Integrand size = 140, antiderivative size = 24 \[ \int \frac {15-8 \log \left (x^2\right )+\log ^2\left (x^2\right )+\left (-64+128 x-64 x^2+\left (16-32 x+16 x^2\right ) \log \left (x^2\right )\right ) \log ^3\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )+\left (-30 x+30 x^2+\left (16 x-16 x^2\right ) \log \left (x^2\right )+\left (-2 x+2 x^2\right ) \log ^2\left (x^2\right )\right ) \log ^4\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )}{15 x-8 x \log \left (x^2\right )+x \log ^2\left (x^2\right )} \, dx=\log (x)+(-1+x)^2 \log ^4\left (1-\left (-4+\log \left (x^2\right )\right )^2\right ) \]
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\[ \int \frac {15-8 \log \left (x^2\right )+\log ^2\left (x^2\right )+\left (-64+128 x-64 x^2+\left (16-32 x+16 x^2\right ) \log \left (x^2\right )\right ) \log ^3\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )+\left (-30 x+30 x^2+\left (16 x-16 x^2\right ) \log \left (x^2\right )+\left (-2 x+2 x^2\right ) \log ^2\left (x^2\right )\right ) \log ^4\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )}{15 x-8 x \log \left (x^2\right )+x \log ^2\left (x^2\right )} \, dx=\int \frac {15-8 \log \left (x^2\right )+\log ^2\left (x^2\right )+\left (-64+128 x-64 x^2+\left (16-32 x+16 x^2\right ) \log \left (x^2\right )\right ) \log ^3\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )+\left (-30 x+30 x^2+\left (16 x-16 x^2\right ) \log \left (x^2\right )+\left (-2 x+2 x^2\right ) \log ^2\left (x^2\right )\right ) \log ^4\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )}{15 x-8 x \log \left (x^2\right )+x \log ^2\left (x^2\right )} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {1}{x}+\frac {16 (-1+x)^2 \left (-4+\log \left (x^2\right )\right ) \log ^3\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )}{x \left (-5+\log \left (x^2\right )\right ) \left (-3+\log \left (x^2\right )\right )}+2 (-1+x) \log ^4\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )\right ) \, dx \\ & = \log (x)+2 \int (-1+x) \log ^4\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right ) \, dx+16 \int \frac {(-1+x)^2 \left (-4+\log \left (x^2\right )\right ) \log ^3\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )}{x \left (-5+\log \left (x^2\right )\right ) \left (-3+\log \left (x^2\right )\right )} \, dx \\ & = \log (x)+2 \int \left (-\log ^4\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )+x \log ^4\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )\right ) \, dx+16 \int \left (-\frac {2 \left (-4+\log \left (x^2\right )\right ) \log ^3\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )}{\left (-5+\log \left (x^2\right )\right ) \left (-3+\log \left (x^2\right )\right )}+\frac {\left (-4+\log \left (x^2\right )\right ) \log ^3\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )}{x \left (-5+\log \left (x^2\right )\right ) \left (-3+\log \left (x^2\right )\right )}+\frac {x \left (-4+\log \left (x^2\right )\right ) \log ^3\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )}{\left (-5+\log \left (x^2\right )\right ) \left (-3+\log \left (x^2\right )\right )}\right ) \, dx \\ & = \log (x)-2 \int \log ^4\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right ) \, dx+2 \int x \log ^4\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right ) \, dx+16 \int \frac {\left (-4+\log \left (x^2\right )\right ) \log ^3\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )}{x \left (-5+\log \left (x^2\right )\right ) \left (-3+\log \left (x^2\right )\right )} \, dx+16 \int \frac {x \left (-4+\log \left (x^2\right )\right ) \log ^3\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )}{\left (-5+\log \left (x^2\right )\right ) \left (-3+\log \left (x^2\right )\right )} \, dx-32 \int \frac {\left (-4+\log \left (x^2\right )\right ) \log ^3\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )}{\left (-5+\log \left (x^2\right )\right ) \left (-3+\log \left (x^2\right )\right )} \, dx \\ & = \log (x)-2 \int \log ^4\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right ) \, dx+8 \text {Subst}\left (\int \frac {(-4+x) \log ^3\left (-15+8 x-x^2\right )}{(-5+x) (-3+x)} \, dx,x,\log \left (x^2\right )\right )+8 \text {Subst}\left (\int \frac {(-4+\log (x)) \log ^3\left (-15+8 \log (x)-\log ^2(x)\right )}{(-5+\log (x)) (-3+\log (x))} \, dx,x,x^2\right )-32 \int \left (-\frac {4 \log ^3\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )}{15-8 \log \left (x^2\right )+\log ^2\left (x^2\right )}+\frac {\log \left (x^2\right ) \log ^3\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )}{15-8 \log \left (x^2\right )+\log ^2\left (x^2\right )}\right ) \, dx+\text {Subst}\left (\int \log ^4\left (-15+8 \log (x)-\log ^2(x)\right ) \, dx,x,x^2\right ) \\ & = \log (x)-2 \int \log ^4\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right ) \, dx+8 \text {Subst}\left (\int \left (\frac {\log ^3\left (-15+8 x-x^2\right )}{2 (-5+x)}+\frac {\log ^3\left (-15+8 x-x^2\right )}{2 (-3+x)}\right ) \, dx,x,\log \left (x^2\right )\right )+8 \text {Subst}\left (\int \left (-\frac {4 \log ^3\left (-15+8 \log (x)-\log ^2(x)\right )}{15-8 \log (x)+\log ^2(x)}+\frac {\log (x) \log ^3\left (-15+8 \log (x)-\log ^2(x)\right )}{15-8 \log (x)+\log ^2(x)}\right ) \, dx,x,x^2\right )-32 \int \frac {\log \left (x^2\right ) \log ^3\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )}{15-8 \log \left (x^2\right )+\log ^2\left (x^2\right )} \, dx+128 \int \frac {\log ^3\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )}{15-8 \log \left (x^2\right )+\log ^2\left (x^2\right )} \, dx+\text {Subst}\left (\int \log ^4\left (-15+8 \log (x)-\log ^2(x)\right ) \, dx,x,x^2\right ) \\ & = \log (x)-2 \int \log ^4\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right ) \, dx+4 \text {Subst}\left (\int \frac {\log ^3\left (-15+8 x-x^2\right )}{-5+x} \, dx,x,\log \left (x^2\right )\right )+4 \text {Subst}\left (\int \frac {\log ^3\left (-15+8 x-x^2\right )}{-3+x} \, dx,x,\log \left (x^2\right )\right )+8 \text {Subst}\left (\int \frac {\log (x) \log ^3\left (-15+8 \log (x)-\log ^2(x)\right )}{15-8 \log (x)+\log ^2(x)} \, dx,x,x^2\right )-32 \int \frac {\log \left (x^2\right ) \log ^3\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )}{15-8 \log \left (x^2\right )+\log ^2\left (x^2\right )} \, dx-32 \text {Subst}\left (\int \frac {\log ^3\left (-15+8 \log (x)-\log ^2(x)\right )}{15-8 \log (x)+\log ^2(x)} \, dx,x,x^2\right )+128 \int \frac {\log ^3\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )}{15-8 \log \left (x^2\right )+\log ^2\left (x^2\right )} \, dx+\text {Subst}\left (\int \log ^4\left (-15+8 \log (x)-\log ^2(x)\right ) \, dx,x,x^2\right ) \\ & = \log (x)+4 \log \left (-5+\log \left (x^2\right )\right ) \log ^3\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )+4 \log \left (-3+\log \left (x^2\right )\right ) \log ^3\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )-2 \int \log ^4\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right ) \, dx+8 \text {Subst}\left (\int \frac {\log (x) \log ^3\left (-15+8 \log (x)-\log ^2(x)\right )}{15-8 \log (x)+\log ^2(x)} \, dx,x,x^2\right )-12 \text {Subst}\left (\int \frac {(8-2 x) \log (-5+x) \log ^2\left (-15+8 x-x^2\right )}{-15+8 x-x^2} \, dx,x,\log \left (x^2\right )\right )-12 \text {Subst}\left (\int \frac {(8-2 x) \log (-3+x) \log ^2\left (-15+8 x-x^2\right )}{-15+8 x-x^2} \, dx,x,\log \left (x^2\right )\right )-32 \int \frac {\log \left (x^2\right ) \log ^3\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )}{15-8 \log \left (x^2\right )+\log ^2\left (x^2\right )} \, dx-32 \text {Subst}\left (\int \frac {\log ^3\left (-15+8 \log (x)-\log ^2(x)\right )}{15-8 \log (x)+\log ^2(x)} \, dx,x,x^2\right )+128 \int \frac {\log ^3\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )}{15-8 \log \left (x^2\right )+\log ^2\left (x^2\right )} \, dx+\text {Subst}\left (\int \log ^4\left (-15+8 \log (x)-\log ^2(x)\right ) \, dx,x,x^2\right ) \\ & = \log (x)+4 \log \left (-5+\log \left (x^2\right )\right ) \log ^3\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )+4 \log \left (-3+\log \left (x^2\right )\right ) \log ^3\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )-2 \int \log ^4\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right ) \, dx+8 \text {Subst}\left (\int \frac {\log (x) \log ^3\left (-15+8 \log (x)-\log ^2(x)\right )}{15-8 \log (x)+\log ^2(x)} \, dx,x,x^2\right )-12 \text {Subst}\left (\int \left (\frac {\log (-5+x) \log ^2\left (-15+8 x-x^2\right )}{-5+x}+\frac {\log (-5+x) \log ^2\left (-15+8 x-x^2\right )}{-3+x}\right ) \, dx,x,\log \left (x^2\right )\right )-12 \text {Subst}\left (\int \left (\frac {\log (-3+x) \log ^2\left (-15+8 x-x^2\right )}{-5+x}+\frac {\log (-3+x) \log ^2\left (-15+8 x-x^2\right )}{-3+x}\right ) \, dx,x,\log \left (x^2\right )\right )-32 \int \frac {\log \left (x^2\right ) \log ^3\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )}{15-8 \log \left (x^2\right )+\log ^2\left (x^2\right )} \, dx-32 \text {Subst}\left (\int \frac {\log ^3\left (-15+8 \log (x)-\log ^2(x)\right )}{15-8 \log (x)+\log ^2(x)} \, dx,x,x^2\right )+128 \int \frac {\log ^3\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )}{15-8 \log \left (x^2\right )+\log ^2\left (x^2\right )} \, dx+\text {Subst}\left (\int \log ^4\left (-15+8 \log (x)-\log ^2(x)\right ) \, dx,x,x^2\right ) \\ & = \log (x)+4 \log \left (-5+\log \left (x^2\right )\right ) \log ^3\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )+4 \log \left (-3+\log \left (x^2\right )\right ) \log ^3\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )-2 \int \log ^4\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right ) \, dx+8 \text {Subst}\left (\int \frac {\log (x) \log ^3\left (-15+8 \log (x)-\log ^2(x)\right )}{15-8 \log (x)+\log ^2(x)} \, dx,x,x^2\right )-12 \text {Subst}\left (\int \frac {\log (-5+x) \log ^2\left (-15+8 x-x^2\right )}{-5+x} \, dx,x,\log \left (x^2\right )\right )-12 \text {Subst}\left (\int \frac {\log (-5+x) \log ^2\left (-15+8 x-x^2\right )}{-3+x} \, dx,x,\log \left (x^2\right )\right )-12 \text {Subst}\left (\int \frac {\log (-3+x) \log ^2\left (-15+8 x-x^2\right )}{-5+x} \, dx,x,\log \left (x^2\right )\right )-12 \text {Subst}\left (\int \frac {\log (-3+x) \log ^2\left (-15+8 x-x^2\right )}{-3+x} \, dx,x,\log \left (x^2\right )\right )-32 \int \frac {\log \left (x^2\right ) \log ^3\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )}{15-8 \log \left (x^2\right )+\log ^2\left (x^2\right )} \, dx-32 \text {Subst}\left (\int \frac {\log ^3\left (-15+8 \log (x)-\log ^2(x)\right )}{15-8 \log (x)+\log ^2(x)} \, dx,x,x^2\right )+128 \int \frac {\log ^3\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )}{15-8 \log \left (x^2\right )+\log ^2\left (x^2\right )} \, dx+\text {Subst}\left (\int \log ^4\left (-15+8 \log (x)-\log ^2(x)\right ) \, dx,x,x^2\right ) \\ \end{align*}
Time = 0.07 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.17 \[ \int \frac {15-8 \log \left (x^2\right )+\log ^2\left (x^2\right )+\left (-64+128 x-64 x^2+\left (16-32 x+16 x^2\right ) \log \left (x^2\right )\right ) \log ^3\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )+\left (-30 x+30 x^2+\left (16 x-16 x^2\right ) \log \left (x^2\right )+\left (-2 x+2 x^2\right ) \log ^2\left (x^2\right )\right ) \log ^4\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )}{15 x-8 x \log \left (x^2\right )+x \log ^2\left (x^2\right )} \, dx=\log (x)+(-1+x)^2 \log ^4\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. \(67\) vs. \(2(24)=48\).
