\right )+(3+x-\log (48)) \log \left (\frac {5}{3+x-\log (48)}\right )}{(3+x-\log (48)) \left (1+\log \left (\frac {5}{3+x-\log (48)}\right )\right ) \left (x+\log \left (1+\log \left (\frac {5}{3+x-\log (48)}\right )\right )\right )} \, dx \\ & = \log \left (x+\log \left (1+\log \left (\frac {5}{3+x-\log (48)}\right )\right )\right ) \\ \end{align*}
Time = 0.58 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.22 \[ \int \frac {-2-x+\log (48)+(-3-x+\log (48)) \log \left (-\frac {5}{-3-x+\log (48)}\right )}{-3 x-x^2+x \log (48)+\left (-3 x-x^2+x \log (48)\right ) \log \left (-\frac {5}{-3-x+\log (48)}\right )+\left (-3-x+\log (48)+(-3-x+\log (48)) \log \left (-\frac {5}{-3-x+\log (48)}\right )\right ) \log \left (1+\log \left (-\frac {5}{-3-x+\log (48)}\right )\right )} \, dx=\log \left (-x-\log \left (1+\log \left (\frac {5}{3+x-\log (48)}\right )\right )\right ) \]
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Time = 9.31 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.06
method | result | size |
norman | \(\ln \left (\ln \left (\ln \left (-\frac {5}{\ln \left (48\right )-3-x}\right )+1\right )+x \right )\) | \(19\) |
parallelrisch | \(\ln \left (\ln \left (\ln \left (-\frac {5}{\ln \left (48\right )-3-x}\right )+1\right )+x \right )\) | \(19\) |
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Time = 0.25 (sec) , antiderivative size = 18, normalized size of antiderivative = 1.00 \[ \int \frac {-2-x+\log (48)+(-3-x+\log (48)) \log \left (-\frac {5}{-3-x+\log (48)}\right )}{-3 x-x^2+x \log (48)+\left (-3 x-x^2+x \log (48)\right ) \log \left (-\frac {5}{-3-x+\log (48)}\right )+\left (-3-x+\log (48)+(-3-x+\log (48)) \log \left (-\frac {5}{-3-x+\log (48)}\right )\right ) \log \left (1+\log \left (-\frac {5}{-3-x+\log (48)}\right )\right )} \, dx=\log \left (x + \log \left (\log \left (\frac {5}{x - \log \left (48\right ) + 3}\right ) + 1\right )\right ) \]
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Time = 0.33 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.94 \[ \int \frac {-2-x+\log (48)+(-3-x+\log (48)) \log \left (-\frac {5}{-3-x+\log (48)}\right )}{-3 x-x^2+x \log (48)+\left (-3 x-x^2+x \log (48)\right ) \log \left (-\frac {5}{-3-x+\log (48)}\right )+\left (-3-x+\log (48)+(-3-x+\log (48)) \log \left (-\frac {5}{-3-x+\log (48)}\right )\right ) \log \left (1+\log \left (-\frac {5}{-3-x+\log (48)}\right )\right )} \, dx=\log {\left (x + \log {\left (\log {\left (- \frac {5}{- x - 3 + \log {\left (48 \right )}} \right )} + 1 \right )} \right )} \]
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Time = 0.33 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.22 \[ \int \frac {-2-x+\log (48)+(-3-x+\log (48)) \log \left (-\frac {5}{-3-x+\log (48)}\right )}{-3 x-x^2+x \log (48)+\left (-3 x-x^2+x \log (48)\right ) \log \left (-\frac {5}{-3-x+\log (48)}\right )+\left (-3-x+\log (48)+(-3-x+\log (48)) \log \left (-\frac {5}{-3-x+\log (48)}\right )\right ) \log \left (1+\log \left (-\frac {5}{-3-x+\log (48)}\right )\right )} \, dx=\log \left (x + \log \left (\log \left (5\right ) - \log \left (x - \log \left (3\right ) - 4 \, \log \left (2\right ) + 3\right ) + 1\right )\right ) \]
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Result contains complex when optimal does not.
Time = 0.34 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.17 \[ \int \frac {-2-x+\log (48)+(-3-x+\log (48)) \log \left (-\frac {5}{-3-x+\log (48)}\right )}{-3 x-x^2+x \log (48)+\left (-3 x-x^2+x \log (48)\right ) \log \left (-\frac {5}{-3-x+\log (48)}\right )+\left (-3-x+\log (48)+(-3-x+\log (48)) \log \left (-\frac {5}{-3-x+\log (48)}\right )\right ) \log \left (1+\log \left (-\frac {5}{-3-x+\log (48)}\right )\right )} \, dx=\log \left (x + \log \left (2 i \, \pi + \log \left (5\right ) - \log \left (x - \log \left (48\right ) + 3\right ) + 1\right )\right ) \]
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Timed out. \[ \int \frac {-2-x+\log (48)+(-3-x+\log (48)) \log \left (-\frac {5}{-3-x+\log (48)}\right )}{-3 x-x^2+x \log (48)+\left (-3 x-x^2+x \log (48)\right ) \log \left (-\frac {5}{-3-x+\log (48)}\right )+\left (-3-x+\log (48)+(-3-x+\log (48)) \log \left (-\frac {5}{-3-x+\log (48)}\right )\right ) \log \left (1+\log \left (-\frac {5}{-3-x+\log (48)}\right )\right )} \, dx=\text {Hanged} \]
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