Integrand size = 141, antiderivative size = 27 \[ \int \frac {24-6 x+\left (12+24 x-6 x^2\right ) \log \left (\frac {2}{x^2}\right )+(12-3 x) \log \left (\frac {2}{x^2}\right ) \log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )}{\left (-4 x^4+x^5\right ) \log \left (\frac {2}{x^2}\right )+\left (-8 x^3+2 x^4\right ) \log \left (\frac {2}{x^2}\right ) \log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )+\left (-4 x^2+x^3\right ) \log \left (\frac {2}{x^2}\right ) \log ^2\left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )} \, dx=\frac {3}{x \left (x+\log \left (\frac {x}{(4-x) \log \left (\frac {2}{x^2}\right )}\right )\right )} \]
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\[ \int \frac {24-6 x+\left (12+24 x-6 x^2\right ) \log \left (\frac {2}{x^2}\right )+(12-3 x) \log \left (\frac {2}{x^2}\right ) \log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )}{\left (-4 x^4+x^5\right ) \log \left (\frac {2}{x^2}\right )+\left (-8 x^3+2 x^4\right ) \log \left (\frac {2}{x^2}\right ) \log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )+\left (-4 x^2+x^3\right ) \log \left (\frac {2}{x^2}\right ) \log ^2\left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )} \, dx=\int \frac {24-6 x+\left (12+24 x-6 x^2\right ) \log \left (\frac {2}{x^2}\right )+(12-3 x) \log \left (\frac {2}{x^2}\right ) \log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )}{\left (-4 x^4+x^5\right ) \log \left (\frac {2}{x^2}\right )+\left (-8 x^3+2 x^4\right ) \log \left (\frac {2}{x^2}\right ) \log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )+\left (-4 x^2+x^3\right ) \log \left (\frac {2}{x^2}\right ) \log ^2\left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {3 \left (2 (-4+x)+\log \left (\frac {2}{x^2}\right ) \left (2 \left (-2-4 x+x^2\right )+(-4+x) \log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )\right )}{(4-x) x^2 \log \left (\frac {2}{x^2}\right ) \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2} \, dx \\ & = 3 \int \frac {2 (-4+x)+\log \left (\frac {2}{x^2}\right ) \left (2 \left (-2-4 x+x^2\right )+(-4+x) \log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )}{(4-x) x^2 \log \left (\frac {2}{x^2}\right ) \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2} \, dx \\ & = 3 \int \left (\frac {8-2 x+4 \log \left (\frac {2}{x^2}\right )+4 x \log \left (\frac {2}{x^2}\right )-x^2 \log \left (\frac {2}{x^2}\right )}{(-4+x) x^2 \log \left (\frac {2}{x^2}\right ) \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2}-\frac {1}{x^2 \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )}\right ) \, dx \\ & = 3 \int \frac {8-2 x+4 \log \left (\frac {2}{x^2}\right )+4 x \log \left (\frac {2}{x^2}\right )-x^2 \log \left (\frac {2}{x^2}\right )}{(-4+x) x^2 \log \left (\frac {2}{x^2}\right ) \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2} \, dx-3 \int \frac {1}{x^2 \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )} \, dx \\ & = -\left (3 \int \frac {1}{x^2 \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )} \, dx\right )+3 \int \left (\frac {8-2 x+4 \log \left (\frac {2}{x^2}\right )+4 x \log \left (\frac {2}{x^2}\right )-x^2 \log \left (\frac {2}{x^2}\right )}{16 (-4+x) \log \left (\frac {2}{x^2}\right ) \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2}+\frac {-8+2 x-4 \log \left (\frac {2}{x^2}\right )-4 x \log \left (\frac {2}{x^2}\right )+x^2 \log \left (\frac {2}{x^2}\right )}{4 x^2 \log \left (\frac {2}{x^2}\right ) \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2}+\frac {-8+2 x-4 \log \left (\frac {2}{x^2}\right )-4 x \log \left (\frac {2}{x^2}\right )+x^2 \log \left (\frac {2}{x^2}\right )}{16 x \log \left (\frac {2}{x^2}\right ) \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2}\right ) \, dx \\ & = \frac {3}{16} \int \frac {8-2 x+4 \log \left (\frac {2}{x^2}\right )+4 x \log \left (\frac {2}{x^2}\right )-x^2 \log \left (\frac {2}{x^2}\right )}{(-4+x) \log \left (\frac {2}{x^2}\right ) \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2} \, dx+\frac {3}{16} \int \frac {-8+2 x-4 \log \left (\frac {2}{x^2}\right )-4 x \log \left (\frac {2}{x^2}\right )+x^2 \log \left (\frac {2}{x^2}\right )}{x \log \left (\frac {2}{x^2}\right ) \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2} \, dx+\frac {3}{4} \int \frac {-8+2 x-4 \log \left (\frac {2}{x^2}\right )-4 x \log \left (\frac {2}{x^2}\right )+x^2 \log \left (\frac {2}{x^2}\right )}{x^2 \log \left (\frac {2}{x^2}\right ) \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2} \, dx-3 \int \frac {1}{x^2 \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )} \, dx \\ & = \frac {3}{16} \int \frac {2 (-4+x)+\left (-4-4 x+x^2\right ) \log \left (\frac {2}{x^2}\right )}{x \log \left (\frac {2}{x^2}\right ) \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2} \, dx+\frac {3}{16} \int \left (\frac {4}{(-4+x) \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2}+\frac {4 x}{(-4+x) \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2}-\frac {x^2}{(-4+x) \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2}+\frac {8}{(-4+x) \log \left (\frac {2}{x^2}\right ) \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2}-\frac {2 x}{(-4+x) \log \left (\frac {2}{x^2}\right ) \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2}\right ) \, dx+\frac {3}{4} \int \frac {2 (-4+x)+\left (-4-4 x+x^2\right ) \log \left (\frac {2}{x^2}\right )}{x^2 \log \left (\frac {2}{x^2}\right ) \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2} \, dx-3 \int \frac {1}{x^2 \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )} \, dx \\ & = -\left (\frac {3}{16} \int \frac {x^2}{(-4+x) \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2} \, dx\right )+\frac {3}{16} \int \left (-\frac {4}{\left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2}-\frac {4}{x \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2}+\frac {x}{\left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2}+\frac {2}{\log \left (\frac {2}{x^2}\right ) \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2}-\frac {8}{x \log \left (\frac {2}{x^2}\right ) \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2}\right ) \, dx-\frac {3}{8} \int \frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right ) \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2} \, dx+\frac {3}{4} \int \frac {1}{(-4+x) \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2} \, dx+\frac {3}{4} \int \frac {x}{(-4+x) \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2} \, dx+\frac {3}{4} \int \left (\frac {1}{\left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2}-\frac {4}{x^2 \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2}-\frac {4}{x \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2}-\frac {8}{x^2 \log \left (\frac {2}{x^2}\right ) \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2}+\frac {2}{x \log \left (\frac {2}{x^2}\right ) \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2}\right ) \, dx+\frac {3}{2} \int \frac {1}{(-4+x) \log \left (\frac {2}{x^2}\right ) \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2} \, dx-3 \int \frac {1}{x^2 \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )} \, dx \\ & = \frac {3}{16} \int \frac {x}{\left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2} \, dx-\frac {3}{16} \int \left (\frac {4}{\left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2}+\frac {16}{(-4+x) \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2}+\frac {x}{\left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2}\right ) \, dx+\frac {3}{8} \int \frac {1}{\log \left (\frac {2}{x^2}\right ) \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2} \, dx-\frac {3}{8} \int \left (\frac {1}{\log \left (\frac {2}{x^2}\right ) \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2}+\frac {4}{(-4+x) \log \left (\frac {2}{x^2}\right ) \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2}\right ) \, dx+\frac {3}{4} \int \frac {1}{(-4+x) \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2} \, dx-\frac {3}{4} \int \frac {1}{x \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2} \, dx+\frac {3}{4} \int \left (\frac {1}{\left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2}+\frac {4}{(-4+x) \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2}\right ) \, dx+\frac {3}{2} \int \frac {1}{(-4+x) \log \left (\frac {2}{x^2}\right ) \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2} \, dx-3 \int \frac {1}{x^2 \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2} \, dx-3 \int \frac {1}{x \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2} \, dx-3 \int \frac {1}{x^2 \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )} \, dx-6 \int \frac {1}{x^2 \log \left (\frac {2}{x^2}\right ) \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2} \, dx \\ & = \frac {3}{4} \int \frac {1}{(-4+x) \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2} \, dx-\frac {3}{4} \int \frac {1}{x \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2} \, dx-3 \int \frac {1}{x^2 \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2} \, dx-3 \int \frac {1}{x \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2} \, dx-3 \int \frac {1}{x^2 \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )} \, dx-6 \int \frac {1}{x^2 \log \left (\frac {2}{x^2}\right ) \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )^2} \, dx \\ \end{align*}
Time = 0.13 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.96 \[ \int \frac {24-6 x+\left (12+24 x-6 x^2\right ) \log \left (\frac {2}{x^2}\right )+(12-3 x) \log \left (\frac {2}{x^2}\right ) \log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )}{\left (-4 x^4+x^5\right ) \log \left (\frac {2}{x^2}\right )+\left (-8 x^3+2 x^4\right ) \log \left (\frac {2}{x^2}\right ) \log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )+\left (-4 x^2+x^3\right ) \log \left (\frac {2}{x^2}\right ) \log ^2\left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )} \, dx=\frac {3}{x \left (x+\log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )\right )} \]
