Integrand size = 178, antiderivative size = 32 \[ \int \frac {-6 \log (4)+\left (6 x^2-9 x^3\right ) \log ^2(x)+\left (6 \log (4) \log (x)+\left (3 x^2-3 x^3\right ) \log ^2(x)\right ) \log \left (\frac {4 \log (4)+\left (2 x^2-2 x^3\right ) \log (x)}{\log (x)}\right ) \log \left (\log \left (\frac {4 \log (4)+\left (2 x^2-2 x^3\right ) \log (x)}{\log (x)}\right )\right )}{\left (-2 x^2 \log (4) \log (x)+\left (-x^4+x^5\right ) \log ^2(x)\right ) \log \left (\frac {4 \log (4)+\left (2 x^2-2 x^3\right ) \log (x)}{\log (x)}\right ) \log ^2\left (\log \left (\frac {4 \log (4)+\left (2 x^2-2 x^3\right ) \log (x)}{\log (x)}\right )\right )} \, dx=\frac {3}{x \log \left (\log \left (x \log \left (e^{2 x-2 x^2}\right )+\frac {4 \log (4)}{\log (x)}\right )\right )} \]
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\[ \int \frac {-6 \log (4)+\left (6 x^2-9 x^3\right ) \log ^2(x)+\left (6 \log (4) \log (x)+\left (3 x^2-3 x^3\right ) \log ^2(x)\right ) \log \left (\frac {4 \log (4)+\left (2 x^2-2 x^3\right ) \log (x)}{\log (x)}\right ) \log \left (\log \left (\frac {4 \log (4)+\left (2 x^2-2 x^3\right ) \log (x)}{\log (x)}\right )\right )}{\left (-2 x^2 \log (4) \log (x)+\left (-x^4+x^5\right ) \log ^2(x)\right ) \log \left (\frac {4 \log (4)+\left (2 x^2-2 x^3\right ) \log (x)}{\log (x)}\right ) \log ^2\left (\log \left (\frac {4 \log (4)+\left (2 x^2-2 x^3\right ) \log (x)}{\log (x)}\right )\right )} \, dx=\int \frac {-6 \log (4)+\left (6 x^2-9 x^3\right ) \log ^2(x)+\left (6 \log (4) \log (x)+\left (3 x^2-3 x^3\right ) \log ^2(x)\right ) \log \left (\frac {4 \log (4)+\left (2 x^2-2 x^3\right ) \log (x)}{\log (x)}\right ) \log \left (\log \left (\frac {4 \log (4)+\left (2 x^2-2 x^3\right ) \log (x)}{\log (x)}\right )\right )}{\left (-2 x^2 \log (4) \log (x)+\left (-x^4+x^5\right ) \log ^2(x)\right ) \log \left (\frac {4 \log (4)+\left (2 x^2-2 x^3\right ) \log (x)}{\log (x)}\right ) \log ^2\left (\log \left (\frac {4 \log (4)+\left (2 x^2-2 x^3\right ) \log (x)}{\log (x)}\right )\right )} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {6 \log (4)-\left (6 x^2-9 x^3\right ) \log ^2(x)-\left (6 \log (4) \log (x)+\left (3 x^2-3 x^3\right ) \log ^2(x)\right ) \log \left (\frac {4 \log (4)+\left (2 x^2-2 x^3\right ) \log (x)}{\log (x)}\right ) \log \left (\log \left (\frac {4 \log (4)+\left (2 x^2-2 x^3\right ) \log (x)}{\log (x)}\right )\right )}{x^2 \log (x) \left (2 \log (4)+x^2 \log (x)-x^3 \log (x)\right ) \log \left (\frac {4 \log (4)+\left (2 x^2-2 x^3\right ) \log (x)}{\log (x)}\right ) \log ^2\left (\log \left (\frac {4 \log (4)+\left (2 x^2-2 x^3\right ) \log (x)}{\log (x)}\right )\right )} \, dx \\ & = \int \frac {6 \log (4)+3 x^2 (-2+3 x) \log ^2(x)-\log (x) \left (6 \log (4)-3 (-1+x) x^2 \log (x)\right ) \log \left (-2 (-1+x) x^2+\frac {\log (256)}{\log (x)}\right ) \log \left (\log \left (-2 (-1+x) x^2+\frac {\log (256)}{\log (x)}\right )\right )}{x^2 \log (x) \left (\log (16)-(-1+x) x^2 \log (x)\right ) \log \left (-2 (-1+x) x^2+\frac {\log (256)}{\log (x)}\right ) \log ^2\left (\log \left (-2 (-1+x) x^2+\frac {\log (256)}{\log (x)}\right )\right )} \, dx \\ & = \int \left (-\frac {3 \left (2 \log (4)-2 x^2 \log ^2(x)+3 x^3 \log ^2(x)\right )}{x^2 \log (x) \left (-\log (16)-x^2 \log (x)+x^3 \log (x)\right ) \log \left (-2 (-1+x) x^2+\frac {\log (256)}{\log (x)}\right ) \log ^2\left (\log \left (-2 (-1+x) x^2+\frac {\log (256)}{\log (x)}\right )\right )}-\frac {3 \left (-2 \log (4)-x^2 \log (x)+x^3 \log (x)\right )}{x^2 \left (-\log (16)-x^2 \log (x)+x^3 \log (x)\right ) \log \left (\log \left (-2 (-1+x) x^2+\frac {\log (256)}{\log (x)}\right )\right )}\right ) \, dx \\ & = -\left (3 \int \frac {2 \log (4)-2 x^2 \log ^2(x)+3 x^3 \log ^2(x)}{x^2 \log (x) \left (-\log (16)-x^2 \log (x)+x^3 \log (x)\right ) \log \left (-2 (-1+x) x^2+\frac {\log (256)}{\log (x)}\right ) \log ^2\left (\log \left (-2 (-1+x) x^2+\frac {\log (256)}{\log (x)}\right )\right )} \, dx\right )-3 \int \frac {-2 \log (4)-x^2 \log (x)+x^3 \log (x)}{x^2 \left (-\log (16)-x^2 \log (x)+x^3 \log (x)\right ) \log \left (\log \left (-2 (-1+x) x^2+\frac {\log (256)}{\log (x)}\right )\right )} \, dx \\ & = -\left (3 \int \left (\frac {2 \log (x)}{\left (\log (16)+x^2 \log (x)-x^3 \log (x)\right ) \log \left (-2 (-1+x) x^2+\frac {\log (256)}{\log (x)}\right ) \log ^2\left (\log \left (-2 (-1+x) x^2+\frac {\log (256)}{\log (x)}\right )\right )}+\frac {\log (16)}{x^2 \log (x) \left (-\log (16)-x^2 \log (x)+x^3 \log (x)\right ) \log \left (-2 (-1+x) x^2+\frac {\log (256)}{\log (x)}\right ) \log ^2\left (\log \left (-2 (-1+x) x^2+\frac {\log (256)}{\log (x)}\right )\right )}+\frac {3 x \log (x)}{\left (-\log (16)-x^2 \log (x)+x^3 \log (x)\right ) \log \left (-2 (-1+x) x^2+\frac {\log (256)}{\log (x)}\right ) \log ^2\left (\log \left (-2 (-1+x) x^2+\frac {\log (256)}{\log (x)}\right )\right )}\right ) \, dx\right )-3 \int \frac {1}{x^2 \log \left (\log \left (-2 (-1+x) x^2+\frac {\log (256)}{\log (x)}\right )\right )} \, dx \\ & = -\left (3 \int \frac {1}{x^2 \log \left (\log \left (-2 (-1+x) x^2+\frac {\log (256)}{\log (x)}\right )\right )} \, dx\right )-6 \int \frac {\log (x)}{\left (\log (16)+x^2 \log (x)-x^3 \log (x)\right ) \log \left (-2 (-1+x) x^2+\frac {\log (256)}{\log (x)}\right ) \log ^2\left (\log \left (-2 (-1+x) x^2+\frac {\log (256)}{\log (x)}\right )\right )} \, dx-9 \int \frac {x \log (x)}{\left (-\log (16)-x^2 \log (x)+x^3 \log (x)\right ) \log \left (-2 (-1+x) x^2+\frac {\log (256)}{\log (x)}\right ) \log ^2\left (\log \left (-2 (-1+x) x^2+\frac {\log (256)}{\log (x)}\right )\right )} \, dx-(3 \log (16)) \int \frac {1}{x^2 \log (x) \left (-\log (16)-x^2 \log (x)+x^3 \log (x)\right ) \log \left (-2 (-1+x) x^2+\frac {\log (256)}{\log (x)}\right ) \log ^2\left (\log \left (-2 (-1+x) x^2+\frac {\log (256)}{\log (x)}\right )\right )} \, dx \\ \end{align*}
Leaf count is larger than twice the leaf count of optimal. \(89\) vs. \(2(32)=64\).