Time = 1.64 (sec) , antiderivative size = 68, normalized size of antiderivative = 2.83
method | result | size |
parallelrisch | \({\ln \left (-\ln \left (x^{2}\right )^{2}+8 \ln \left (x^{2}\right )-15\right )}^{4} x^{2}-2 x {\ln \left (-\ln \left (x^{2}\right )^{2}+8 \ln \left (x^{2}\right )-15\right )}^{4}+{\ln \left (-\ln \left (x^{2}\right )^{2}+8 \ln \left (x^{2}\right )-15\right )}^{4}+\ln \left (x \right )\) | \(68\) |
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Time = 0.25 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.46 \[ \int \frac {15-8 \log \left (x^2\right )+\log ^2\left (x^2\right )+\left (-64+128 x-64 x^2+\left (16-32 x+16 x^2\right ) \log \left (x^2\right )\right ) \log ^3\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )+\left (-30 x+30 x^2+\left (16 x-16 x^2\right ) \log \left (x^2\right )+\left (-2 x+2 x^2\right ) \log ^2\left (x^2\right )\right ) \log ^4\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )}{15 x-8 x \log \left (x^2\right )+x \log ^2\left (x^2\right )} \, dx={\left (x^{2} - 2 \, x + 1\right )} \log \left (-\log \left (x^{2}\right )^{2} + 8 \, \log \left (x^{2}\right ) - 15\right )^{4} + \frac {1}{2} \, \log \left (x^{2}\right ) \]
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Time = 0.21 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.21 \[ \int \frac {15-8 \log \left (x^2\right )+\log ^2\left (x^2\right )+\left (-64+128 x-64 x^2+\left (16-32 x+16 x^2\right ) \log \left (x^2\right )\right ) \log ^3\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )+\left (-30 x+30 x^2+\left (16 x-16 x^2\right ) \log \left (x^2\right )+\left (-2 x+2 x^2\right ) \log ^2\left (x^2\right )\right ) \log ^4\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )}{15 x-8 x \log \left (x^2\right )+x \log ^2\left (x^2\right )} \, dx=\left (x^{2} - 2 x + 1\right ) \log {\left (- \log {\left (x^{2} \right )}^{2} + 8 \log {\left (x^{2} \right )} - 15 \right )}^{4} + \log {\left (x \right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 284 vs. \(2 (24) = 48\).
