Integrand size = 142, antiderivative size = 28 \[ \int \frac {\left (4 x^3+\left (32 x^3-4 x^3 \log (x)\right ) \log (16-2 \log (x))+\left (-16+18 \log (x)-2 \log ^2(x)\right ) \log ^3(16-2 \log (x))\right ) \log \left (\frac {x^3+(-x-\log (x)) \log ^2(16-2 \log (x))}{x \log ^2(16-2 \log (x))}\right )}{\left (8 x^4-x^4 \log (x)\right ) \log (16-2 \log (x))+\left (-8 x^2+\left (-8 x+x^2\right ) \log (x)+x \log ^2(x)\right ) \log ^3(16-2 \log (x))} \, dx=\log ^2\left (-\frac {x+\log (x)}{x}+\frac {x^2}{\log ^2(2 (8-\log (x)))}\right ) \]
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\[ \int \frac {\left (4 x^3+\left (32 x^3-4 x^3 \log (x)\right ) \log (16-2 \log (x))+\left (-16+18 \log (x)-2 \log ^2(x)\right ) \log ^3(16-2 \log (x))\right ) \log \left (\frac {x^3+(-x-\log (x)) \log ^2(16-2 \log (x))}{x \log ^2(16-2 \log (x))}\right )}{\left (8 x^4-x^4 \log (x)\right ) \log (16-2 \log (x))+\left (-8 x^2+\left (-8 x+x^2\right ) \log (x)+x \log ^2(x)\right ) \log ^3(16-2 \log (x))} \, dx=\int \frac {\left (4 x^3+\left (32 x^3-4 x^3 \log (x)\right ) \log (16-2 \log (x))+\left (-16+18 \log (x)-2 \log ^2(x)\right ) \log ^3(16-2 \log (x))\right ) \log \left (\frac {x^3+(-x-\log (x)) \log ^2(16-2 \log (x))}{x \log ^2(16-2 \log (x))}\right )}{\left (8 x^4-x^4 \log (x)\right ) \log (16-2 \log (x))+\left (-8 x^2+\left (-8 x+x^2\right ) \log (x)+x \log ^2(x)\right ) \log ^3(16-2 \log (x))} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {\left (4 x^3+\left (32 x^3-4 x^3 \log (x)\right ) \log (16-2 \log (x))+\left (-16+18 \log (x)-2 \log ^2(x)\right ) \log ^3(16-2 \log (x))\right ) \log \left (\frac {x^3+(-x-\log (x)) \log ^2(16-2 \log (x))}{x \log ^2(-2 (-8+\log (x)))}\right )}{x (8-\log (x)) \log (-2 (-8+\log (x))) \left (x^3-x \log ^2(-2 (-8+\log (x)))-\log (x) \log ^2(-2 (-8+\log (x)))\right )} \, dx \\ & = \int \left (\frac {16 \log ^2(-2 (-8+\log (x))) \log \left (-1-\frac {\log (x)}{x}+\frac {x^2}{\log ^2(-2 (-8+\log (x)))}\right )}{x (-8+\log (x)) \left (x^3-x \log ^2(-2 (-8+\log (x)))-\log (x) \log ^2(-2 (-8+\log (x)))\right )}-\frac {18 \log (x) \log ^2(-2 (-8+\log (x))) \log \left (-1-\frac {\log (x)}{x}+\frac {x^2}{\log ^2(-2 (-8+\log (x)))}\right )}{x (-8+\log (x)) \left (x^3-x \log ^2(-2 (-8+\log (x)))-\log (x) \log ^2(-2 (-8+\log (x)))\right )}+\frac {2 \log ^2(x) \log ^2(-2 (-8+\log (x))) \log \left (-1-\frac {\log (x)}{x}+\frac {x^2}{\log ^2(-2 (-8+\log (x)))}\right )}{x (-8+\log (x)) \left (x^3-x \log ^2(-2 (-8+\log (x)))-\log (x) \log ^2(-2 (-8+\log (x)))\right )}+\frac {32 x^2 \log \left (-1-\frac {\log (x)}{x}+\frac {x^2}{\log ^2(-2 (-8+\log (x)))}\right )}{(-8+\log (x)) \left (-x^3+x \log ^2(-2 (-8+\log (x)))+\log (x) \log ^2(-2 (-8+\log (x)))\right )}-\frac {4 x^2 \log (x) \log \left (-1-\frac {\log (x)}{x}+\frac {x^2}{\log ^2(-2 (-8+\log (x)))}\right )}{(-8+\log (x)) \left (-x^3+x \log ^2(-2 (-8+\log (x)))+\log (x) \log ^2(-2 (-8+\log (x)))\right )}+\frac {4 x^2 \log \left (-1-\frac {\log (x)}{x}+\frac {x^2}{\log ^2(-2 (-8+\log (x)))}\right )}{(-8+\log (x)) \log (-2 (-8+\log (x))) \left (-x^3+x \log ^2(-2 (-8+\log (x)))+\log (x) \log ^2(-2 (-8+\log (x)))\right )}\right ) \, dx \\ & = 2 \int \frac {\log ^2(x) \log ^2(-2 (-8+\log (x))) \log \left (-1-\frac {\log (x)}{x}+\frac {x^2}{\log ^2(-2 (-8+\log (x)))}\right )}{x (-8+\log (x)) \left (x^3-x \log ^2(-2 (-8+\log (x)))-\log (x) \log ^2(-2 (-8+\log (x)))\right )} \, dx-4 \int \frac {x^2 \log (x) \log \left (-1-\frac {\log (x)}{x}+\frac {x^2}{\log ^2(-2 (-8+\log (x)))}\right )}{(-8+\log (x)) \left (-x^3+x \log ^2(-2 (-8+\log (x)))+\log (x) \log ^2(-2 (-8+\log (x)))\right )} \, dx+4 \int \frac {x^2 \log \left (-1-\frac {\log (x)}{x}+\frac {x^2}{\log ^2(-2 (-8+\log (x)))}\right )}{(-8+\log (x)) \log (-2 (-8+\log (x))) \left (-x^3+x \log ^2(-2 (-8+\log (x)))+\log (x) \log ^2(-2 (-8+\log (x)))\right )} \, dx+16 \int \frac {\log ^2(-2 (-8+\log (x))) \log \left (-1-\frac {\log (x)}{x}+\frac {x^2}{\log ^2(-2 (-8+\log (x)))}\right )}{x (-8+\log (x)) \left (x^3-x \log ^2(-2 (-8+\log (x)))-\log (x) \log ^2(-2 (-8+\log (x)))\right )} \, dx-18 \int \frac {\log (x) \log ^2(-2 (-8+\log (x))) \log \left (-1-\frac {\log (x)}{x}+\frac {x^2}{\log ^2(-2 (-8+\log (x)))}\right )}{x (-8+\log (x)) \left (x^3-x \log ^2(-2 (-8+\log (x)))-\log (x) \log ^2(-2 (-8+\log (x)))\right )} \, dx+32 \int \frac {x^2 \log \left (-1-\frac {\log (x)}{x}+\frac {x^2}{\log ^2(-2 (-8+\log (x)))}\right )}{(-8+\log (x)) \left (-x^3+x \log ^2(-2 (-8+\log (x)))+\log (x) \log ^2(-2 (-8+\log (x)))\right )} \, dx \\ & = 2 \int \frac {\log ^2(x) \log ^2(-2 (-8+\log (x))) \log \left (-1-\frac {\log (x)}{x}+\frac {x^2}{\log ^2(-2 (-8+\log (x)))}\right )}{x (-8+\log (x)) \left (x^3-(x+\log (x)) \log ^2(-2 (-8+\log (x)))\right )} \, dx-4 \int \frac {x^2 \log (x) \log \left (-1-\frac {\log (x)}{x}+\frac {x^2}{\log ^2(-2 (-8+\log (x)))}\right )}{(-8+\log (x)) \left (-x^3+x \log ^2(-2 (-8+\log (x)))+\log (x) \log ^2(-2 (-8+\log (x)))\right )} \, dx+4 \int \frac {x^2 \log \left (-1-\frac {\log (x)}{x}+\frac {x^2}{\log ^2(-2 (-8+\log (x)))}\right )}{(-8+\log (x)) \log (-2 (-8+\log (x))) \left (-x^3+x \log ^2(-2 (-8+\log (x)))+\log (x) \log ^2(-2 (-8+\log (x)))\right )} \, dx+16 \int \frac {\log ^2(-2 (-8+\log (x))) \log \left (-1-\frac {\log (x)}{x}+\frac {x^2}{\log ^2(-2 (-8+\log (x)))}\right )}{x (-8+\log (x)) \left (x^3-(x+\log (x)) \log ^2(-2 (-8+\log (x)))\right )} \, dx-18 \int \frac {\log (x) \log ^2(-2 (-8+\log (x))) \log \left (-1-\frac {\log (x)}{x}+\frac {x^2}{\log ^2(-2 (-8+\log (x)))}\right )}{x (-8+\log (x)) \left (x^3-(x+\log (x)) \log ^2(-2 (-8+\log (x)))\right )} \, dx+32 \int \frac {x^2 \log \left (-1-\frac {\log (x)}{x}+\frac {x^2}{\log ^2(-2 (-8+\log (x)))}\right )}{(-8+\log (x)) \left (-x^3+x \log ^2(-2 (-8+\log (x)))+\log (x) \log ^2(-2 (-8+\log (x)))\right )} \, dx \\ \end{align*}
