Integrand size = 261, antiderivative size = 28 \[ \int \frac {-10 x-5 x^2+\left (40 x+40 x^2\right ) \log (x)+(70+35 x) \log ^2(x)+20 x \log ^3(x)+\left (\left (-10 x-10 x^2\right ) \log (x)+(-20-10 x) \log ^2(x)-5 x \log ^3(x)\right ) \log (\log (x))}{\left (64 x^3+64 x^4+16 x^5\right ) \log (x)+\left (128 x^2+128 x^3+32 x^4\right ) \log ^3(x)+\left (64 x+64 x^2+16 x^3\right ) \log ^5(x)+\left (\left (-32 x^3-32 x^4-8 x^5\right ) \log (x)+\left (-64 x^2-64 x^3-16 x^4\right ) \log ^3(x)+\left (-32 x-32 x^2-8 x^3\right ) \log ^5(x)\right ) \log (\log (x))+\left (\left (4 x^3+4 x^4+x^5\right ) \log (x)+\left (8 x^2+8 x^3+2 x^4\right ) \log ^3(x)+\left (4 x+4 x^2+x^3\right ) \log ^5(x)\right ) \log ^2(\log (x))} \, dx=\frac {5}{2 \left (1+\frac {x}{2}\right ) \left (x+\log ^2(x)\right ) (-4+\log (\log (x)))} \]
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\[ \int \frac {-10 x-5 x^2+\left (40 x+40 x^2\right ) \log (x)+(70+35 x) \log ^2(x)+20 x \log ^3(x)+\left (\left (-10 x-10 x^2\right ) \log (x)+(-20-10 x) \log ^2(x)-5 x \log ^3(x)\right ) \log (\log (x))}{\left (64 x^3+64 x^4+16 x^5\right ) \log (x)+\left (128 x^2+128 x^3+32 x^4\right ) \log ^3(x)+\left (64 x+64 x^2+16 x^3\right ) \log ^5(x)+\left (\left (-32 x^3-32 x^4-8 x^5\right ) \log (x)+\left (-64 x^2-64 x^3-16 x^4\right ) \log ^3(x)+\left (-32 x-32 x^2-8 x^3\right ) \log ^5(x)\right ) \log (\log (x))+\left (\left (4 x^3+4 x^4+x^5\right ) \log (x)+\left (8 x^2+8 x^3+2 x^4\right ) \log ^3(x)+\left (4 x+4 x^2+x^3\right ) \log ^5(x)\right ) \log ^2(\log (x))} \, dx=\int \frac {-10 x-5 x^2+\left (40 x+40 x^2\right ) \log (x)+(70+35 x) \log ^2(x)+20 x \log ^3(x)+\left (\left (-10 x-10 x^2\right ) \log (x)+(-20-10 x) \log ^2(x)-5 x \log ^3(x)\right ) \log (\log (x))}{\left (64 x^3+64 x^4+16 x^5\right ) \log (x)+\left (128 x^2+128 x^3+32 x^4\right ) \log ^3(x)+\left (64 x+64 x^2+16 x^3\right ) \log ^5(x)+\left (\left (-32 x^3-32 x^4-8 x^5\right ) \log (x)+\left (-64 x^2-64 x^3-16 x^4\right ) \log ^3(x)+\left (-32 x-32 x^2-8 x^3\right ) \log ^5(x)\right ) \log (\log (x))+\left (\left (4 x^3+4 x^4+x^5\right ) \log (x)+\left (8 x^2+8 x^3+2 x^4\right ) \log ^3(x)+\left (4 x+4 x^2+x^3\right ) \log ^5(x)\right ) \log ^2(\log (x))} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {5 \left (-x (2+x)-2 x (1+x) \log (x) (-4+\log (\log (x)))-x \log ^3(x) (-4+\log (\log (x)))-(2+x) \log ^2(x) (-7+2 \log (\log (x)))\right )}{x (2+x)^2 \log (x) \left (x+\log ^2(x)\right )^2 (4-\log (\log (x)))^2} \, dx \\ & = 5 \int \frac {-x (2+x)-2 x (1+x) \log (x) (-4+\log (\log (x)))-x \log ^3(x) (-4+\log (\log (x)))-(2+x) \log ^2(x) (-7+2 \log (\log (x)))}{x (2+x)^2 \log (x) \left (x+\log ^2(x)\right )^2 (4-\log (\log (x)))^2} \, dx \\ & = 5 \int \left (-\frac {1}{x (2+x) \log (x) \left (x+\log ^2(x)\right ) (-4+\log (\log (x)))^2}+\frac {-2 x-2 x^2-4 \log (x)-2 x \log (x)-x \log ^2(x)}{x (2+x)^2 \left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))}\right ) \, dx \\ & = -\left (5 \int \frac {1}{x (2+x) \log (x) \left (x+\log ^2(x)\right ) (-4+\log (\log (x)))^2} \, dx\right )+5 \int \frac {-2 x-2 x^2-4 \log (x)-2 x \log (x)-x \log ^2(x)}{x (2+x)^2 \left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))} \, dx \\ & = -\left (5 \int \left (\frac {1}{2 x \log (x) \left (x+\log ^2(x)\right ) (-4+\log (\log (x)))^2}-\frac {1}{2 (2+x) \log (x) \left (x+\log ^2(x)\right ) (-4+\log (\log (x)))^2}\right ) \, dx\right )+5 \int \left (\frac {-2 x-2 x^2-4 \log (x)-2 x \log (x)-x \log ^2(x)}{4 x \left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))}+\frac {2 x+2 x^2+4 \log (x)+2 x \log (x)+x \log ^2(x)}{2 (2+x)^2 \left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))}+\frac {2 x+2 x^2+4 \log (x)+2 x \log (x)+x \log ^2(x)}{4 (2+x) \left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))}\right ) \, dx \\ & = \frac {5}{4} \int \frac {-2 x-2 x^2-4 \log (x)-2 x \log (x)-x \log ^2(x)}{x \left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))} \, dx+\frac {5}{4} \int \frac {2 x+2 x^2+4 \log (x)+2 x \log (x)+x \log ^2(x)}{(2+x) \left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))} \, dx-\frac {5}{2} \int \frac {1}{x \log (x) \left (x+\log ^2(x)\right ) (-4+\log (\log (x)))^2} \, dx+\frac {5}{2} \int \frac {1}{(2+x) \log (x) \left (x+\log ^2(x)\right ) (-4+\log (\log (x)))^2} \, dx+\frac {5}{2} \int \frac {2 x+2 x^2+4 \log (x)+2 x \log (x)+x \log ^2(x)}{(2+x)^2 \left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))} \, dx \\ & = \frac {5}{4} \int \left (-\frac {2}{\left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))}-\frac {2 x}{\left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))}-\frac {2 \log (x)}{\left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))}-\frac {4 \log (x)}{x \left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))}-\frac {\log ^2(x)}{\left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))}\right ) \, dx+\frac {5}{4} \int \left (\frac {2 x}{(2+x) \left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))}+\frac {2 x^2}{(2+x) \left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))}+\frac {4 \log (x)}{(2+x) \left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))}+\frac {2 x \log (x)}{(2+x) \left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))}+\frac {x \log ^2(x)}{(2+x) \left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))}\right ) \, dx+\frac {5}{2} \int \left (\frac {2 x}{(2+x)^2 \left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))}+\frac {2 x^2}{(2+x)^2 \left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))}+\frac {4 \log (x)}{(2+x)^2 \left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))}+\frac {2 x \log (x)}{(2+x)^2 \left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))}+\frac {x \log ^2(x)}{(2+x)^2 \left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))}\right ) \, dx-\frac {5}{2} \int \frac {1}{x \log (x) \left (x+\log ^2(x)\right ) (-4+\log (\log (x)))^2} \, dx+\frac {5}{2} \int \frac {1}{(2+x) \log (x) \left (x+\log ^2(x)\right ) (-4+\log (\log (x)))^2} \, dx \\ & = -\left (\frac {5}{4} \int \frac {\log ^2(x)}{\left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))} \, dx\right )+\frac {5}{4} \int \frac {x \log ^2(x)}{(2+x) \left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))} \, dx-\frac {5}{2} \int \frac {1}{x \log (x) \left (x+\log ^2(x)\right ) (-4+\log (\log (x)))^2} \, dx+\frac {5}{2} \int \frac {1}{(2+x) \log (x) \left (x+\log ^2(x)\right ) (-4+\log (\log (x)))^2} \, dx-\frac {5}{2} \int \frac {1}{\left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))} \, dx-\frac {5}{2} \int \frac {x}{\left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))} \, dx+\frac {5}{2} \int \frac {x}{(2+x) \left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))} \, dx+\frac {5}{2} \int \frac {x^2}{(2+x) \left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))} \, dx-\frac {5}{2} \int \frac {\log (x)}{\left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))} \, dx+\frac {5}{2} \int \frac {x \log (x)}{(2+x) \left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))} \, dx+\frac {5}{2} \int \frac {x \log ^2(x)}{(2+x)^2 \left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))} \, dx+5 \int \frac {x}{(2+x)^2 \left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))} \, dx+5 \int \frac {x^2}{(2+x)^2 \left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))} \, dx-5 \int \frac {\log (x)}{x \left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))} \, dx+5 \int \frac {x \log (x)}{(2+x)^2 \left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))} \, dx+5 \int \frac {\log (x)}{(2+x) \left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))} \, dx+10 \int \frac {\log (x)}{(2+x)^2 \left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))} \, dx \\ & = \frac {5}{4} \int \left (\frac {\log ^2(x)}{\left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))}-\frac {2 \log ^2(x)}{(2+x) \left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))}\right ) \, dx-\frac {5}{4} \int \frac {\log ^2(x)}{\left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))} \, dx+\frac {5}{2} \int \left (\frac {1}{\left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))}-\frac {2}{(2+x) \left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))}\right ) \, dx+\frac {5}{2} \int \left (-\frac {2}{\left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))}+\frac {x}{\left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))}+\frac {4}{(2+x) \left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))}\right ) \, dx+\frac {5}{2} \int \left (\frac {\log (x)}{\left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))}-\frac {2 \log (x)}{(2+x) \left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))}\right ) \, dx+\frac {5}{2} \int \left (-\frac {2 \log ^2(x)}{(2+x)^2 \left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))}+\frac {\log ^2(x)}{(2+x) \left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))}\right ) \, dx-\frac {5}{2} \int \frac {1}{x \log (x) \left (x+\log ^2(x)\right ) (-4+\log (\log (x)))^2} \, dx+\frac {5}{2} \int \frac {1}{(2+x) \log (x) \left (x+\log ^2(x)\right ) (-4+\log (\log (x)))^2} \, dx-\frac {5}{2} \int \frac {1}{\left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))} \, dx-\frac {5}{2} \int \frac {x}{\left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))} \, dx-\frac {5}{2} \int \frac {\log (x)}{\left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))} \, dx+5 \int \left (\frac {1}{\left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))}+\frac {4}{(2+x)^2 \left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))}-\frac {4}{(2+x) \left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))}\right ) \, dx+5 \int \left (-\frac {2}{(2+x)^2 \left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))}+\frac {1}{(2+x) \left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))}\right ) \, dx+5 \int \left (-\frac {2 \log (x)}{(2+x)^2 \left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))}+\frac {\log (x)}{(2+x) \left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))}\right ) \, dx-5 \int \frac {\log (x)}{x \left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))} \, dx+5 \int \frac {\log (x)}{(2+x) \left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))} \, dx+10 \int \frac {\log (x)}{(2+x)^2 \left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))} \, dx \\ & = -\left (\frac {5}{2} \int \frac {1}{x \log (x) \left (x+\log ^2(x)\right ) (-4+\log (\log (x)))^2} \, dx\right )+\frac {5}{2} \int \frac {1}{(2+x) \log (x) \left (x+\log ^2(x)\right ) (-4+\log (\log (x)))^2} \, dx-5 \int \frac {\log (x)}{x \left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))} \, dx+5 \int \frac {\log (x)}{(2+x) \left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))} \, dx-5 \int \frac {\log ^2(x)}{(2+x)^2 \left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))} \, dx-10 \int \frac {1}{(2+x)^2 \left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))} \, dx+10 \int \frac {1}{(2+x) \left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))} \, dx+20 \int \frac {1}{(2+x)^2 \left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))} \, dx-20 \int \frac {1}{(2+x) \left (x+\log ^2(x)\right )^2 (-4+\log (\log (x)))} \, dx \\ \end{align*}