Time = 0.16 (sec) , antiderivative size = 89, normalized size of antiderivative = 2.78 \[ \int \frac {-6 \log (4)+\left (6 x^2-9 x^3\right ) \log ^2(x)+\left (6 \log (4) \log (x)+\left (3 x^2-3 x^3\right ) \log ^2(x)\right ) \log \left (\frac {4 \log (4)+\left (2 x^2-2 x^3\right ) \log (x)}{\log (x)}\right ) \log \left (\log \left (\frac {4 \log (4)+\left (2 x^2-2 x^3\right ) \log (x)}{\log (x)}\right )\right )}{\left (-2 x^2 \log (4) \log (x)+\left (-x^4+x^5\right ) \log ^2(x)\right ) \log \left (\frac {4 \log (4)+\left (2 x^2-2 x^3\right ) \log (x)}{\log (x)}\right ) \log ^2\left (\log \left (\frac {4 \log (4)+\left (2 x^2-2 x^3\right ) \log (x)}{\log (x)}\right )\right )} \, dx=-\frac {3 \left (\log (256)-2 (-1+x) x^2 \log (x)\right ) \left (\log (16)+x^2 (-2+3 x) \log ^2(x)\right )}{x \left (-2 \log (4)+(-1+x) x^2 \log (x)\right ) \left (\log (256)+2 x^2 (-2+3 x) \log ^2(x)\right ) \log \left (\log \left (-2 (-1+x) x^2+\frac {\log (256)}{\log (x)}\right )\right )} \]
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Result contains higher order function than in optimal. Order 9 vs. order 3.
Time = 24.52 (sec) , antiderivative size = 151, normalized size of antiderivative = 4.72
\[\frac {3}{x \ln \left (3 \ln \left (2\right )-\ln \left (\ln \left (x \right )\right )+\ln \left (-\frac {x^{3} \ln \left (x \right )}{4}+\frac {x^{2} \ln \left (x \right )}{4}+\ln \left (2\right )\right )-\frac {i \pi \,\operatorname {csgn}\left (\frac {i \left (-\frac {x^{3} \ln \left (x \right )}{4}+\frac {x^{2} \ln \left (x \right )}{4}+\ln \left (2\right )\right )}{\ln \left (x \right )}\right ) \left (-\operatorname {csgn}\left (\frac {i \left (-\frac {x^{3} \ln \left (x \right )}{4}+\frac {x^{2} \ln \left (x \right )}{4}+\ln \left (2\right )\right )}{\ln \left (x \right )}\right )+\operatorname {csgn}\left (\frac {i}{\ln \left (x \right )}\right )\right ) \left (-\operatorname {csgn}\left (\frac {i \left (-\frac {x^{3} \ln \left (x \right )}{4}+\frac {x^{2} \ln \left (x \right )}{4}+\ln \left (2\right )\right )}{\ln \left (x \right )}\right )+\operatorname {csgn}\left (i \left (-\frac {x^{3} \ln \left (x \right )}{4}+\frac {x^{2} \ln \left (x \right )}{4}+\ln \left (2\right )\right )\right )\right )}{2}\right )}\]
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Time = 0.25 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.00 \[ \int \frac {-6 \log (4)+\left (6 x^2-9 x^3\right ) \log ^2(x)+\left (6 \log (4) \log (x)+\left (3 x^2-3 x^3\right ) \log ^2(x)\right ) \log \left (\frac {4 \log (4)+\left (2 x^2-2 x^3\right ) \log (x)}{\log (x)}\right ) \log \left (\log \left (\frac {4 \log (4)+\left (2 x^2-2 x^3\right ) \log (x)}{\log (x)}\right )\right )}{\left (-2 x^2 \log (4) \log (x)+\left (-x^4+x^5\right ) \log ^2(x)\right ) \log \left (\frac {4 \log (4)+\left (2 x^2-2 x^3\right ) \log (x)}{\log (x)}\right ) \log ^2\left (\log \left (\frac {4 \log (4)+\left (2 x^2-2 x^3\right ) \log (x)}{\log (x)}\right )\right )} \, dx=\frac {3}{x \log \left (\log \left (-\frac {2 \, {\left ({\left (x^{3} - x^{2}\right )} \log \left (x\right ) - 4 \, \log \left (2\right )\right )}}{\log \left (x\right )}\right )\right )} \]
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Time = 1.97 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.84 \[ \int \frac {-6 \log (4)+\left (6 x^2-9 x^3\right ) \log ^2(x)+\left (6 \log (4) \log (x)+\left (3 x^2-3 x^3\right ) \log ^2(x)\right ) \log \left (\frac {4 \log (4)+\left (2 x^2-2 x^3\right ) \log (x)}{\log (x)}\right ) \log \left (\log \left (\frac {4 \log (4)+\left (2 x^2-2 x^3\right ) \log (x)}{\log (x)}\right )\right )}{\left (-2 x^2 \log (4) \log (x)+\left (-x^4+x^5\right ) \log ^2(x)\right ) \log \left (\frac {4 \log (4)+\left (2 x^2-2 x^3\right ) \log (x)}{\log (x)}\right ) \log ^2\left (\log \left (\frac {4 \log (4)+\left (2 x^2-2 x^3\right ) \log (x)}{\log (x)}\right )\right )} \, dx=\frac {3}{x \log {\left (\log {\left (\frac {\left (- 2 x^{3} + 2 x^{2}\right ) \log {\left (x \right )} + 8 \log {\left (2 \right )}}{\log {\left (x \right )}} \right )} \right )}} \]
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Result contains complex when optimal does not.
