Integrand size = 77, antiderivative size = 23 \[ \int \frac {-729 x+162 x^3+729 x \log (x)}{729 x^3-972 x^4+432 x^5-64 x^6+\left (4374 x^2-3888 x^3+864 x^4\right ) \log (x)+\left (8748 x-3888 x^2\right ) \log ^2(x)+5832 \log ^3(x)} \, dx=\frac {x^2}{\left (-2 x-\frac {8 x^2}{9}+4 (x+\log (x))\right )^2} \]
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\[ \int \frac {-729 x+162 x^3+729 x \log (x)}{729 x^3-972 x^4+432 x^5-64 x^6+\left (4374 x^2-3888 x^3+864 x^4\right ) \log (x)+\left (8748 x-3888 x^2\right ) \log ^2(x)+5832 \log ^3(x)} \, dx=\int \frac {-729 x+162 x^3+729 x \log (x)}{729 x^3-972 x^4+432 x^5-64 x^6+\left (4374 x^2-3888 x^3+864 x^4\right ) \log (x)+\left (8748 x-3888 x^2\right ) \log ^2(x)+5832 \log ^3(x)} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {81 x \left (9-2 x^2-9 \log (x)\right )}{(x (-9+4 x)-18 \log (x))^3} \, dx \\ & = 81 \int \frac {x \left (9-2 x^2-9 \log (x)\right )}{(x (-9+4 x)-18 \log (x))^3} \, dx \\ & = 81 \int \left (-\frac {x \left (-18-9 x+8 x^2\right )}{2 \left (-9 x+4 x^2-18 \log (x)\right )^3}+\frac {x}{2 \left (-9 x+4 x^2-18 \log (x)\right )^2}\right ) \, dx \\ & = -\left (\frac {81}{2} \int \frac {x \left (-18-9 x+8 x^2\right )}{\left (-9 x+4 x^2-18 \log (x)\right )^3} \, dx\right )+\frac {81}{2} \int \frac {x}{\left (-9 x+4 x^2-18 \log (x)\right )^2} \, dx \\ & = -\left (\frac {81}{2} \int \left (-\frac {18 x}{\left (-9 x+4 x^2-18 \log (x)\right )^3}-\frac {9 x^2}{\left (-9 x+4 x^2-18 \log (x)\right )^3}+\frac {8 x^3}{\left (-9 x+4 x^2-18 \log (x)\right )^3}\right ) \, dx\right )+\frac {81}{2} \int \frac {x}{\left (-9 x+4 x^2-18 \log (x)\right )^2} \, dx \\ & = \frac {81}{2} \int \frac {x}{\left (-9 x+4 x^2-18 \log (x)\right )^2} \, dx-324 \int \frac {x^3}{\left (-9 x+4 x^2-18 \log (x)\right )^3} \, dx+\frac {729}{2} \int \frac {x^2}{\left (-9 x+4 x^2-18 \log (x)\right )^3} \, dx+729 \int \frac {x}{\left (-9 x+4 x^2-18 \log (x)\right )^3} \, dx \\ \end{align*}
Time = 0.16 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.96 \[ \int \frac {-729 x+162 x^3+729 x \log (x)}{729 x^3-972 x^4+432 x^5-64 x^6+\left (4374 x^2-3888 x^3+864 x^4\right ) \log (x)+\left (8748 x-3888 x^2\right ) \log ^2(x)+5832 \log ^3(x)} \, dx=\frac {81 x^2}{4 \left (9 x-4 x^2+18 \log (x)\right )^2} \]
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Time = 0.71 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.91
method | result | size |
default | \(\frac {81 x^{2}}{4 \left (-4 x^{2}+18 \ln \left (x \right )+9 x \right )^{2}}\) | \(21\) |
risch | \(\frac {81 x^{2}}{4 \left (4 x^{2}-9 x -18 \ln \left (x \right )\right )^{2}}\) | \(21\) |
parallelrisch | \(\frac {81 x^{2}}{4 \left (16 x^{4}-72 x^{3}-144 x^{2} \ln \left (x \right )+81 x^{2}+324 x \ln \left (x \right )+324 \ln \left (x \right )^{2}\right )}\) | \(42\) |
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Leaf count of result is larger than twice the leaf count of optimal. 42 vs. \(2 (20) = 40\).
