Integrand size = 122, antiderivative size = 32 \[ \int \frac {-20+6 x^2+\left (20-6 x^2\right ) \log (x) \log (4 \log (x))+\left (-10-3 x^2\right ) \log (x) \log (4 \log (x)) \log \left (\frac {\log (4 \log (x))}{2 x}\right ) \log \left (\log ^2\left (\frac {\log (4 \log (x))}{2 x}\right )\right )}{\left (-10 x+3 x^3\right ) \log (x) \log (4 \log (x)) \log \left (\frac {\log (4 \log (x))}{2 x}\right ) \log \left (\log ^2\left (\frac {\log (4 \log (x))}{2 x}\right )\right )} \, dx=\log \left (\frac {4 \log \left (\log ^2\left (\frac {\log (4 \log (x))}{2 x}\right )\right )}{-\frac {2}{x}+\frac {3 x}{5}}\right ) \]
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Time = 2.57 (sec) , antiderivative size = 30, normalized size of antiderivative = 0.94, number of steps used = 7, number of rules used = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.041, Rules used = {1607, 6857, 457, 78, 6816} \[ \int \frac {-20+6 x^2+\left (20-6 x^2\right ) \log (x) \log (4 \log (x))+\left (-10-3 x^2\right ) \log (x) \log (4 \log (x)) \log \left (\frac {\log (4 \log (x))}{2 x}\right ) \log \left (\log ^2\left (\frac {\log (4 \log (x))}{2 x}\right )\right )}{\left (-10 x+3 x^3\right ) \log (x) \log (4 \log (x)) \log \left (\frac {\log (4 \log (x))}{2 x}\right ) \log \left (\log ^2\left (\frac {\log (4 \log (x))}{2 x}\right )\right )} \, dx=-\log \left (10-3 x^2\right )+\log \left (\log \left (\log ^2\left (\frac {\log (4 \log (x))}{2 x}\right )\right )\right )+\log (x) \]
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Rule 78
Rule 457
Rule 1607
Rule 6816
Rule 6857
Rubi steps \begin{align*} \text {integral}& = \int \frac {-20+6 x^2+\left (20-6 x^2\right ) \log (x) \log (4 \log (x))+\left (-10-3 x^2\right ) \log (x) \log (4 \log (x)) \log \left (\frac {\log (4 \log (x))}{2 x}\right ) \log \left (\log ^2\left (\frac {\log (4 \log (x))}{2 x}\right )\right )}{x \left (-10+3 x^2\right ) \log (x) \log (4 \log (x)) \log \left (\frac {\log (4 \log (x))}{2 x}\right ) \log \left (\log ^2\left (\frac {\log (4 \log (x))}{2 x}\right )\right )} \, dx \\ & = \int \left (\frac {-10-3 x^2}{x \left (-10+3 x^2\right )}-\frac {2 (-1+\log (x) \log (4 \log (x)))}{x \log (x) \log (4 \log (x)) \log \left (\frac {\log (4 \log (x))}{2 x}\right ) \log \left (\log ^2\left (\frac {\log (4 \log (x))}{2 x}\right )\right )}\right ) \, dx \\ & = -\left (2 \int \frac {-1+\log (x) \log (4 \log (x))}{x \log (x) \log (4 \log (x)) \log \left (\frac {\log (4 \log (x))}{2 x}\right ) \log \left (\log ^2\left (\frac {\log (4 \log (x))}{2 x}\right )\right )} \, dx\right )+\int \frac {-10-3 x^2}{x \left (-10+3 x^2\right )} \, dx \\ & = \log \left (\log \left (\log ^2\left (\frac {\log (4 \log (x))}{2 x}\right )\right )\right )+\frac {1}{2} \text {Subst}\left (\int \frac {-10-3 x}{x (-10+3 x)} \, dx,x,x^2\right ) \\ & = \log \left (\log \left (\log ^2\left (\frac {\log (4 \log (x))}{2 x}\right )\right )\right )+\frac {1}{2} \text {Subst}\left (\int \left (\frac {1}{x}-\frac {6}{-10+3 x}\right ) \, dx,x,x^2\right ) \\ & = \log (x)-\log \left (10-3 x^2\right )+\log \left (\log \left (\log ^2\left (\frac {\log (4 \log (x))}{2 x}\right )\right )\right ) \\ \end{align*}
Time = 0.11 (sec) , antiderivative size = 30, normalized size of antiderivative = 0.94 \[ \int \frac {-20+6 x^2+\left (20-6 x^2\right ) \log (x) \log (4 \log (x))+\left (-10-3 x^2\right ) \log (x) \log (4 \log (x)) \log \left (\frac {\log (4 \log (x))}{2 x}\right ) \log \left (\log ^2\left (\frac {\log (4 \log (x))}{2 x}\right )\right )}{\left (-10 x+3 x^3\right ) \log (x) \log (4 \log (x)) \log \left (\frac {\log (4 \log (x))}{2 x}\right ) \log \left (\log ^2\left (\frac {\log (4 \log (x))}{2 x}\right )\right )} \, dx=\log (x)-\log \left (10-3 x^2\right )+\log \left (\log \left (\log ^2\left (\frac {\log (4 \log (x))}{2 x}\right )\right )\right ) \]
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Time = 198.05 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.84
