Integrand size = 249, antiderivative size = 27 \[ \int \frac {162+54 x+4 x^2+2 x^3-2 x^4+\left (-18 x-2 x^2-2 x^3\right ) \log (2 x)+\left (81+36 x-11 x^2-4 x^3+x^4+\left (-18 x-4 x^2+2 x^3\right ) \log (2 x)+x^2 \log ^2(2 x)\right ) \log \left (\frac {486+216 x-66 x^2-24 x^3+6 x^4+\left (-108 x-24 x^2+12 x^3\right ) \log (2 x)+6 x^2 \log ^2(2 x)}{x^2}\right )}{\left (81+36 x-11 x^2-4 x^3+x^4+\left (-18 x-4 x^2+2 x^3\right ) \log (2 x)+x^2 \log ^2(2 x)\right ) \log ^2\left (\frac {486+216 x-66 x^2-24 x^3+6 x^4+\left (-108 x-24 x^2+12 x^3\right ) \log (2 x)+6 x^2 \log ^2(2 x)}{x^2}\right )} \, dx=\frac {x}{\log \left (6 \left (3+\left (2+\frac {9}{x}-x-\log (2 x)\right )^2\right )\right )} \]
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\[ \int \frac {162+54 x+4 x^2+2 x^3-2 x^4+\left (-18 x-2 x^2-2 x^3\right ) \log (2 x)+\left (81+36 x-11 x^2-4 x^3+x^4+\left (-18 x-4 x^2+2 x^3\right ) \log (2 x)+x^2 \log ^2(2 x)\right ) \log \left (\frac {486+216 x-66 x^2-24 x^3+6 x^4+\left (-108 x-24 x^2+12 x^3\right ) \log (2 x)+6 x^2 \log ^2(2 x)}{x^2}\right )}{\left (81+36 x-11 x^2-4 x^3+x^4+\left (-18 x-4 x^2+2 x^3\right ) \log (2 x)+x^2 \log ^2(2 x)\right ) \log ^2\left (\frac {486+216 x-66 x^2-24 x^3+6 x^4+\left (-108 x-24 x^2+12 x^3\right ) \log (2 x)+6 x^2 \log ^2(2 x)}{x^2}\right )} \, dx=\int \frac {162+54 x+4 x^2+2 x^3-2 x^4+\left (-18 x-2 x^2-2 x^3\right ) \log (2 x)+\left (81+36 x-11 x^2-4 x^3+x^4+\left (-18 x-4 x^2+2 x^3\right ) \log (2 x)+x^2 \log ^2(2 x)\right ) \log \left (\frac {486+216 x-66 x^2-24 x^3+6 x^4+\left (-108 x-24 x^2+12 x^3\right ) \log (2 x)+6 x^2 \log ^2(2 x)}{x^2}\right )}{\left (81+36 x-11 x^2-4 x^3+x^4+\left (-18 x-4 x^2+2 x^3\right ) \log (2 x)+x^2 \log ^2(2 x)\right ) \log ^2\left (\frac {486+216 x-66 x^2-24 x^3+6 x^4+\left (-108 x-24 x^2+12 x^3\right ) \log (2 x)+6 x^2 \log ^2(2 x)}{x^2}\right )} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {162+54 x+4 x^2+2 x^3-2 x^4+\left (-18 x-2 x^2-2 x^3\right ) \log (2 x)+\left (81+36 x-11 x^2-4 x^3+x^4+\left (-18 x-4 x^2+2 x^3\right ) \log (2 x)+x^2 \log ^2(2 x)\right ) \log \left (\frac {486+216 x-66 x^2-24 x^3+6 x^4+\left (-108 x-24 x^2+12 x^3\right ) \log (2 x)+6 x^2 \log ^2(2 x)}{x^2}\right )}{\left (81+36 x-11 x^2-4 x^3+x^4+\left (-18 x-4 x^2+2 x^3\right ) \log (2 x)+x^2 \log ^2(2 x)\right ) \log ^2\left (-66+\frac {486}{x^2}+\frac {216}{x}-24 x+6 x^2+\frac {\left (-108 x-24 x^2+12 x^3\right ) \log (2 x)}{x^2}+6 \log ^2(2 x)\right )} \, dx \\ & = \int \left (\frac {162}{\left (81+36 x-11 x^2-4 x^3+x^4-18 x \log (2 x)-4 x^2 \log (2 x)+2 x^3 \log (2 x)+x^2 \log ^2(2 x)\right ) \log ^2\left (\frac {6 \left (81+36 x-11 x^2-4 x^3+x^4+2 x \left (-9-2 x+x^2\right ) \log (2 x)+x^2 \log ^2(2 x)\right )}{x^2}\right )}+\frac {54 x}{\left (81+36 x-11 x^2-4 x^3+x^4-18 x \log (2 x)-4 x^2 \log (2 x)+2 x^3 \log (2 x)+x^2 \log ^2(2 x)\right ) \log ^2\left (\frac {6 \left (81+36 x-11 x^2-4 x^3+x^4+2 x \left (-9-2 x+x^2\right ) \log (2 x)+x^2 \log ^2(2 x)\right )}{x^2}\right )}+\frac {4 x^2}{\left (81+36 x-11 x^2-4 x^3+x^4-18 x \log (2 x)-4 x^2 \log (2 x)+2 x^3 \log (2 x)+x^2 \log ^2(2 x)\right ) \log ^2\left (\frac {6 \left (81+36 x-11 x^2-4 x^3+x^4+2 x \left (-9-2 x+x^2\right ) \log (2 x)+x^2 \log ^2(2 x)\right )}{x^2}\right )}+\frac {2 x^3}{\left (81+36 x-11 x^2-4 x^3+x^4-18 x \log (2 x)-4 x^2 \log (2 x)+2 x^3 \log (2 x)+x^2 \log ^2(2 x)\right ) \log ^2\left (\frac {6 \left (81+36 x-11 x^2-4 x^3+x^4+2 x \left (-9-2 x+x^2\right ) \log (2 x)+x^2 \log ^2(2 x)\right )}{x^2}\right )}-\frac {2 x^4}{\left (81+36 x-11 x^2-4 x^3+x^4-18 x \log (2 x)-4 x^2 \log (2 x)+2 x^3 \log (2 x)+x^2 \log ^2(2 x)\right ) \log ^2\left (\frac {6 \left (81+36 x-11 x^2-4 x^3+x^4+2 x \left (-9-2 x+x^2\right ) \log (2 x)+x^2 \log ^2(2 x)\right )}{x^2}\right )}-\frac {2 x \left (9+x+x^2\right ) \log (2 x)}{\left (81+36 x-11 x^2-4 x^3+x^4-18 x \log (2 x)-4 x^2 \log (2 x)+2 x^3 \log (2 x)+x^2 \log ^2(2 x)\right ) \log ^2\left (\frac {6 \left (81+36 x-11 x^2-4 x^3+x^4+2 x \left (-9-2 x+x^2\right ) \log (2 x)+x^2 \log ^2(2 x)\right )}{x^2}\right )}+\frac {1}{\log \left (\frac {6 \left (81+36 x-11 x^2-4 x^3+x^4+2 x \left (-9-2 x+x^2\right ) \log (2 x)+x^2 \log ^2(2 x)\right )}{x^2}\right )}\right ) \, dx \\ & = 2 \int \frac {x^3}{\left (81+36 x-11 x^2-4 x^3+x^4-18 x \log (2 x)-4 x^2 \log (2 x)+2 x^3 \log (2 x)+x^2 \log ^2(2 x)\right ) \log ^2\left (\frac {6 \left (81+36 x-11 x^2-4 x^3+x^4+2 x \left (-9-2 x+x^2\right ) \log (2 x)+x^2 \log ^2(2 x)\right )}{x^2}\right )} \, dx-2 \int \frac {x^4}{\left (81+36 x-11 x^2-4 x^3+x^4-18 x \log (2 x)-4 x^2 \log (2 x)+2 x^3 \log (2 x)+x^2 \log ^2(2 x)\right ) \log ^2\left (\frac {6 \left (81+36 x-11 x^2-4 