Integrand size = 111, antiderivative size = 29 \[ \int \frac {36-108 x+216 x^2-126 x^3-72 x^5-18 x^6}{\left (3 x-12 x^2+36 x^3-42 x^4+43 x^5+24 x^6+3 x^7+x^5 \log (2)\right ) \log ^2\left (\frac {3-12 x+36 x^2-42 x^3+43 x^4+24 x^5+3 x^6+x^4 \log (2)}{x^4}\right )} \, dx=\frac {3}{\log \left (4+3 \left (1+\left (3+\frac {(1-x)^2}{x^2}+x\right )^2\right )+\log (2)\right )} \]
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Time = 0.13 (sec) , antiderivative size = 45, normalized size of antiderivative = 1.55, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.018, Rules used = {6, 6818} \[ \int \frac {36-108 x+216 x^2-126 x^3-72 x^5-18 x^6}{\left (3 x-12 x^2+36 x^3-42 x^4+43 x^5+24 x^6+3 x^7+x^5 \log (2)\right ) \log ^2\left (\frac {3-12 x+36 x^2-42 x^3+43 x^4+24 x^5+3 x^6+x^4 \log (2)}{x^4}\right )} \, dx=\frac {3}{\log \left (\frac {3 x^6+24 x^5+43 x^4+x^4 \log (2)-42 x^3+36 x^2-12 x+3}{x^4}\right )} \]
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Rule 6
Rule 6818
Rubi steps \begin{align*} \text {integral}& = \int \frac {36-108 x+216 x^2-126 x^3-72 x^5-18 x^6}{\left (3 x-12 x^2+36 x^3-42 x^4+24 x^6+3 x^7+x^5 (43+\log (2))\right ) \log ^2\left (\frac {3-12 x+36 x^2-42 x^3+43 x^4+24 x^5+3 x^6+x^4 \log (2)}{x^4}\right )} \, dx \\ & = \frac {3}{\log \left (\frac {3-12 x+36 x^2-42 x^3+43 x^4+24 x^5+3 x^6+x^4 \log (2)}{x^4}\right )} \\ \end{align*}
Time = 0.04 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.28 \[ \int \frac {36-108 x+216 x^2-126 x^3-72 x^5-18 x^6}{\left (3 x-12 x^2+36 x^3-42 x^4+43 x^5+24 x^6+3 x^7+x^5 \log (2)\right ) \log ^2\left (\frac {3-12 x+36 x^2-42 x^3+43 x^4+24 x^5+3 x^6+x^4 \log (2)}{x^4}\right )} \, dx=\frac {3}{\log \left (43+\frac {3}{x^4}-\frac {12}{x^3}+\frac {36}{x^2}-\frac {42}{x}+24 x+3 x^2+\log (2)\right )} \]
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Time = 0.78 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.59
method | result | size |
default | \(\frac {3}{\ln \left (\frac {x^{4} \ln \left (2\right )+3 x^{6}+24 x^{5}+43 x^{4}-42 x^{3}+36 x^{2}-12 x +3}{x^{4}}\right )}\) | \(46\) |
norman | \(\frac {3}{\ln \left (\frac {x^{4} \ln \left (2\right )+3 x^{6}+24 x^{5}+43 x^{4}-42 x^{3}+36 x^{2}-12 x +3}{x^{4}}\right )}\) | \(46\) |
risch | \(\frac {3}{\ln \left (\frac {x^{4} \ln \left (2\right )+3 x^{6}+24 x^{5}+43 x^{4}-42 x^{3}+36 x^{2}-12 x +3}{x^{4}}\right )}\) | \(46\) |
parallelrisch | \(\frac {3}{\ln \left (\frac {x^{4} \ln \left (2\right )+3 x^{6}+24 x^{5}+43 x^{4}-42 x^{3}+36 x^{2}-12 x +3}{x^{4}}\right )}\) | \(46\) |
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Time = 0.25 (sec) , antiderivative size = 45, normalized size of antiderivative = 1.55 \[ \int \frac {36-108 x+216 x^2-126 x^3-72 x^5-18 x^6}{\left (3 x-12 x^2+36 x^3-42 x^4+43 x^5+24 x^6+3 x^7+x^5 \log (2)\right ) \log ^2\left (\frac {3-12 x+36 x^2-42 x^3+43 x^4+24 x^5+3 x^6+x^4 \log (2)}{x^4}\right )} \, dx=\frac {3}{\log \left (\frac {3 \, x^{6} + 24 \, x^{5} + x^{4} \log \left (2\right ) + 43 \, x^{4} - 42 \, x^{3} + 36 \, x^{2} - 12 \, x + 3}{x^{4}}\right )} \]
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Time = 0.09 (sec) , antiderivative size = 42, normalized size of antiderivative = 1.45 \[ \int \frac {36-108 x+216 x^2-126 x^3-72 x^5-18 x^6}{\left (3 x-12 x^2+36 x^3-42 x^4+43 x^5+24 x^6+3 x^7+x^5 \log (2)\right ) \log ^2\left (\frac {3-12 x+36 x^2-42 x^3+43 x^4+24 x^5+3 x^6+x^4 \log (2)}{x^4}\right )} \, dx=\frac {3}{\log {\left (\frac {3 x^{6} + 24 x^{5} + x^{4} \log {\left (2 \right )} + 43 x^{4} - 42 x^{3} + 36 x^{2} - 12 x + 3}{x^{4}} \right )}} \]
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Time = 0.31 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.48 \[ \int \frac {36-108 x+216 x^2-126 x^3-72 x^5-18 x^6}{\left (3 x-12 x^2+36 x^3-42 x^4+43 x^5+24 x^6+3 x^7+x^5 \log (2)\right ) \log ^2\left (\frac {3-12 x+36 x^2-42 x^3+43 x^4+24 x^5+3 x^6+x^4 \log (2)}{x^4}\right )} \, dx=\frac {3}{\log \left (3 \, x^{6} + 24 \, x^{5} + x^{4} {\left (\log \left (2\right ) + 43\right )} - 42 \, x^{3} + 36 \, x^{2} - 12 \, x + 3\right ) - 4 \, \log \left (x\right )} \]
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Time = 0.36 (sec) , antiderivative size = 48, normalized size of antiderivative = 1.66 \[ \int \frac {36-108 x+216 x^2-126 x^3-72 x^5-18 x^6}{\left (3 x-12 x^2+36 x^3-42 x^4+43 x^5+24 x^6+3 x^7+x^5 \log (2)\right ) \log ^2\left (\frac {3-12 x+36 x^2-42 x^3+43 x^4+24 x^5+3 x^6+x^4 \log (2)}{x^4}\right )} \, dx=\frac {3}{\log \left (3 \, x^{6} + 24 \, x^{5} + x^{4} \log \left (2\right ) + 43 \, x^{4} - 42 \, x^{3} + 36 \, x^{2} - 12 \, x + 3\right ) - \log \left (x^{4}\right )} \]
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Time = 7.83 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.59 \[ \int \frac {36-108 x+216 x^2-126 x^3-72 x^5-18 x^6}{\left (3 x-12 x^2+36 x^3-42 x^4+43 x^5+24 x^6+3 x^7+x^5 \log (2)\right ) \log ^2\left (\frac {3-12 x+36 x^2-42 x^3+43 x^4+24 x^5+3 x^6+x^4 \log (2)}{x^4}\right )} \, dx=\frac {3}{\ln \left (\frac {1}{x^4}\right )+\ln \left (x^4\,\ln \left (2\right )-12\,x+36\,x^2-42\,x^3+43\,x^4+24\,x^5+3\,x^6+3\right )} \]
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