Time = 0.33 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.16 \[ \int \frac {-6 \log (4)+\left (6 x^2-9 x^3\right ) \log ^2(x)+\left (6 \log (4) \log (x)+\left (3 x^2-3 x^3\right ) \log ^2(x)\right ) \log \left (\frac {4 \log (4)+\left (2 x^2-2 x^3\right ) \log (x)}{\log (x)}\right ) \log \left (\log \left (\frac {4 \log (4)+\left (2 x^2-2 x^3\right ) \log (x)}{\log (x)}\right )\right )}{\left (-2 x^2 \log (4) \log (x)+\left (-x^4+x^5\right ) \log ^2(x)\right ) \log \left (\frac {4 \log (4)+\left (2 x^2-2 x^3\right ) \log (x)}{\log (x)}\right ) \log ^2\left (\log \left (\frac {4 \log (4)+\left (2 x^2-2 x^3\right ) \log (x)}{\log (x)}\right )\right )} \, dx=\frac {3}{x \log \left (i \, \pi + \log \left (2\right ) + \log \left ({\left (x^{3} - x^{2}\right )} \log \left (x\right ) - 4 \, \log \left (2\right )\right ) - \log \left (\log \left (x\right )\right )\right )} \]
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Time = 0.63 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.09 \[ \int \frac {-6 \log (4)+\left (6 x^2-9 x^3\right ) \log ^2(x)+\left (6 \log (4) \log (x)+\left (3 x^2-3 x^3\right ) \log ^2(x)\right ) \log \left (\frac {4 \log (4)+\left (2 x^2-2 x^3\right ) \log (x)}{\log (x)}\right ) \log \left (\log \left (\frac {4 \log (4)+\left (2 x^2-2 x^3\right ) \log (x)}{\log (x)}\right )\right )}{\left (-2 x^2 \log (4) \log (x)+\left (-x^4+x^5\right ) \log ^2(x)\right ) \log \left (\frac {4 \log (4)+\left (2 x^2-2 x^3\right ) \log (x)}{\log (x)}\right ) \log ^2\left (\log \left (\frac {4 \log (4)+\left (2 x^2-2 x^3\right ) \log (x)}{\log (x)}\right )\right )} \, dx=\frac {3}{x \log \left (\log \left (2\right ) + \log \left (-x^{3} \log \left (x\right ) + x^{2} \log \left (x\right ) + 4 \, \log \left (2\right )\right ) - \log \left (\log \left (x\right )\right )\right )} \]
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Timed out. \[ \int \frac {-6 \log (4)+\left (6 x^2-9 x^3\right ) \log ^2(x)+\left (6 \log (4) \log (x)+\left (3 x^2-3 x^3\right ) \log ^2(x)\right ) \log \left (\frac {4 \log (4)+\left (2 x^2-2 x^3\right ) \log (x)}{\log (x)}\right ) \log \left (\log \left (\frac {4 \log (4)+\left (2 x^2-2 x^3\right ) \log (x)}{\log (x)}\right )\right )}{\left (-2 x^2 \log (4) \log (x)+\left (-x^4+x^5\right ) \log ^2(x)\right ) \log \left (\frac {4 \log (4)+\left (2 x^2-2 x^3\right ) \log (x)}{\log (x)}\right ) \log ^2\left (\log \left (\frac {4 \log (4)+\left (2 x^2-2 x^3\right ) \log (x)}{\log (x)}\right )\right )} \, dx=\text {Hanged} \]
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