Time = 0.53 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.79 \[ \int \frac {-10 x-5 x^2+\left (40 x+40 x^2\right ) \log (x)+(70+35 x) \log ^2(x)+20 x \log ^3(x)+\left (\left (-10 x-10 x^2\right ) \log (x)+(-20-10 x) \log ^2(x)-5 x \log ^3(x)\right ) \log (\log (x))}{\left (64 x^3+64 x^4+16 x^5\right ) \log (x)+\left (128 x^2+128 x^3+32 x^4\right ) \log ^3(x)+\left (64 x+64 x^2+16 x^3\right ) \log ^5(x)+\left (\left (-32 x^3-32 x^4-8 x^5\right ) \log (x)+\left (-64 x^2-64 x^3-16 x^4\right ) \log ^3(x)+\left (-32 x-32 x^2-8 x^3\right ) \log ^5(x)\right ) \log (\log (x))+\left (\left (4 x^3+4 x^4+x^5\right ) \log (x)+\left (8 x^2+8 x^3+2 x^4\right ) \log ^3(x)+\left (4 x+4 x^2+x^3\right ) \log ^5(x)\right ) \log ^2(\log (x))} \, dx=\frac {5}{(2+x) \left (x+\log ^2(x)\right ) (-4+\log (\log (x)))} \]
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Time = 13.24 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.11
method | result | size |
default | \(\frac {5}{\left (x \ln \left (x \right )^{2}+2 \ln \left (x \right )^{2}+x^{2}+2 x \right ) \left (\ln \left (\ln \left (x \right )\right )-4\right )}\) | \(31\) |
risch | \(\frac {5}{\left (x \ln \left (x \right )^{2}+2 \ln \left (x \right )^{2}+x^{2}+2 x \right ) \left (\ln \left (\ln \left (x \right )\right )-4\right )}\) | \(31\) |
parallelrisch | \(\frac {5}{\left (x \ln \left (x \right )^{2}+2 \ln \left (x \right )^{2}+x^{2}+2 x \right ) \left (\ln \left (\ln \left (x \right )\right )-4\right )}\) | \(31\) |
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Time = 0.25 (sec) , antiderivative size = 42, normalized size of antiderivative = 1.50 \[ \int \frac {-10 x-5 x^2+\left (40 x+40 x^2\right ) \log (x)+(70+35 x) \log ^2(x)+20 x \log ^3(x)+\left (\left (-10 x-10 x^2\right ) \log (x)+(-20-10 x) \log ^2(x)-5 x \log ^3(x)\right ) \log (\log (x))}{\left (64 x^3+64 x^4+16 x^5\right ) \log (x)+\left (128 x^2+128 x^3+32 x^4\right ) \log ^3(x)+\left (64 x+64 x^2+16 x^3\right ) \log ^5(x)+\left (\left (-32 x^3-32 x^4-8 x^5\right ) \log (x)+\left (-64 x^2-64 x^3-16 x^4\right ) \log ^3(x)+\left (-32 x-32 x^2-8 x^3\right ) \log ^5(x)\right ) \log (\log (x))+\left (\left (4 x^3+4 x^4+x^5\right ) \log (x)+\left (8 x^2+8 x^3+2 x^4\right ) \log ^3(x)+\left (4 x+4 x^2+x^3\right ) \log ^5(x)\right ) \log ^2(\log (x))} \, dx=-\frac {5}{4 \, {\left (x + 2\right )} \log \left (x\right )^{2} + 4 \, x^{2} - {\left ({\left (x + 2\right )} \log \left (x\right )^{2} + x^{2} + 2 \, x\right )} \log \left (\log \left (x\right )\right ) + 8 \, x} \]
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Leaf count of result is larger than twice the leaf count of optimal. 49 vs. \(2 (20) = 40\).
Time = 0.13 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.75 \[ \int \frac {-10 x-5 x^2+\left (40 x+40 x^2\right ) \log (x)+(70+35 x) \log ^2(x)+20 x \log ^3(x)+\left (\left (-10 x-10 x^2\right ) \log (x)+(-20-10 x) \log ^2(x)-5 x \log ^3(x)\right ) \log (\log (x))}{\left (64 x^3+64 x^4+16 x^5\right ) \log (x)+\left (128 x^2+128 x^3+32 x^4\right ) \log ^3(x)+\left (64 x+64 x^2+16 x^3\right ) \log ^5(x)+\left (\left (-32 x^3-32 x^4-8 x^5\right ) \log (x)+\left (-64 x^2-64 x^3-16 x^4\right ) \log ^3(x)+\left (-32 x-32 x^2-8 x^3\right ) \log ^5(x)\right ) \log (\log (x))+\left (\left (4 x^3+4 x^4+x^5\right ) \log (x)+\left (8 x^2+8 x^3+2 x^4\right ) \log ^3(x)+\left (4 x+4 x^2+x^3\right ) \log ^5(x)\right ) \log ^2(\log (x))} \, dx=\frac {5}{- 4 x^{2} - 4 x \log {\left (x \right )}^{2} - 8 x + \left (x^{2} + x \log {\left (x \right )}^{2} + 2 x + 2 \log {\left (x \right )}^{2}\right ) \log {\left (\log {\left (x \right )} \right )} - 8 \log {\left (x \right )}^{2}} \]
