Integrand size = 188, antiderivative size = 28 \[ \int \frac {-8+\left (-x-2 x^2\right ) \log \left (\frac {1}{2} \left (4 x^2-x^2 \log (3)\right )\right ) \log ^2\left (\log \left (\frac {1}{2} \left (4 x^2-x^2 \log (3)\right )\right )\right )}{16 x \log \left (\frac {1}{2} \left (4 x^2-x^2 \log (3)\right )\right )+\left (-8 x-8 x^2-8 x^3\right ) \log \left (\frac {1}{2} \left (4 x^2-x^2 \log (3)\right )\right ) \log \left (\log \left (\frac {1}{2} \left (4 x^2-x^2 \log (3)\right )\right )\right )+\left (x+2 x^2+3 x^3+2 x^4+x^5\right ) \log \left (\frac {1}{2} \left (4 x^2-x^2 \log (3)\right )\right ) \log ^2\left (\log \left (\frac {1}{2} \left (4 x^2-x^2 \log (3)\right )\right )\right )} \, dx=\frac {1}{1+x (1+x)-\frac {4}{\log \left (\log \left (\frac {1}{2} x^2 (4-\log (3))\right )\right )}} \]
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\[ \int \frac {-8+\left (-x-2 x^2\right ) \log \left (\frac {1}{2} \left (4 x^2-x^2 \log (3)\right )\right ) \log ^2\left (\log \left (\frac {1}{2} \left (4 x^2-x^2 \log (3)\right )\right )\right )}{16 x \log \left (\frac {1}{2} \left (4 x^2-x^2 \log (3)\right )\right )+\left (-8 x-8 x^2-8 x^3\right ) \log \left (\frac {1}{2} \left (4 x^2-x^2 \log (3)\right )\right ) \log \left (\log \left (\frac {1}{2} \left (4 x^2-x^2 \log (3)\right )\right )\right )+\left (x+2 x^2+3 x^3+2 x^4+x^5\right ) \log \left (\frac {1}{2} \left (4 x^2-x^2 \log (3)\right )\right ) \log ^2\left (\log \left (\frac {1}{2} \left (4 x^2-x^2 \log (3)\right )\right )\right )} \, dx=\int \frac {-8+\left (-x-2 x^2\right ) \log \left (\frac {1}{2} \left (4 x^2-x^2 \log (3)\right )\right ) \log ^2\left (\log \left (\frac {1}{2} \left (4 x^2-x^2 \log (3)\right )\right )\right )}{16 x \log \left (\frac {1}{2} \left (4 x^2-x^2 \log (3)\right )\right )+\left (-8 x-8 x^2-8 x^3\right ) \log \left (\frac {1}{2} \left (4 x^2-x^2 \log (3)\right )\right ) \log \left (\log \left (\frac {1}{2} \left (4 x^2-x^2 \log (3)\right )\right )\right )+\left (x+2 x^2+3 x^3+2 x^4+x^5\right ) \log \left (\frac {1}{2} \left (4 x^2-x^2 \log (3)\right )\right ) \log ^2\left (\log \left (\frac {1}{2} \left (4 x^2-x^2 \log (3)\right )\right )\right )} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {-8-x (1+2 x) \log \left (-\frac {1}{2} x^2 (-4+\log (3))\right ) \log ^2\left (\log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )\right )}{x \log \left (-\frac {1}{2} x^2 (-4+\log (3))\right ) \left (4-\left (1+x+x^2\right ) \log \left (\log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )\right )\right )^2} \, dx \\ & = \int \left (\frac {-1-2 x}{\left (1+x+x^2\right )^2}-\frac {8 \left (1+2 x+3 x^2+2 x^3+x^4+2 x \log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )+4 x^2 \log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )\right )}{x \left (1+x+x^2\right )^2 \log \left (-\frac {1}{2} x^2 (-4+\log (3))\right ) \left (-4+\log \left (\log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )\right )+x \log \left (\log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )\right )+x^2 \log \left (\log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )\right )\right )^2}-\frac {8 (1+2 x)}{\left (1+x+x^2\right )^2 \left (-4+\log \left (\log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )\right )+x \log \left (\log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )\right )+x^2 \log \left (\log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )\right )\right )}\right ) \, dx \\ & = -\left (8 \int \frac {1+2 x+3 x^2+2 x^3+x^4+2 x \log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )+4 x^2 \log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )}{x \left (1+x+x^2\right )^2 \log \left (-\frac {1}{2} x^2 (-4+\log (3))\right ) \left (-4+\log \left (\log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )\right )+x \log \left (\log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )\right )+x^2 \log \left (\log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )\right )\right )^2} \, dx\right )-8 \int \frac {1+2 x}{\left (1+x+x^2\right )^2 \left (-4+\log \left (\log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )\right )+x \log \left (\log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )\right )+x^2 \log \left (\log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )\right )\right )} \, dx+\int \frac {-1-2 x}{\left (1+x+x^2\right )^2} \, dx \\ & = \frac {1}{1+x+x^2}-8 \int \frac {\left (1+x+x^2\right )^2+2 x (1+2 x) \log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )}{x \left (1+x+x^2\right )^2 \log \left (-\frac {1}{2} x^2 (-4+\log (3))\right ) \left (4-\left (1+x+x^2\right ) \log \left (\log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )\right )\right )^2} \, dx-8 \int \frac {-1-2 x}{\left (1+x+x^2\right )^2 \left (4-\left (1+x+x^2\right ) \log \left (\log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )\right )\right )} \, dx \\ & = \frac {1}{1+x+x^2}-8 \int \left (\frac {1+2 x+3 x^2+2 x^3+x^4+2 x \log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )+4 x^2 \log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )}{x \log \left (-\frac {1}{2} x^2 (-4+\log (3))\right ) \left (-4+\log \left (\log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )\right )+x \log \left (\log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )\right )+x^2 \log \left (\log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )\right )\right )^2}-\frac {(1+x) \left (1+2 x+3 x^2+2 x^3+x^4+2 x \log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )+4 x^2 \log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )\right )}{\left (1+x+x^2\right )^2 \log \left (-\frac {1}{2} x^2 (-4+\log (3))\right ) \left (-4+\log \left (\log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )\right )+x \log \left (\log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )\right )+x^2 \log \left (\log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )\right )\right )^2}-\frac {(1+x) \left (1+2 x+3 x^2+2 x^3+x^4+2 x \log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )+4 x^2 \log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )\right )}{\left (1+x+x^2\right ) \log \left (-\frac {1}{2} x^2 (-4+\log (3))\right ) \left (-4+\log \left (\log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )\right )+x \log \left (\log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )\right )+x^2 \log \left (\log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )\right )\right )^2}\right ) \, dx-8 \int \left (\frac {1}{\left (1+x+x^2\right )^2 \left (-4+\log \left (\log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )\right )+x \log \left (\log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )\right )+x^2 \log \left (\log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )\right )\right )}+\frac {2 x}{\left (1+x+x^2\right )^2 \left (-4+\log \left (\log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )\right )+x \log \left (\log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )\right )+x^2 \log \left (\log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )\right )\right )}\right ) \, dx \\ & = \frac {1}{1+x+x^2}-8 \int \frac {1+2 x+3 x^2+2 x^3+x^4+2 x \log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )+4 x^2 \log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )}{x \log \left (-\frac {1}{2} x^2 (-4+\log (3))\right ) \left (-4+\log \left (\log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )\right )+x \log \left (\log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )\right )+x^2 \log \left (\log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )\right )\right )^2} \, dx+8 \int \frac {(1+x) \left (1+2 x+3 x^2+2 x^3+x^4+2 x \log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )+4 x^2 \log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )\right )}{\left (1+x+x^2\right )^2 \log \left (-\frac {1}{2} x^2 (-4+\log (3))\right ) \left (-4+\log \left (\log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )\right )+x \log \left (\log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )\right )+x^2 \log \left (\log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )\right )\right )^2} \, dx+8 \int \frac {(1+x) \left (1+2 x+3 x^2+2 x^3+x^4+2 x \log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )+4 x^2 \log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )\right )}{\left (1+x+x^2\right ) \log \left (-\frac {1}{2} x^2 (-4+\log (3))\right ) \left (-4+\log \left (\log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )\right )+x \log \left (\log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )\right )+x^2 \log \left (\log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )\right )\right )^2} \, dx-8 \int \frac {1}{\left (1+x+x^2\right )^2 \left (-4+\log \left (\log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )\right )+x \log \left (\log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )\right )+x^2 \log \left (\log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )\right )\right )} \, dx-16 \int \frac {x}{\left (1+x+x^2\right )^2 \left (-4+\log \left (\log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )\right )+x \log \left (\log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )\right )+x^2 \log \left (\log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )\right )\right )} \, dx \\ & = \frac {1}{1+x+x^2}-8 \int \frac {\left (1+x+x^2\right )^2+2 x (1+2 x) \log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )}{x \log \left (-\frac {1}{2} x^2 (-4+\log (3))\right ) \left (4-\left (1+x+x^2\right ) \log \left (\log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )\right )\right )^2} \, dx+8 \int \frac {(1+x) \left (\left (1+x+x^2\right )^2+2 x (1+2 x) \log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )\right )}{\left (1+x+x^2\right )^2 \log \left (-\frac {1}{2} x^2 (-4+\log (3))\right ) \left (4-\left (1+x+x^2\right ) \log \left (\log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )\right )\right )^2} \, dx+8 \int \frac {(1+x) \left (\left (1+x+x^2\right )^2+2 x (1+2 x) \log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )\right )}{\left (1+x+x^2\right ) \log \left (-\frac {1}{2} x^2 (-4+\log (3))\right ) \left (4-\left (1+x+x^2\right ) \log \left (\log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )\right )\right )^2} \, dx-8 \int \frac {1}{\left (1+x+x^2\right )^2 \left (-4+\left (1+x+x^2\right ) \log \left (\log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )\right )\right )} \, dx-16 \int \frac {x}{\left (1+x+x^2\right )^2 \left (-4+\left (1+x+x^2\right ) \log \left (\log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )\right )\right )} \, dx \\ & = \text {Too large to display} \\ \end{align*}
Time = 0.66 (sec) , antiderivative size = 38, normalized size of antiderivative = 1.36 \[ \int \frac {-8+\left (-x-2 x^2\right ) \log \left (\frac {1}{2} \left (4 x^2-x^2 \log (3)\right )\right ) \log ^2\left (\log \left (\frac {1}{2} \left (4 x^2-x^2 \log (3)\right )\right )\right )}{16 x \log \left (\frac {1}{2} \left (4 x^2-x^2 \log (3)\right )\right )+\left (-8 x-8 x^2-8 x^3\right ) \log \left (\frac {1}{2} \left (4 x^2-x^2 \log (3)\right )\right ) \log \left (\log \left (\frac {1}{2} \left (4 x^2-x^2 \log (3)\right )\right )\right )+\left (x+2 x^2+3 x^3+2 x^4+x^5\right ) \log \left (\frac {1}{2} \left (4 x^2-x^2 \log (3)\right )\right ) \log ^2\left (\log \left (\frac {1}{2} \left (4 x^2-x^2 \log (3)\right )\right )\right )} \, dx=\frac {\log \left (\log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )\right )}{-4+\left (1+x+x^2\right ) \log \left (\log \left (-\frac {1}{2} x^2 (-4+\log (3))\right )\right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. \(55\) vs. \(2(26)=52\).
