Integrand size = 84, antiderivative size = 26 \[ \int \frac {9-3 x-3 x^2+\left (-3 x-6 x^2\right ) \log (x)+\left (144 x^2-96 x^3-80 x^4+32 x^5+16 x^6\right ) \log ^2(x)}{\left (180 x-120 x^2-100 x^3+40 x^4+20 x^5\right ) \log ^2(x)} \, dx=\frac {2}{5} x \left (x+\frac {3}{8 x \left (-3+x+x^2\right ) \log (x)}\right ) \]
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\[ \int \frac {9-3 x-3 x^2+\left (-3 x-6 x^2\right ) \log (x)+\left (144 x^2-96 x^3-80 x^4+32 x^5+16 x^6\right ) \log ^2(x)}{\left (180 x-120 x^2-100 x^3+40 x^4+20 x^5\right ) \log ^2(x)} \, dx=\int \frac {9-3 x-3 x^2+\left (-3 x-6 x^2\right ) \log (x)+\left (144 x^2-96 x^3-80 x^4+32 x^5+16 x^6\right ) \log ^2(x)}{\left (180 x-120 x^2-100 x^3+40 x^4+20 x^5\right ) \log ^2(x)} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {1}{20} \left (16 x-\frac {3}{x \left (-3+x+x^2\right ) \log ^2(x)}-\frac {3 (1+2 x)}{\left (-3+x+x^2\right )^2 \log (x)}\right ) \, dx \\ & = \frac {1}{20} \int \left (16 x-\frac {3}{x \left (-3+x+x^2\right ) \log ^2(x)}-\frac {3 (1+2 x)}{\left (-3+x+x^2\right )^2 \log (x)}\right ) \, dx \\ & = \frac {2 x^2}{5}-\frac {3}{20} \int \frac {1}{x \left (-3+x+x^2\right ) \log ^2(x)} \, dx-\frac {3}{20} \int \frac {1+2 x}{\left (-3+x+x^2\right )^2 \log (x)} \, dx \\ \end{align*}
Time = 1.97 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.92 \[ \int \frac {9-3 x-3 x^2+\left (-3 x-6 x^2\right ) \log (x)+\left (144 x^2-96 x^3-80 x^4+32 x^5+16 x^6\right ) \log ^2(x)}{\left (180 x-120 x^2-100 x^3+40 x^4+20 x^5\right ) \log ^2(x)} \, dx=\frac {1}{20} \left (8 x^2+\frac {3}{\left (-3+x+x^2\right ) \log (x)}\right ) \]
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Time = 7.83 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.81
method | result | size |
risch | \(\frac {2 x^{2}}{5}+\frac {3}{20 \left (x^{2}+x -3\right ) \ln \left (x \right )}\) | \(21\) |
norman | \(\frac {\frac {3}{20}-\frac {18 \ln \left (x \right )}{5}+\frac {6 x \ln \left (x \right )}{5}+\frac {2 x^{3} \ln \left (x \right )}{5}+\frac {2 x^{4} \ln \left (x \right )}{5}}{\left (x^{2}+x -3\right ) \ln \left (x \right )}\) | \(39\) |
default | \(\frac {3-72 \ln \left (x \right )+24 x \ln \left (x \right )+8 x^{3} \ln \left (x \right )+8 x^{4} \ln \left (x \right )}{20 \left (x^{2}+x -3\right ) \ln \left (x \right )}\) | \(40\) |
parallelrisch | \(\frac {3-72 \ln \left (x \right )+24 x \ln \left (x \right )+8 x^{3} \ln \left (x \right )+8 x^{4} \ln \left (x \right )}{20 \left (x^{2}+x -3\right ) \ln \left (x \right )}\) | \(40\) |
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Time = 0.24 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.23 \[ \int \frac {9-3 x-3 x^2+\left (-3 x-6 x^2\right ) \log (x)+\left (144 x^2-96 x^3-80 x^4+32 x^5+16 x^6\right ) \log ^2(x)}{\left (180 x-120 x^2-100 x^3+40 x^4+20 x^5\right ) \log ^2(x)} \, dx=\frac {8 \, {\left (x^{4} + x^{3} - 3 \, x^{2}\right )} \log \left (x\right ) + 3}{20 \, {\left (x^{2} + x - 3\right )} \log \left (x\right )} \]
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Time = 0.06 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.77 \[ \int \frac {9-3 x-3 x^2+\left (-3 x-6 x^2\right ) \log (x)+\left (144 x^2-96 x^3-80 x^4+32 x^5+16 x^6\right ) \log ^2(x)}{\left (180 x-120 x^2-100 x^3+40 x^4+20 x^5\right ) \log ^2(x)} \, dx=\frac {2 x^{2}}{5} + \frac {3}{\left (20 x^{2} + 20 x - 60\right ) \log {\left (x \right )}} \]
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Time = 0.22 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.23 \[ \int \frac {9-3 x-3 x^2+\left (-3 x-6 x^2\right ) \log (x)+\left (144 x^2-96 x^3-80 x^4+32 x^5+16 x^6\right ) \log ^2(x)}{\left (180 x-120 x^2-100 x^3+40 x^4+20 x^5\right ) \log ^2(x)} \, dx=\frac {8 \, {\left (x^{4} + x^{3} - 3 \, x^{2}\right )} \log \left (x\right ) + 3}{20 \, {\left (x^{2} + x - 3\right )} \log \left (x\right )} \]
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Time = 0.28 (sec) , antiderivative size = 25, normalized size of antiderivative = 0.96 \[ \int \frac {9-3 x-3 x^2+\left (-3 x-6 x^2\right ) \log (x)+\left (144 x^2-96 x^3-80 x^4+32 x^5+16 x^6\right ) \log ^2(x)}{\left (180 x-120 x^2-100 x^3+40 x^4+20 x^5\right ) \log ^2(x)} \, dx=\frac {2}{5} \, x^{2} + \frac {3}{20 \, {\left (x^{2} \log \left (x\right ) + x \log \left (x\right ) - 3 \, \log \left (x\right )\right )}} \]
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Time = 13.46 (sec) , antiderivative size = 40, normalized size of antiderivative = 1.54 \[ \int \frac {9-3 x-3 x^2+\left (-3 x-6 x^2\right ) \log (x)+\left (144 x^2-96 x^3-80 x^4+32 x^5+16 x^6\right ) \log ^2(x)}{\left (180 x-120 x^2-100 x^3+40 x^4+20 x^5\right ) \log ^2(x)} \, dx=\frac {\frac {2\,x^4}{5}+\frac {2\,x^3}{5}-\frac {6\,x^2}{5}}{x^2+x-3}+\frac {3}{20\,\ln \left (x\right )\,\left (x^2+x-3\right )} \]
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