x^3+x^4+2 x \left (-9-2 x+x^2\right ) \log (2 x)+x^2 \log ^2(2 x)\right )}{x^2}\right )} \, dx-2 \int \frac {x \left (9+x+x^2\right ) \log (2 x)}{\left (81+36 x-11 x^2-4 x^3+x^4-18 x \log (2 x)-4 x^2 \log (2 x)+2 x^3 \log (2 x)+x^2 \log ^2(2 x)\right ) \log ^2\left (\frac {6 \left (81+36 x-11 x^2-4 x^3+x^4+2 x \left (-9-2 x+x^2\right ) \log (2 x)+x^2 \log ^2(2 x)\right )}{x^2}\right )} \, dx+4 \int \frac {x^2}{\left (81+36 x-11 x^2-4 x^3+x^4-18 x \log (2 x)-4 x^2 \log (2 x)+2 x^3 \log (2 x)+x^2 \log ^2(2 x)\right ) \log ^2\left (\frac {6 \left (81+36 x-11 x^2-4 x^3+x^4+2 x \left (-9-2 x+x^2\right ) \log (2 x)+x^2 \log ^2(2 x)\right )}{x^2}\right )} \, dx+54 \int \frac {x}{\left (81+36 x-11 x^2-4 x^3+x^4-18 x \log (2 x)-4 x^2 \log (2 x)+2 x^3 \log (2 x)+x^2 \log ^2(2 x)\right ) \log ^2\left (\frac {6 \left (81+36 x-11 x^2-4 x^3+x^4+2 x \left (-9-2 x+x^2\right ) \log (2 x)+x^2 \log ^2(2 x)\right )}{x^2}\right )} \, dx+162 \int \frac {1}{\left (81+36 x-11 x^2-4 x^3+x^4-18 x \log (2 x)-4 x^2 \log (2 x)+2 x^3 \log (2 x)+x^2 \log ^2(2 x)\right ) \log ^2\left (\frac {6 \left (81+36 x-11 x^2-4 x^3+x^4+2 x \left (-9-2 x+x^2\right ) \log (2 x)+x^2 \log ^2(2 x)\right )}{x^2}\right )} \, dx+\int \frac {1}{\log \left (\frac {6 \left (81+36 x-11 x^2-4 x^3+x^4+2 x \left (-9-2 x+x^2\right ) \log (2 x)+x^2 \log ^2(2 x)\right )}{x^2}\right )} \, dx \\ & = -\left (2 \int \left (\frac {9 x \log (2 x)}{\left (81+36 x-11 x^2-4 x^3+x^4-18 x \log (2 x)-4 x^2 \log (2 x)+2 x^3 \log (2 x)+x^2 \log ^2(2 x)\right ) \log ^2\left (\frac {6 \left (81+36 x-11 x^2-4 x^3+x^4+2 x \left (-9-2 x+x^2\right ) \log (2 x)+x^2 \log ^2(2 x)\right )}{x^2}\right )}+\frac {x^2 \log (2 x)}{\left (81+36 x-11 x^2-4 x^3+x^4-18 x \log (2 x)-4 x^2 \log (2 x)+2 x^3 \log (2 x)+x^2 \log ^2(2 x)\right ) \log ^2\left (\frac {6 \left (81+36 x-11 x^2-4 x^3+x^4+2 x \left (-9-2 x+x^2\right ) \log (2 x)+x^2 \log ^2(2 x)\right )}{x^2}\right )}+\frac {x^3 \log (2 x)}{\left (81+36 x-11 x^2-4 x^3+x^4-18 x \log (2 x)-4 x^2 \log (2 x)+2 x^3 \log (2 x)+x^2 \log ^2(2 x)\right ) \log ^2\left (\frac {6 \left (81+36 x-11 x^2-4 x^3+x^4+2 x \left (-9-2 x+x^2\right ) \log (2 x)+x^2 \log ^2(2 x)\right )}{x^2}\right )}\right ) \, dx\right )+2 \int \frac {x^3}{\left (81+36 x-11 x^2-4 x^3+x^4-18 x \log (2 x)-4 x^2 \log (2 x)+2 x^3 \log (2 x)+x^2 \log ^2(2 x)\right ) \log ^2\left (\frac {6 \left (81+36 x-11 x^2-4 x^3+x^4+2 x \left (-9-2 x+x^2\right ) \log (2 x)+x^2 \log ^2(2 x)\right )}{x^2}\right )} \, dx-2 \int \frac {x^4}{\left (81+36 x-11 x^2-4 x^3+x^4-18 x \log (2 x)-4 x^2 \log (2 x)+2 x^3 \log (2 x)+x^2 \log ^2(2 x)\right ) \log ^2\left (\frac {6 \left (81+36 x-11 x^2-4 x^3+x^4+2 x \left (-9-2 x+x^2\right ) \log (2 x)+x^2 \log ^2(2 x)\right )}{x^2}\right )} \, dx+4 \int \frac {x^2}{\left (81+36 x-11 x^2-4 x^3+x^4-18 x \log (2 x)-4 x^2 \log (2 x)+2 x^3 \log (2 x)+x^2 \log ^2(2 x)\right ) \log ^2\left (\frac {6 \left (81+36 x-11 x^2-4 x^3+x^4+2 x \left (-9-2 x+x^2\right ) \log (2 x)+x^2 \log ^2(2 x)\right )}{x^2}\right )} \, dx+54 \int \frac {x}{\left (81+36 x-11 x^2-4 x^3+x^4-18 x \log (2 x)-4 x^2 \log (2 x)+2 x^3 \log (2 x)+x^2 \log ^2(2 x)\right ) \log ^2\left (\frac {6 \left (81+36 x-11 x^2-4 x^3+x^4+2 x \left (-9-2 x+x^2\right ) \log (2 x)+x^2 \log ^2(2 x)\right )}{x^2}\right )} \, dx+162 \int \frac {1}{\left (81+36 x-11 x^2-4 x^3+x^4-18 x \log (2 x)-4 x^2 \log (2 x)+2 x^3 \log (2 x)+x^2 \log ^2(2 x)\right ) \log ^2\left (\frac {6 \left (81+36 x-11 x^2-4 x^3+x^4+2 x \left (-9-2 x+x^2\right ) \log (2 x)+x^2 \log ^2(2 x)\right )}{x^2}\right )} \, dx+\int \frac {1}{\log \left (\frac {6 \left (81+36 x-11 x^2-4 x^3+x^4+2 x \left (-9-2 x+x^2\right ) \log (2 x)+x^2 \log ^2(2 x)\right )}{x^2}\right )} \, dx \\ & = 2 \int \frac {x^3}{\left (81+36 x-11 x^2-4 x^3+x^4-18 x \log (2 x)-4 x^2 \log (2 x)+2 x^3 \log (2 x)+x^2 \log ^2(2 x)\right ) \log ^2\left (\frac {6 \left (81+36 x-11 x^2-4 x^3+x^4+2 x \left (-9-2 x+x^2\right ) \log (2 x)+x^2 \log ^2(2 x)\right )}{x^2}\right )} \, dx-2 \int \frac {x^4}{\left (81+36 x-11 x^2-4 x^3+x^4-18 x \log (2 x)-4 x^2 \log (2 x)+2 x^3 \log (2 x)+x^2 \log ^2(2 x)\right ) \log ^2\left (\frac {6 \left (81+36 x-11 x^2-4 x^3+x^4+2 x \left (-9-2 x+x^2\right ) \log (2 x)+x^2 \log ^2(2 x)\right )}{x^2}\right )} \, dx-2 \int \frac {x^2 \log (2 x)}{\left (81+36 x-11 x^2-4 x^3+x^4-18 x \log (2 x)-4 x^2 \log (2 x)+2 x^3 \log (2 x)+x^2 \log ^2(2 x)\right ) \log ^2\left (\frac {6 \left (81+36 x-11 x^2-4 x^3+x^4+2 x \left (-9-2 x+x^2\right ) \log (2 x)+x^2 \log ^2(2 x)\right )}{x^2}\right )} \, dx-2 \int \frac {x^3 \log (2 x)}{\left (81+36 x-11 x^2-4 x^3+x^4-18 x \log (2 x)-4 x^2 \log (2 x)+2 x^3 \log (2 x)+x^2 \log ^2(2 x)\right ) \log ^2\left (\frac {6 \left (81+36 x-11 x^2-4 x^3+x^4+2 x \left (-9-2 x+x^2\right ) \log (2 x)+x^2 \log ^2(2 x)\right )}{x^2}\right )} \, dx+4 \int \frac {x^2}{\left (81+36 x-11 x^2-4 x^3+x^4-18 x \log (2 x)-4 x^2 \log (2 x)+2 x^3 \log (2 x)+x^2 \log ^2(2 x)\right ) \log ^2\left (\frac {6 \left (81+36 x-11 x^2-4 x^3+x^4+2 x \left (-9-2 x+x^2\right ) \log (2 x)+x^2 \log ^2(2 x)\right )}{x^2}\right )} \, dx-18 \int \frac {x \log (2 x)}{\left (81+36 x-11 x^2-4 x^3+x^4-18 x \log (2 x)-4 x^2 \log (2 x)+2 x^3 \log (2 x)+x^2 \log ^2(2 x)\right ) \log ^2\left (\frac {6 \left (81+36 x-11 x^2-4 x^3+x^4+2 x \left (-9-2 x+x^2\right ) \log (2 x)+x^2 \log ^2(2 x)\right )}{x^2}\right )} \, dx+54 \int \frac {x}{\left (81+36 x-11 x^2-4 x^3+x^4-18 x \log (2 x)-4 x^2 \log (2 x)+2 x^3 \log (2 x)+x^2 \log ^2(2 x)\right ) \log ^2\left (\frac {6 \left (81+36 x-11 x^2-4 x^3+x^4+2 x \left (-9-2 x+x^2\right ) \log (2 x)+x^2 \log ^2(2 x)\right )}{x^2}\right )} \, dx+162 \int \frac {1}{\left (81+36 x-11 x^2-4 x^3+x^4-18 x \log (2 x)-4 x^2 \log (2 x)+2 x^3 \log (2 x)+x^2 \log ^2(2 x)\right ) \log ^2\left (\frac {6 \left (81+36 x-11 x^2-4 x^3+x^4+2 x \left (-9-2 x+x^2\right ) \log (2 x)+x^2 \log ^2(2 x)\right )}{x^2}\right )} \, dx+\int \frac {1}{\log \left (\frac {6 \left (81+36 x-11 x^2-4 x^3+x^4+2 x \left (-9-2 x+x^2\right ) \log (2 x)+x^2 \log ^2(2 x)\right )}{x^2}\right )} \, dx \\ \end{align*}
Time = 0.13 (sec) , antiderivative size = 53, normalized size of antiderivative = 1.96 \[ \int \frac {162+54 x+4 x^2+2 x^3-2 x^4+\left (-18 x-2 x^2-2 x^3\right ) \log (2 x)+\left (81+36 x-11 x^2-4 x^3+x^4+\left (-18 x-4 x^2+2 x^3\right ) \log (2 x)+x^2 \log ^2(2 x)\right ) \log \left (\frac {486+216 x-66 x^2-24 x^3+6 x^4+\left (-108 x-24 x^2+12 x^3\right ) \log (2 x)+6 x^2 \log ^2(2 x)}{x^2}\right )}{\left (81+36 x-11 x^2-4 x^3+x^4+\left (-18 x-4 x^2+2 x^3\right ) \log (2 x)+x^2 \log ^2(2 x)\right ) \log ^2\left (\frac {486+216 x-66 x^2-24 x^3+6 x^4+\left (-108 x-24 x^2+12 x^3\right ) \log (2 x)+6 x^2 \log ^2(2 x)}{x^2}\right )} \, dx=\frac {x}{\log \left (\frac {6 \left (81+36 x-11 x^2-4 x^3+x^4+2 x \left (-9-2 x+x^2\right ) \log (2 x)+x^2 \log ^2(2 x)\right )}{x^2}\right )} \]
[In]
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Leaf count of result is larger than twice the leaf count of optimal. \(59\) vs. \(2(27)=54\).