Time = 3.63 (sec) , antiderivative size = 56, normalized size of antiderivative = 2.00
method | result | size |
parallelrisch | \(\frac {\ln \left (\ln \left (-\frac {\left (-4+\ln \left (3\right )\right ) x^{2}}{2}\right )\right )}{\ln \left (\ln \left (-\frac {\left (-4+\ln \left (3\right )\right ) x^{2}}{2}\right )\right ) x^{2}+\ln \left (\ln \left (-\frac {\left (-4+\ln \left (3\right )\right ) x^{2}}{2}\right )\right ) x +\ln \left (\ln \left (-\frac {\left (-4+\ln \left (3\right )\right ) x^{2}}{2}\right )\right )-4}\) | \(56\) |
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Time = 0.27 (sec) , antiderivative size = 42, normalized size of antiderivative = 1.50 \[ \int \frac {-8+\left (-x-2 x^2\right ) \log \left (\frac {1}{2} \left (4 x^2-x^2 \log (3)\right )\right ) \log ^2\left (\log \left (\frac {1}{2} \left (4 x^2-x^2 \log (3)\right )\right )\right )}{16 x \log \left (\frac {1}{2} \left (4 x^2-x^2 \log (3)\right )\right )+\left (-8 x-8 x^2-8 x^3\right ) \log \left (\frac {1}{2} \left (4 x^2-x^2 \log (3)\right )\right ) \log \left (\log \left (\frac {1}{2} \left (4 x^2-x^2 \log (3)\right )\right )\right )+\left (x+2 x^2+3 x^3+2 x^4+x^5\right ) \log \left (\frac {1}{2} \left (4 x^2-x^2 \log (3)\right )\right ) \log ^2\left (\log \left (\frac {1}{2} \left (4 x^2-x^2 \log (3)\right )\right )\right )} \, dx=\frac {\log \left (\log \left (-\frac {1}{2} \, x^{2} \log \left (3\right ) + 2 \, x^{2}\right )\right )}{{\left (x^{2} + x + 1\right )} \log \left (\log \left (-\frac {1}{2} \, x^{2} \log \left (3\right ) + 2 \, x^{2}\right )\right ) - 4} \]
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Leaf count of result is larger than twice the leaf count of optimal. 54 vs. \(2 (22) = 44\).
Time = 0.14 (sec) , antiderivative size = 54, normalized size of antiderivative = 1.93 \[ \int \frac {-8+\left (-x-2 x^2\right ) \log \left (\frac {1}{2} \left (4 x^2-x^2 \log (3)\right )\right ) \log ^2\left (\log \left (\frac {1}{2} \left (4 x^2-x^2 \log (3)\right )\right )\right )}{16 x \log \left (\frac {1}{2} \left (4 x^2-x^2 \log (3)\right )\right )+\left (-8 x-8 x^2-8 x^3\right ) \log \left (\frac {1}{2} \left (4 x^2-x^2 \log (3)\right )\right ) \log \left (\log \left (\frac {1}{2} \left (4 x^2-x^2 \log (3)\right )\right )\right )+\left (x+2 x^2+3 x^3+2 x^4+x^5\right ) \log \left (\frac {1}{2} \left (4 x^2-x^2 \log (3)\right )\right ) \log ^2\left (\log \left (\frac {1}{2} \left (4 x^2-x^2 \log (3)\right )\right )\right )} \, dx=\frac {4}{- 4 x^{2} - 4 x + \left (x^{4} + 2 x^{3} + 3 x^{2} + 2 x + 1\right ) \log {\left (\log {\left (- \frac {x^{2} \log {\left (3 \right )}}{2} + 2 x^{2} \right )} \right )} - 4} + \frac {1}{x^{2} + x + 1} \]
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Time = 0.35 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.64 \[ \int \frac {-8+\left (-x-2 x^2\right ) \log \left (\frac {1}{2} \left (4 x^2-x^2 \log (3)\right )\right ) \log ^2\left (\log \left (\frac {1}{2} \left (4 x^2-x^2 \log (3)\right )\right )\right )}{16 x \log \left (\frac {1}{2} \left (4 x^2-x^2 \log (3)\right )\right )+\left (-8 x-8 x^2-8 x^3\right ) \log \left (\frac {1}{2} \left (4 x^2-x^2 \log (3)\right )\right ) \log \left (\log \left (\frac {1}{2} \left (4 x^2-x^2 \log (3)\right )\right )\right )+\left (x+2 x^2+3 x^3+2 x^4+x^5\right ) \log \left (\frac {1}{2} \left (4 x^2-x^2 \log (3)\right )\right ) \log ^2\left (\log \left (\frac {1}{2} \left (4 x^2-x^2 \log (3)\right )\right )\right )} \, dx=\frac {\log \left (-\log \left (2\right ) + 2 \, \log \left (x\right ) + \log \left (-\log \left (3\right ) + 4\right )\right )}{{\left (x^{2} + x + 1\right )} \log \left (-\log \left (2\right ) + 2 \, \log \left (x\right ) + \log \left (-\log \left (3\right ) + 4\right )\right ) - 4} \]
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Leaf count of result is larger than twice the leaf count of optimal. 140 vs. \(2 (24) = 48\).