Time = 0.12 (sec) , antiderivative size = 25, normalized size of antiderivative = 0.89 \[ \int \frac {\left (4 x^3+\left (32 x^3-4 x^3 \log (x)\right ) \log (16-2 \log (x))+\left (-16+18 \log (x)-2 \log ^2(x)\right ) \log ^3(16-2 \log (x))\right ) \log \left (\frac {x^3+(-x-\log (x)) \log ^2(16-2 \log (x))}{x \log ^2(16-2 \log (x))}\right )}{\left (8 x^4-x^4 \log (x)\right ) \log (16-2 \log (x))+\left (-8 x^2+\left (-8 x+x^2\right ) \log (x)+x \log ^2(x)\right ) \log ^3(16-2 \log (x))} \, dx=\log ^2\left (-1-\frac {\log (x)}{x}+\frac {x^2}{\log ^2(-2 (-8+\log (x)))}\right ) \]
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\[\int \frac {\left (\left (-2 \ln \left (x \right )^{2}+18 \ln \left (x \right )-16\right ) \ln \left (-2 \ln \left (x \right )+16\right )^{3}+\left (-4 x^{3} \ln \left (x \right )+32 x^{3}\right ) \ln \left (-2 \ln \left (x \right )+16\right )+4 x^{3}\right ) \ln \left (\frac {\left (-x -\ln \left (x \right )\right ) \ln \left (-2 \ln \left (x \right )+16\right )^{2}+x^{3}}{x \ln \left (-2 \ln \left (x \right )+16\right )^{2}}\right )}{\left (x \ln \left (x \right )^{2}+\left (x^{2}-8 x \right ) \ln \left (x \right )-8 x^{2}\right ) \ln \left (-2 \ln \left (x \right )+16\right )^{3}+\left (-x^{4} \ln \left (x \right )+8 x^{4}\right ) \ln \left (-2 \ln \left (x \right )+16\right )}d x\]
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Time = 0.23 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.25 \[ \int \frac {\left (4 x^3+\left (32 x^3-4 x^3 \log (x)\right ) \log (16-2 \log (x))+\left (-16+18 \log (x)-2 \log ^2(x)\right ) \log ^3(16-2 \log (x))\right ) \log \left (\frac {x^3+(-x-\log (x)) \log ^2(16-2 \log (x))}{x \log ^2(16-2 \log (x))}\right )}{\left (8 x^4-x^4 \log (x)\right ) \log (16-2 \log (x))+\left (-8 x^2+\left (-8 x+x^2\right ) \log (x)+x \log ^2(x)\right ) \log ^3(16-2 \log (x))} \, dx=\log \left (\frac {x^{3} - {\left (x + \log \left (x\right )\right )} \log \left (-2 \, \log \left (x\right ) + 16\right )^{2}}{x \log \left (-2 \, \log \left (x\right ) + 16\right )^{2}}\right )^{2} \]
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Time = 2.31 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.21 \[ \int \frac {\left (4 x^3+\left (32 x^3-4 x^3 \log (x)\right ) \log (16-2 \log (x))+\left (-16+18 \log (x)-2 \log ^2(x)\right ) \log ^3(16-2 \log (x))\right ) \log \left (\frac {x^3+(-x-\log (x)) \log ^2(16-2 \log (x))}{x \log ^2(16-2 \log (x))}\right )}{\left (8 x^4-x^4 \log (x)\right ) \log (16-2 \log (x))+\left (-8 x^2+\left (-8 x+x^2\right ) \log (x)+x \log ^2(x)\right ) \log ^3(16-2 \log (x))} \, dx=\log {\left (\frac {x^{3} + \left (- x - \log {\left (x \right )}\right ) \log {\left (16 - 2 \log {\left (x \right )} \right )}^{2}}{x \log {\left (16 - 2 \log {\left (x \right )} \right )}^{2}} \right )}^{2} \]