Time = 0.24 (sec) , antiderivative size = 42, normalized size of antiderivative = 1.83 \[ \int \frac {-729 x+162 x^3+729 x \log (x)}{729 x^3-972 x^4+432 x^5-64 x^6+\left (4374 x^2-3888 x^3+864 x^4\right ) \log (x)+\left (8748 x-3888 x^2\right ) \log ^2(x)+5832 \log ^3(x)} \, dx=\frac {81 \, x^{2}}{4 \, {\left (16 \, x^{4} - 72 \, x^{3} + 81 \, x^{2} - 36 \, {\left (4 \, x^{2} - 9 \, x\right )} \log \left (x\right ) + 324 \, \log \left (x\right )^{2}\right )}} \]
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Time = 0.09 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.61 \[ \int \frac {-729 x+162 x^3+729 x \log (x)}{729 x^3-972 x^4+432 x^5-64 x^6+\left (4374 x^2-3888 x^3+864 x^4\right ) \log (x)+\left (8748 x-3888 x^2\right ) \log ^2(x)+5832 \log ^3(x)} \, dx=\frac {81 x^{2}}{64 x^{4} - 288 x^{3} + 324 x^{2} + \left (- 576 x^{2} + 1296 x\right ) \log {\left (x \right )} + 1296 \log {\left (x \right )}^{2}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 42 vs. \(2 (20) = 40\).
Time = 0.21 (sec) , antiderivative size = 42, normalized size of antiderivative = 1.83 \[ \int \frac {-729 x+162 x^3+729 x \log (x)}{729 x^3-972 x^4+432 x^5-64 x^6+\left (4374 x^2-3888 x^3+864 x^4\right ) \log (x)+\left (8748 x-3888 x^2\right ) \log ^2(x)+5832 \log ^3(x)} \, dx=\frac {81 \, x^{2}}{4 \, {\left (16 \, x^{4} - 72 \, x^{3} + 81 \, x^{2} - 36 \, {\left (4 \, x^{2} - 9 \, x\right )} \log \left (x\right ) + 324 \, \log \left (x\right )^{2}\right )}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 94 vs. \(2 (20) = 40\).
Time = 0.27 (sec) , antiderivative size = 94, normalized size of antiderivative = 4.09 \[ \int \frac {-729 x+162 x^3+729 x \log (x)}{729 x^3-972 x^4+432 x^5-64 x^6+\left (4374 x^2-3888 x^3+864 x^4\right ) \log (x)+\left (8748 x-3888 x^2\right ) \log ^2(x)+5832 \log ^3(x)} \, dx=\frac {81 \, {\left (8 \, x^{4} - 9 \, x^{3} - 18 \, x^{2}\right )}}{4 \, {\left (128 \, x^{6} - 720 \, x^{5} - 1152 \, x^{4} \log \left (x\right ) + 1008 \, x^{4} + 3888 \, x^{3} \log \left (x\right ) + 2592 \, x^{2} \log \left (x\right )^{2} + 567 \, x^{3} - 324 \, x^{2} \log \left (x\right ) - 2916 \, x \log \left (x\right )^{2} - 1458 \, x^{2} - 5832 \, x \log \left (x\right ) - 5832 \, \log \left (x\right )^{2}\right )}} \]
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Timed out. \[ \int \frac {-729 x+162 x^3+729 x \log (x)}{729 x^3-972 x^4+432 x^5-64 x^6+\left (4374 x^2-3888 x^3+864 x^4\right ) \log (x)+\left (8748 x-3888 x^2\right ) \log ^2(x)+5832 \log ^3(x)} \, dx=\int \frac {729\,x\,\ln \left (x\right )-729\,x+162\,x^3}{{\ln \left (x\right )}^2\,\left (8748\,x-3888\,x^2\right )+5832\,{\ln \left (x\right )}^3+\ln \left (x\right )\,\left (864\,x^4-3888\,x^3+4374\,x^2\right )+729\,x^3-972\,x^4+432\,x^5-64\,x^6} \,d x \]
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