Time = 0.95 (sec) , antiderivative size = 140, normalized size of antiderivative = 5.00 \[ \int \frac {-8+\left (-x-2 x^2\right ) \log \left (\frac {1}{2} \left (4 x^2-x^2 \log (3)\right )\right ) \log ^2\left (\log \left (\frac {1}{2} \left (4 x^2-x^2 \log (3)\right )\right )\right )}{16 x \log \left (\frac {1}{2} \left (4 x^2-x^2 \log (3)\right )\right )+\left (-8 x-8 x^2-8 x^3\right ) \log \left (\frac {1}{2} \left (4 x^2-x^2 \log (3)\right )\right ) \log \left (\log \left (\frac {1}{2} \left (4 x^2-x^2 \log (3)\right )\right )\right )+\left (x+2 x^2+3 x^3+2 x^4+x^5\right ) \log \left (\frac {1}{2} \left (4 x^2-x^2 \log (3)\right )\right ) \log ^2\left (\log \left (\frac {1}{2} \left (4 x^2-x^2 \log (3)\right )\right )\right )} \, dx=\frac {4}{x^{4} \log \left (-\log \left (2\right ) + \log \left (-x^{2} \log \left (3\right ) + 4 \, x^{2}\right )\right ) + 2 \, x^{3} \log \left (-\log \left (2\right ) + \log \left (-x^{2} \log \left (3\right ) + 4 \, x^{2}\right )\right ) + 3 \, x^{2} \log \left (-\log \left (2\right ) + \log \left (-x^{2} \log \left (3\right ) + 4 \, x^{2}\right )\right ) - 4 \, x^{2} + 2 \, x \log \left (-\log \left (2\right ) + \log \left (-x^{2} \log \left (3\right ) + 4 \, x^{2}\right )\right ) - 4 \, x + \log \left (-\log \left (2\right ) + \log \left (-x^{2} \log \left (3\right ) + 4 \, x^{2}\right )\right ) - 4} + \frac {1}{x^{2} + x + 1} \]
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Timed out. \[ \int \frac {-8+\left (-x-2 x^2\right ) \log \left (\frac {1}{2} \left (4 x^2-x^2 \log (3)\right )\right ) \log ^2\left (\log \left (\frac {1}{2} \left (4 x^2-x^2 \log (3)\right )\right )\right )}{16 x \log \left (\frac {1}{2} \left (4 x^2-x^2 \log (3)\right )\right )+\left (-8 x-8 x^2-8 x^3\right ) \log \left (\frac {1}{2} \left (4 x^2-x^2 \log (3)\right )\right ) \log \left (\log \left (\frac {1}{2} \left (4 x^2-x^2 \log (3)\right )\right )\right )+\left (x+2 x^2+3 x^3+2 x^4+x^5\right ) \log \left (\frac {1}{2} \left (4 x^2-x^2 \log (3)\right )\right ) \log ^2\left (\log \left (\frac {1}{2} \left (4 x^2-x^2 \log (3)\right )\right )\right )} \, dx=\int -\frac {\ln \left (2\,x^2-\frac {x^2\,\ln \left (3\right )}{2}\right )\,\left (2\,x^2+x\right )\,{\ln \left (\ln \left (2\,x^2-\frac {x^2\,\ln \left (3\right )}{2}\right )\right )}^2+8}{\ln \left (2\,x^2-\frac {x^2\,\ln \left (3\right )}{2}\right )\,\left (x^5+2\,x^4+3\,x^3+2\,x^2+x\right )\,{\ln \left (\ln \left (2\,x^2-\frac {x^2\,\ln \left (3\right )}{2}\right )\right )}^2-\ln \left (2\,x^2-\frac {x^2\,\ln \left (3\right )}{2}\right )\,\left (8\,x^3+8\,x^2+8\,x\right )\,\ln \left (\ln \left (2\,x^2-\frac {x^2\,\ln \left (3\right )}{2}\right )\right )+16\,x\,\ln \left (2\,x^2-\frac {x^2\,\ln \left (3\right )}{2}\right )} \,d x \]
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