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Time = 0.28 (sec) , antiderivative size = 42, normalized size of antiderivative = 1.50 \[ \int \frac {-10 x-5 x^2+\left (40 x+40 x^2\right ) \log (x)+(70+35 x) \log ^2(x)+20 x \log ^3(x)+\left (\left (-10 x-10 x^2\right ) \log (x)+(-20-10 x) \log ^2(x)-5 x \log ^3(x)\right ) \log (\log (x))}{\left (64 x^3+64 x^4+16 x^5\right ) \log (x)+\left (128 x^2+128 x^3+32 x^4\right ) \log ^3(x)+\left (64 x+64 x^2+16 x^3\right ) \log ^5(x)+\left (\left (-32 x^3-32 x^4-8 x^5\right ) \log (x)+\left (-64 x^2-64 x^3-16 x^4\right ) \log ^3(x)+\left (-32 x-32 x^2-8 x^3\right ) \log ^5(x)\right ) \log (\log (x))+\left (\left (4 x^3+4 x^4+x^5\right ) \log (x)+\left (8 x^2+8 x^3+2 x^4\right ) \log ^3(x)+\left (4 x+4 x^2+x^3\right ) \log ^5(x)\right ) \log ^2(\log (x))} \, dx=-\frac {5}{4 \, {\left (x + 2\right )} \log \left (x\right )^{2} + 4 \, x^{2} - {\left ({\left (x + 2\right )} \log \left (x\right )^{2} + x^{2} + 2 \, x\right )} \log \left (\log \left (x\right )\right ) + 8 \, x} \]
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Leaf count of result is larger than twice the leaf count of optimal. 57 vs. \(2 (22) = 44\).
Time = 0.49 (sec) , antiderivative size = 57, normalized size of antiderivative = 2.04 \[ \int \frac {-10 x-5 x^2+\left (40 x+40 x^2\right ) \log (x)+(70+35 x) \log ^2(x)+20 x \log ^3(x)+\left (\left (-10 x-10 x^2\right ) \log (x)+(-20-10 x) \log ^2(x)-5 x \log ^3(x)\right ) \log (\log (x))}{\left (64 x^3+64 x^4+16 x^5\right ) \log (x)+\left (128 x^2+128 x^3+32 x^4\right ) \log ^3(x)+\left (64 x+64 x^2+16 x^3\right ) \log ^5(x)+\left (\left (-32 x^3-32 x^4-8 x^5\right ) \log (x)+\left (-64 x^2-64 x^3-16 x^4\right ) \log ^3(x)+\left (-32 x-32 x^2-8 x^3\right ) \log ^5(x)\right ) \log (\log (x))+\left (\left (4 x^3+4 x^4+x^5\right ) \log (x)+\left (8 x^2+8 x^3+2 x^4\right ) \log ^3(x)+\left (4 x+4 x^2+x^3\right ) \log ^5(x)\right ) \log ^2(\log (x))} \, dx=\frac {5}{x \log \left (x\right )^{2} \log \left (\log \left (x\right )\right ) - 4 \, x \log \left (x\right )^{2} + x^{2} \log \left (\log \left (x\right )\right ) + 2 \, \log \left (x\right )^{2} \log \left (\log \left (x\right )\right ) - 4 \, x^{2} - 8 \, \log \left (x\right )^{2} + 2 \, x \log \left (\log \left (x\right )\right ) - 8 \, x} \]
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Time = 9.68 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.79 \[ \int \frac {-10 x-5 x^2+\left (40 x+40 x^2\right ) \log (x)+(70+35 x) \log ^2(x)+20 x \log ^3(x)+\left (\left (-10 x-10 x^2\right ) \log (x)+(-20-10 x) \log ^2(x)-5 x \log ^3(x)\right ) \log (\log (x))}{\left (64 x^3+64 x^4+16 x^5\right ) \log (x)+\left (128 x^2+128 x^3+32 x^4\right ) \log ^3(x)+\left (64 x+64 x^2+16 x^3\right ) \log ^5(x)+\left (\left (-32 x^3-32 x^4-8 x^5\right ) \log (x)+\left (-64 x^2-64 x^3-16 x^4\right ) \log ^3(x)+\left (-32 x-32 x^2-8 x^3\right ) \log ^5(x)\right ) \log (\log (x))+\left (\left (4 x^3+4 x^4+x^5\right ) \log (x)+\left (8 x^2+8 x^3+2 x^4\right ) \log ^3(x)+\left (4 x+4 x^2+x^3\right ) \log ^5(x)\right ) \log ^2(\log (x))} \, dx=\frac {5}{\left ({\ln \left (x\right )}^2+x\right )\,\left (\ln \left (\ln \left (x\right )\right )-4\right )\,\left (x+2\right )} \]
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