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Time = 1.66 (sec) , antiderivative size = 54, normalized size of antiderivative = 2.00
method | result | size |
parallelrisch | \(\frac {48-3 x^{2}-3 \ln \left (-\frac {x}{\left (x -4\right ) \ln \left (\frac {2}{x^{2}}\right )}\right ) x}{16 x \left (\ln \left (-\frac {x}{\left (x -4\right ) \ln \left (\frac {2}{x^{2}}\right )}\right )+x \right )}\) | \(54\) |
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Time = 0.24 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.00 \[ \int \frac {24-6 x+\left (12+24 x-6 x^2\right ) \log \left (\frac {2}{x^2}\right )+(12-3 x) \log \left (\frac {2}{x^2}\right ) \log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )}{\left (-4 x^4+x^5\right ) \log \left (\frac {2}{x^2}\right )+\left (-8 x^3+2 x^4\right ) \log \left (\frac {2}{x^2}\right ) \log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )+\left (-4 x^2+x^3\right ) \log \left (\frac {2}{x^2}\right ) \log ^2\left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )} \, dx=\frac {3}{x^{2} + x \log \left (-\frac {x}{{\left (x - 4\right )} \log \left (\frac {2}{x^{2}}\right )}\right )} \]
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Time = 0.15 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.74 \[ \int \frac {24-6 x+\left (12+24 x-6 x^2\right ) \log \left (\frac {2}{x^2}\right )+(12-3 x) \log \left (\frac {2}{x^2}\right ) \log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )}{\left (-4 x^4+x^5\right ) \log \left (\frac {2}{x^2}\right )+\left (-8 x^3+2 x^4\right ) \log \left (\frac {2}{x^2}\right ) \log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )+\left (-4 x^2+x^3\right ) \log \left (\frac {2}{x^2}\right ) \log ^2\left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )} \, dx=\frac {3}{x^{2} + x \log {\left (- \frac {x}{\left (x - 4\right ) \log {\left (\frac {2}{x^{2}} \right )}} \right )}} \]
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Time = 0.35 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.19 \[ \int \frac {24-6 x+\left (12+24 x-6 x^2\right ) \log \left (\frac {2}{x^2}\right )+(12-3 x) \log \left (\frac {2}{x^2}\right ) \log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )}{\left (-4 x^4+x^5\right ) \log \left (\frac {2}{x^2}\right )+\left (-8 x^3+2 x^4\right ) \log \left (\frac {2}{x^2}\right ) \log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )+\left (-4 x^2+x^3\right ) \log \left (\frac {2}{x^2}\right ) \log ^2\left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )} \, dx=\frac {3}{x^{2} - x \log \left (x - 4\right ) + x \log \left (x\right ) - x \log \left (-\log \left (2\right ) + 2 \, \log \left (x\right )\right )} \]
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Result contains complex when optimal does not.
Time = 2.45 (sec) , antiderivative size = 699, normalized size of antiderivative = 25.89 \[ \int \frac {24-6 x+\left (12+24 x-6 x^2\right ) \log \left (\frac {2}{x^2}\right )+(12-3 x) \log \left (\frac {2}{x^2}\right ) \log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )}{\left (-4 x^4+x^5\right ) \log \left (\frac {2}{x^2}\right )+\left (-8 x^3+2 x^4\right ) \log \left (\frac {2}{x^2}\right ) \log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )+\left (-4 x^2+x^3\right ) \log \left (\frac {2}{x^2}\right ) \log ^2\left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )} \, dx=\text {Too large to display} \]
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Timed out. \[ \int \frac {24-6 x+\left (12+24 x-6 x^2\right ) \log \left (\frac {2}{x^2}\right )+(12-3 x) \log \left (\frac {2}{x^2}\right ) \log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )}{\left (-4 x^4+x^5\right ) \log \left (\frac {2}{x^2}\right )+\left (-8 x^3+2 x^4\right ) \log \left (\frac {2}{x^2}\right ) \log \left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )+\left (-4 x^2+x^3\right ) \log \left (\frac {2}{x^2}\right ) \log ^2\left (-\frac {x}{(-4+x) \log \left (\frac {2}{x^2}\right )}\right )} \, dx=\int \frac {6\,x-\ln \left (\frac {2}{x^2}\right )\,\left (-6\,x^2+24\,x+12\right )+\ln \left (-\frac {x}{\ln \left (\frac {2}{x^2}\right )\,\left (x-4\right )}\right )\,\ln \left (\frac {2}{x^2}\right )\,\left (3\,x-12\right )-24}{\ln \left (\frac {2}{x^2}\right )\,\left (4\,x^2-x^3\right )\,{\ln \left (-\frac {x}{\ln \left (\frac {2}{x^2}\right )\,\left (x-4\right )}\right )}^2+\ln \left (\frac {2}{x^2}\right )\,\left (8\,x^3-2\,x^4\right )\,\ln \left (-\frac {x}{\ln \left (\frac {2}{x^2}\right )\,\left (x-4\right )}\right )+\ln \left (\frac {2}{x^2}\right )\,\left (4\,x^4-x^5\right )} \,d x \]
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