Time = 0.39 (sec) , antiderivative size = 284, normalized size of antiderivative = 11.83 \[ \int \frac {15-8 \log \left (x^2\right )+\log ^2\left (x^2\right )+\left (-64+128 x-64 x^2+\left (16-32 x+16 x^2\right ) \log \left (x^2\right )\right ) \log ^3\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )+\left (-30 x+30 x^2+\left (16 x-16 x^2\right ) \log \left (x^2\right )+\left (-2 x+2 x^2\right ) \log ^2\left (x^2\right )\right ) \log ^4\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )}{15 x-8 x \log \left (x^2\right )+x \log ^2\left (x^2\right )} \, dx={\left (x^{2} - 2 \, x + 1\right )} \log \left (2 \, \log \left (x\right ) - 3\right )^{4} + 4 \, {\left (x^{2} - 2 \, x + 1\right )} \log \left (2 \, \log \left (x\right ) - 3\right )^{3} \log \left (-2 \, \log \left (x\right ) + 5\right ) + 6 \, {\left (x^{2} - 2 \, x + 1\right )} \log \left (2 \, \log \left (x\right ) - 3\right )^{2} \log \left (-2 \, \log \left (x\right ) + 5\right )^{2} + 4 \, {\left (x^{2} - 2 \, x + 1\right )} \log \left (2 \, \log \left (x\right ) - 3\right ) \log \left (-2 \, \log \left (x\right ) + 5\right )^{3} + {\left (x^{2} - 2 \, x + 1\right )} \log \left (-2 \, \log \left (x\right ) + 5\right )^{4} - \frac {1}{4} \, {\left (\log \left (\log \left (x\right ) - \frac {3}{2}\right ) - \log \left (\log \left (x\right ) - \frac {5}{2}\right )\right )} \log \left (x^{2}\right )^{2} + \frac {1}{2} \, {\left ({\left (2 \, \log \left (x\right ) - 3\right )} \log \left (\log \left (x\right ) - \frac {3}{2}\right ) - {\left (2 \, \log \left (x\right ) - 5\right )} \log \left (\log \left (x\right ) - \frac {5}{2}\right ) - 2\right )} \log \left (x^{2}\right ) + 2 \, {\left (\log \left (\log \left (x\right ) - \frac {3}{2}\right ) - \log \left (\log \left (x\right ) - \frac {5}{2}\right )\right )} \log \left (x^{2}\right ) - {\left (\log \left (x\right )^{2} - 3 \, \log \left (x\right )\right )} \log \left (\log \left (x\right ) - \frac {3}{2}\right ) - 2 \, {\left (2 \, \log \left (x\right ) - 3\right )} \log \left (\log \left (x\right ) - \frac {3}{2}\right ) + {\left (\log \left (x\right )^{2} - 5 \, \log \left (x\right )\right )} \log \left (\log \left (x\right ) - \frac {5}{2}\right ) + 2 \, {\left (2 \, \log \left (x\right ) - 5\right )} \log \left (\log \left (x\right ) - \frac {5}{2}\right ) + 3 \, \log \left (x\right ) - \frac {9}{4} \, \log \left (2 \, \log \left (x\right ) - 3\right ) + \frac {25}{4} \, \log \left (2 \, \log \left (x\right ) - 5\right ) - \frac {15}{4} \, \log \left (\log \left (x\right ) - \frac {3}{2}\right ) + \frac {15}{4} \, \log \left (\log \left (x\right ) - \frac {5}{2}\right ) + 4 \]
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Time = 1.73 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.29 \[ \int \frac {15-8 \log \left (x^2\right )+\log ^2\left (x^2\right )+\left (-64+128 x-64 x^2+\left (16-32 x+16 x^2\right ) \log \left (x^2\right )\right ) \log ^3\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )+\left (-30 x+30 x^2+\left (16 x-16 x^2\right ) \log \left (x^2\right )+\left (-2 x+2 x^2\right ) \log ^2\left (x^2\right )\right ) \log ^4\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )}{15 x-8 x \log \left (x^2\right )+x \log ^2\left (x^2\right )} \, dx={\left (x^{2} - 2 \, x + 1\right )} \log \left (-\log \left (x^{2}\right )^{2} + 8 \, \log \left (x^{2}\right ) - 15\right )^{4} + \log \left (x\right ) \]
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Time = 9.15 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.21 \[ \int \frac {15-8 \log \left (x^2\right )+\log ^2\left (x^2\right )+\left (-64+128 x-64 x^2+\left (16-32 x+16 x^2\right ) \log \left (x^2\right )\right ) \log ^3\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )+\left (-30 x+30 x^2+\left (16 x-16 x^2\right ) \log \left (x^2\right )+\left (-2 x+2 x^2\right ) \log ^2\left (x^2\right )\right ) \log ^4\left (-15+8 \log \left (x^2\right )-\log ^2\left (x^2\right )\right )}{15 x-8 x \log \left (x^2\right )+x \log ^2\left (x^2\right )} \, dx=\left (x^2-2\,x+1\right )\,{\ln \left (\ln \left (x^{16}\right )-{\ln \left (x^2\right )}^2-15\right )}^4+\ln \left (x\right ) \]
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