method | result | size |
parallelrisch | \(\ln \left (x \right )+\ln \left (\ln \left (\ln \left (\frac {\ln \left (4 \ln \left (x \right )\right )}{2 x}\right )^{2}\right )\right )-\ln \left (x^{2}-\frac {10}{3}\right )\) | \(27\) |
risch | \(\text {Expression too large to display}\) | \(892\) |
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Time = 0.26 (sec) , antiderivative size = 28, normalized size of antiderivative = 0.88 \[ \int \frac {-20+6 x^2+\left (20-6 x^2\right ) \log (x) \log (4 \log (x))+\left (-10-3 x^2\right ) \log (x) \log (4 \log (x)) \log \left (\frac {\log (4 \log (x))}{2 x}\right ) \log \left (\log ^2\left (\frac {\log (4 \log (x))}{2 x}\right )\right )}{\left (-10 x+3 x^3\right ) \log (x) \log (4 \log (x)) \log \left (\frac {\log (4 \log (x))}{2 x}\right ) \log \left (\log ^2\left (\frac {\log (4 \log (x))}{2 x}\right )\right )} \, dx=-\log \left (3 \, x^{2} - 10\right ) + \log \left (x\right ) + \log \left (\log \left (\log \left (\frac {\log \left (4 \, \log \left (x\right )\right )}{2 \, x}\right )^{2}\right )\right ) \]
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Time = 0.49 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.84 \[ \int \frac {-20+6 x^2+\left (20-6 x^2\right ) \log (x) \log (4 \log (x))+\left (-10-3 x^2\right ) \log (x) \log (4 \log (x)) \log \left (\frac {\log (4 \log (x))}{2 x}\right ) \log \left (\log ^2\left (\frac {\log (4 \log (x))}{2 x}\right )\right )}{\left (-10 x+3 x^3\right ) \log (x) \log (4 \log (x)) \log \left (\frac {\log (4 \log (x))}{2 x}\right ) \log \left (\log ^2\left (\frac {\log (4 \log (x))}{2 x}\right )\right )} \, dx=\log {\left (x \right )} - \log {\left (3 x^{2} - 10 \right )} + \log {\left (\log {\left (\log {\left (\frac {\log {\left (4 \log {\left (x \right )} \right )}}{2 x} \right )}^{2} \right )} \right )} \]
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Time = 0.35 (sec) , antiderivative size = 31, normalized size of antiderivative = 0.97 \[ \int \frac {-20+6 x^2+\left (20-6 x^2\right ) \log (x) \log (4 \log (x))+\left (-10-3 x^2\right ) \log (x) \log (4 \log (x)) \log \left (\frac {\log (4 \log (x))}{2 x}\right ) \log \left (\log ^2\left (\frac {\log (4 \log (x))}{2 x}\right )\right )}{\left (-10 x+3 x^3\right ) \log (x) \log (4 \log (x)) \log \left (\frac {\log (4 \log (x))}{2 x}\right ) \log \left (\log ^2\left (\frac {\log (4 \log (x))}{2 x}\right )\right )} \, dx=-\log \left (3 \, x^{2} - 10\right ) + \log \left (x\right ) + \log \left (\log \left (\log \left (2\right ) + \log \left (x\right ) - \log \left (2 \, \log \left (2\right ) + \log \left (\log \left (x\right )\right )\right )\right )\right ) \]
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Timed out. \[ \int \frac {-20+6 x^2+\left (20-6 x^2\right ) \log (x) \log (4 \log (x))+\left (-10-3 x^2\right ) \log (x) \log (4 \log (x)) \log \left (\frac {\log (4 \log (x))}{2 x}\right ) \log \left (\log ^2\left (\frac {\log (4 \log (x))}{2 x}\right )\right )}{\left (-10 x+3 x^3\right ) \log (x) \log (4 \log (x)) \log \left (\frac {\log (4 \log (x))}{2 x}\right ) \log \left (\log ^2\left (\frac {\log (4 \log (x))}{2 x}\right )\right )} \, dx=\text {Timed out} \]
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Time = 16.70 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.81 \[ \int \frac {-20+6 x^2+\left (20-6 x^2\right ) \log (x) \log (4 \log (x))+\left (-10-3 x^2\right ) \log (x) \log (4 \log (x)) \log \left (\frac {\log (4 \log (x))}{2 x}\right ) \log \left (\log ^2\left (\frac {\log (4 \log (x))}{2 x}\right )\right )}{\left (-10 x+3 x^3\right ) \log (x) \log (4 \log (x)) \log \left (\frac {\log (4 \log (x))}{2 x}\right ) \log \left (\log ^2\left (\frac {\log (4 \log (x))}{2 x}\right )\right )} \, dx=\ln \left (\ln \left ({\ln \left (\frac {\ln \left (4\,\ln \left (x\right )\right )}{2\,x}\right )}^2\right )\right )-\ln \left (x^2-\frac {10}{3}\right )+\ln \left (x\right ) \]
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