Time = 3.25 (sec) , antiderivative size = 60, normalized size of antiderivative = 2.22
method | result | size |
parallelrisch | \(\frac {x}{\ln \left (\frac {6 x^{2} \ln \left (2 x \right )^{2}+\left (12 x^{3}-24 x^{2}-108 x \right ) \ln \left (2 x \right )+6 x^{4}-24 x^{3}-66 x^{2}+216 x +486}{x^{2}}\right )}\) | \(60\) |
default | \(\frac {2 i x}{\pi \,\operatorname {csgn}\left (i \left (x^{2} \ln \left (2\right )^{2}+\left (2 x^{2} \ln \left (x \right )+2 x^{3}-4 x^{2}-18 x \right ) \ln \left (2\right )+x^{2} \ln \left (x \right )^{2}+\left (2 x^{3}-4 x^{2}-18 x \right ) \ln \left (x \right )+x^{4}-4 x^{3}-11 x^{2}+36 x +81\right )\right ) \operatorname {csgn}\left (\frac {i}{x^{2}}\right ) \operatorname {csgn}\left (\frac {i \left (x^{2} \ln \left (2\right )^{2}+\left (2 x^{2} \ln \left (x \right )+2 x^{3}-4 x^{2}-18 x \right ) \ln \left (2\right )+x^{2} \ln \left (x \right )^{2}+\left (2 x^{3}-4 x^{2}-18 x \right ) \ln \left (x \right )+x^{4}-4 x^{3}-11 x^{2}+36 x +81\right )}{x^{2}}\right )-\pi \,\operatorname {csgn}\left (i \left (x^{2} \ln \left (2\right )^{2}+\left (2 x^{2} \ln \left (x \right )+2 x^{3}-4 x^{2}-18 x \right ) \ln \left (2\right )+x^{2} \ln \left (x \right )^{2}+\left (2 x^{3}-4 x^{2}-18 x \right ) \ln \left (x \right )+x^{4}-4 x^{3}-11 x^{2}+36 x +81\right )\right ) {\operatorname {csgn}\left (\frac {i \left (x^{2} \ln \left (2\right )^{2}+\left (2 x^{2} \ln \left (x \right )+2 x^{3}-4 x^{2}-18 x \right ) \ln \left (2\right )+x^{2} \ln \left (x \right )^{2}+\left (2 x^{3}-4 x^{2}-18 x \right ) \ln \left (x \right )+x^{4}-4 x^{3}-11 x^{2}+36 x +81\right )}{x^{2}}\right )}^{2}-\pi \,\operatorname {csgn}\left (\frac {i}{x^{2}}\right ) {\operatorname {csgn}\left (\frac {i \left (x^{2} \ln \left (2\right )^{2}+\left (2 x^{2} \ln \left (x \right )+2 x^{3}-4 x^{2}-18 x \right ) \ln \left (2\right )+x^{2} \ln \left (x \right )^{2}+\left (2 x^{3}-4 x^{2}-18 x \right ) \ln \left (x \right )+x^{4}-4 x^{3}-11 x^{2}+36 x +81\right )}{x^{2}}\right )}^{2}-\pi \operatorname {csgn}\left (i x \right )^{2} \operatorname {csgn}\left (i x^{2}\right )+2 \pi \,\operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (i x^{2}\right )^{2}-\pi \operatorname {csgn}\left (i x^{2}\right )^{3}+\pi {\operatorname {csgn}\left (\frac {i \left (x^{2} \ln \left (2\right )^{2}+\left (2 x^{2} \ln \left (x \right )+2 x^{3}-4 x^{2}-18 x \right ) \ln \left (2\right )+x^{2} \ln \left (x \right )^{2}+\left (2 x^{3}-4 x^{2}-18 x \right ) \ln \left (x \right )+x^{4}-4 x^{3}-11 x^{2}+36 x +81\right )}{x^{2}}\right )}^{3}+2 i \ln \left (3\right )+2 i \ln \left (2\right )+2 i \ln \left (x^{2} \ln \left (2\right )^{2}+\left (2 x^{2} \ln \left (x \right )+2 x^{3}-4 x^{2}-18 x \right ) \ln \left (2\right )+x^{2} \ln \left (x \right )^{2}+\left (2 x^{3}-4 x^{2}-18 x \right ) \ln \left (x \right )+x^{4}-4 x^{3}-11 x^{2}+36 x +81\right )-4 i \ln \left (x \right )}\) | \(664\) |
[In]
[Out]
Leaf count of result is larger than twice the leaf count of optimal. 56 vs. \(2 (23) = 46\).