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\[ \int \frac {\left (4 x^3+\left (32 x^3-4 x^3 \log (x)\right ) \log (16-2 \log (x))+\left (-16+18 \log (x)-2 \log ^2(x)\right ) \log ^3(16-2 \log (x))\right ) \log \left (\frac {x^3+(-x-\log (x)) \log ^2(16-2 \log (x))}{x \log ^2(16-2 \log (x))}\right )}{\left (8 x^4-x^4 \log (x)\right ) \log (16-2 \log (x))+\left (-8 x^2+\left (-8 x+x^2\right ) \log (x)+x \log ^2(x)\right ) \log ^3(16-2 \log (x))} \, dx=\int { -\frac {2 \, {\left ({\left (\log \left (x\right )^{2} - 9 \, \log \left (x\right ) + 8\right )} \log \left (-2 \, \log \left (x\right ) + 16\right )^{3} - 2 \, x^{3} + 2 \, {\left (x^{3} \log \left (x\right ) - 8 \, x^{3}\right )} \log \left (-2 \, \log \left (x\right ) + 16\right )\right )} \log \left (\frac {x^{3} - {\left (x + \log \left (x\right )\right )} \log \left (-2 \, \log \left (x\right ) + 16\right )^{2}}{x \log \left (-2 \, \log \left (x\right ) + 16\right )^{2}}\right )}{{\left (x \log \left (x\right )^{2} - 8 \, x^{2} + {\left (x^{2} - 8 \, x\right )} \log \left (x\right )\right )} \log \left (-2 \, \log \left (x\right ) + 16\right )^{3} - {\left (x^{4} \log \left (x\right ) - 8 \, x^{4}\right )} \log \left (-2 \, \log \left (x\right ) + 16\right )} \,d x } \]
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Timed out. \[ \int \frac {\left (4 x^3+\left (32 x^3-4 x^3 \log (x)\right ) \log (16-2 \log (x))+\left (-16+18 \log (x)-2 \log ^2(x)\right ) \log ^3(16-2 \log (x))\right ) \log \left (\frac {x^3+(-x-\log (x)) \log ^2(16-2 \log (x))}{x \log ^2(16-2 \log (x))}\right )}{\left (8 x^4-x^4 \log (x)\right ) \log (16-2 \log (x))+\left (-8 x^2+\left (-8 x+x^2\right ) \log (x)+x \log ^2(x)\right ) \log ^3(16-2 \log (x))} \, dx=\text {Timed out} \]
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Time = 12.97 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.32 \[ \int \frac {\left (4 x^3+\left (32 x^3-4 x^3 \log (x)\right ) \log (16-2 \log (x))+\left (-16+18 \log (x)-2 \log ^2(x)\right ) \log ^3(16-2 \log (x))\right ) \log \left (\frac {x^3+(-x-\log (x)) \log ^2(16-2 \log (x))}{x \log ^2(16-2 \log (x))}\right )}{\left (8 x^4-x^4 \log (x)\right ) \log (16-2 \log (x))+\left (-8 x^2+\left (-8 x+x^2\right ) \log (x)+x \log ^2(x)\right ) \log ^3(16-2 \log (x))} \, dx={\ln \left (-\frac {{\ln \left (16-2\,\ln \left (x\right )\right )}^2\,\left (x+\ln \left (x\right )\right )-x^3}{x\,{\ln \left (16-2\,\ln \left (x\right )\right )}^2}\right )}^2 \]
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