Time = 0.24 (sec) , antiderivative size = 56, normalized size of antiderivative = 2.07 \[ \int \frac {162+54 x+4 x^2+2 x^3-2 x^4+\left (-18 x-2 x^2-2 x^3\right ) \log (2 x)+\left (81+36 x-11 x^2-4 x^3+x^4+\left (-18 x-4 x^2+2 x^3\right ) \log (2 x)+x^2 \log ^2(2 x)\right ) \log \left (\frac {486+216 x-66 x^2-24 x^3+6 x^4+\left (-108 x-24 x^2+12 x^3\right ) \log (2 x)+6 x^2 \log ^2(2 x)}{x^2}\right )}{\left (81+36 x-11 x^2-4 x^3+x^4+\left (-18 x-4 x^2+2 x^3\right ) \log (2 x)+x^2 \log ^2(2 x)\right ) \log ^2\left (\frac {486+216 x-66 x^2-24 x^3+6 x^4+\left (-108 x-24 x^2+12 x^3\right ) \log (2 x)+6 x^2 \log ^2(2 x)}{x^2}\right )} \, dx=\frac {x}{\log \left (\frac {6 \, {\left (x^{4} + x^{2} \log \left (2 \, x\right )^{2} - 4 \, x^{3} - 11 \, x^{2} + 2 \, {\left (x^{3} - 2 \, x^{2} - 9 \, x\right )} \log \left (2 \, x\right ) + 36 \, x + 81\right )}}{x^{2}}\right )} \]
[In]
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Leaf count of result is larger than twice the leaf count of optimal. 56 vs. \(2 (19) = 38\).
Time = 0.34 (sec) , antiderivative size = 56, normalized size of antiderivative = 2.07 \[ \int \frac {162+54 x+4 x^2+2 x^3-2 x^4+\left (-18 x-2 x^2-2 x^3\right ) \log (2 x)+\left (81+36 x-11 x^2-4 x^3+x^4+\left (-18 x-4 x^2+2 x^3\right ) \log (2 x)+x^2 \log ^2(2 x)\right ) \log \left (\frac {486+216 x-66 x^2-24 x^3+6 x^4+\left (-108 x-24 x^2+12 x^3\right ) \log (2 x)+6 x^2 \log ^2(2 x)}{x^2}\right )}{\left (81+36 x-11 x^2-4 x^3+x^4+\left (-18 x-4 x^2+2 x^3\right ) \log (2 x)+x^2 \log ^2(2 x)\right ) \log ^2\left (\frac {486+216 x-66 x^2-24 x^3+6 x^4+\left (-108 x-24 x^2+12 x^3\right ) \log (2 x)+6 x^2 \log ^2(2 x)}{x^2}\right )} \, dx=\frac {x}{\log {\left (\frac {6 x^{4} - 24 x^{3} + 6 x^{2} \log {\left (2 x \right )}^{2} - 66 x^{2} + 216 x + \left (12 x^{3} - 24 x^{2} - 108 x\right ) \log {\left (2 x \right )} + 486}{x^{2}} \right )}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 76 vs. \(2 (23) = 46\).
Time = 0.36 (sec) , antiderivative size = 76, normalized size of antiderivative = 2.81 \[ \int \frac {162+54 x+4 x^2+2 x^3-2 x^4+\left (-18 x-2 x^2-2 x^3\right ) \log (2 x)+\left (81+36 x-11 x^2-4 x^3+x^4+\left (-18 x-4 x^2+2 x^3\right ) \log (2 x)+x^2 \log ^2(2 x)\right ) \log \left (\frac {486+216 x-66 x^2-24 x^3+6 x^4+\left (-108 x-24 x^2+12 x^3\right ) \log (2 x)+6 x^2 \log ^2(2 x)}{x^2}\right )}{\left (81+36 x-11 x^2-4 x^3+x^4+\left (-18 x-4 x^2+2 x^3\right ) \log (2 x)+x^2 \log ^2(2 x)\right ) \log ^2\left (\frac {486+216 x-66 x^2-24 x^3+6 x^4+\left (-108 x-24 x^2+12 x^3\right ) \log (2 x)+6 x^2 \log ^2(2 x)}{x^2}\right )} \, dx=\frac {x}{\log \left (3\right ) + \log \left (2\right ) + \log \left (x^{4} + 2 \, x^{3} {\left (\log \left (2\right ) - 2\right )} + x^{2} \log \left (x\right )^{2} + {\left (\log \left (2\right )^{2} - 4 \, \log \left (2\right ) - 11\right )} x^{2} - 18 \, x {\left (\log \left (2\right ) - 2\right )} + 2 \, {\left (x^{3} + x^{2} {\left (\log \left (2\right ) - 2\right )} - 9 \, x\right )} \log \left (x\right ) + 81\right ) - 2 \, \log \left (x\right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 3434 vs. \(2 (23) = 46\).
Time = 1.25 (sec) , antiderivative size = 3434, normalized size of antiderivative = 127.19 \[ \int \frac {162+54 x+4 x^2+2 x^3-2 x^4+\left (-18 x-2 x^2-2 x^3\right ) \log (2 x)+\left (81+36 x-11 x^2-4 x^3+x^4+\left (-18 x-4 x^2+2 x^3\right ) \log (2 x)+x^2 \log ^2(2 x)\right ) \log \left (\frac {486+216 x-66 x^2-24 x^3+6 x^4+\left (-108 x-24 x^2+12 x^3\right ) \log (2 x)+6 x^2 \log ^2(2 x)}{x^2}\right )}{\left (81+36 x-11 x^2-4 x^3+x^4+\left (-18 x-4 x^2+2 x^3\right ) \log (2 x)+x^2 \log ^2(2 x)\right ) \log ^2\left (\frac {486+216 x-66 x^2-24 x^3+6 x^4+\left (-108 x-24 x^2+12 x^3\right ) \log (2 x)+6 x^2 \log ^2(2 x)}{x^2}\right )} \, dx=\text {Too large to display} \]
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Time = 8.54 (sec) , antiderivative size = 295, normalized size of antiderivative = 10.93 \[ \int \frac {162+54 x+4 x^2+2 x^3-2 x^4+\left (-18 x-2 x^2-2 x^3\right ) \log (2 x)+\left (81+36 x-11 x^2-4 x^3+x^4+\left (-18 x-4 x^2+2 x^3\right ) \log (2 x)+x^2 \log ^2(2 x)\right ) \log \left (\frac {486+216 x-66 x^2-24 x^3+6 x^4+\left (-108 x-24 x^2+12 x^3\right ) \log (2 x)+6 x^2 \log ^2(2 x)}{x^2}\right )}{\left (81+36 x-11 x^2-4 x^3+x^4+\left (-18 x-4 x^2+2 x^3\right ) \log (2 x)+x^2 \log ^2(2 x)\right ) \log ^2\left (\frac {486+216 x-66 x^2-24 x^3+6 x^4+\left (-108 x-24 x^2+12 x^3\right ) \log (2 x)+6 x^2 \log ^2(2 x)}{x^2}\right )} \, dx=\frac {x}{2}+\frac {\ln \left (x\right )}{2}+\frac {x+\frac {x\,\ln \left (\frac {216\,x-\ln \left (2\,x\right )\,\left (-12\,x^3+24\,x^2+108\,x\right )-66\,x^2-24\,x^3+6\,x^4+6\,x^2\,{\ln \left (2\,x\right )}^2+486}{x^2}\right )\,\left (x^4+2\,x^3\,\ln \left (2\,x\right )-4\,x^3+x^2\,{\ln \left (2\,x\right )}^2-4\,x^2\,\ln \left (2\,x\right )-11\,x^2-18\,x\,\ln \left (2\,x\right )+36\,x+81\right )}{2\,\left (x^2+x+9\right )\,\left (2\,x-x\,\ln \left (2\,x\right )-x^2+9\right )}}{\ln \left (\frac {216\,x-\ln \left (2\,x\right )\,\left (-12\,x^3+24\,x^2+108\,x\right )-66\,x^2-24\,x^3+6\,x^4+6\,x^2\,{\ln \left (2\,x\right )}^2+486}{x^2}\right )}-\frac {\frac {15\,x}{2}-\frac {27}{2}}{x^2+x+9}-\frac {3\,\left (x^7+2\,x^6+19\,x^5+18\,x^4+81\,x^3\right )}{2\,{\left (x^2+x+9\right )}^3\,\left (2\,x-x\,\ln \left (2\,x\right )-x^2+9\right )}-\frac {\ln \left (2\,x\right )\,\left (\frac {x}{2}+\frac {9}{2}\right )}{x^2+x+9} \]
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