Integrand size = 45, antiderivative size = 22 \[ \int \frac {72 x+4 x^3}{1215 \log (3)+270 x^2 \log (3) \log \left (\frac {2}{x}\right )+15 x^4 \log (3) \log ^2\left (\frac {2}{x}\right )} \, dx=\frac {4}{15 \log (3) \left (\frac {9}{x^2}+\log \left (\frac {2}{x}\right )\right )} \]
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\[ \int \frac {72 x+4 x^3}{1215 \log (3)+270 x^2 \log (3) \log \left (\frac {2}{x}\right )+15 x^4 \log (3) \log ^2\left (\frac {2}{x}\right )} \, dx=\int \frac {72 x+4 x^3}{1215 \log (3)+270 x^2 \log (3) \log \left (\frac {2}{x}\right )+15 x^4 \log (3) \log ^2\left (\frac {2}{x}\right )} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {x \left (72+4 x^2\right )}{1215 \log (3)+270 x^2 \log (3) \log \left (\frac {2}{x}\right )+15 x^4 \log (3) \log ^2\left (\frac {2}{x}\right )} \, dx \\ & = \int \frac {4 x \left (18+x^2\right )}{15 \log (3) \left (9+x^2 \log \left (\frac {2}{x}\right )\right )^2} \, dx \\ & = \frac {4 \int \frac {x \left (18+x^2\right )}{\left (9+x^2 \log \left (\frac {2}{x}\right )\right )^2} \, dx}{15 \log (3)} \\ & = \frac {4 \int \left (\frac {18 x}{\left (9+x^2 \log \left (\frac {2}{x}\right )\right )^2}+\frac {x^3}{\left (9+x^2 \log \left (\frac {2}{x}\right )\right )^2}\right ) \, dx}{15 \log (3)} \\ & = \frac {4 \int \frac {x^3}{\left (9+x^2 \log \left (\frac {2}{x}\right )\right )^2} \, dx}{15 \log (3)}+\frac {24 \int \frac {x}{\left (9+x^2 \log \left (\frac {2}{x}\right )\right )^2} \, dx}{5 \log (3)} \\ \end{align*}
Time = 0.10 (sec) , antiderivative size = 25, normalized size of antiderivative = 1.14 \[ \int \frac {72 x+4 x^3}{1215 \log (3)+270 x^2 \log (3) \log \left (\frac {2}{x}\right )+15 x^4 \log (3) \log ^2\left (\frac {2}{x}\right )} \, dx=\frac {4 x^2}{15 \log (3) \left (9+x^2 \log \left (\frac {2}{x}\right )\right )} \]
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Time = 4.29 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.05
method | result | size |
derivativedivides | \(\frac {16}{15 \ln \left (3\right ) \left (\frac {36}{x^{2}}+4 \ln \left (\frac {2}{x}\right )\right )}\) | \(23\) |
default | \(\frac {16}{15 \ln \left (3\right ) \left (\frac {36}{x^{2}}+4 \ln \left (\frac {2}{x}\right )\right )}\) | \(23\) |
norman | \(\frac {4 x^{2}}{15 \ln \left (3\right ) \left (x^{2} \ln \left (\frac {2}{x}\right )+9\right )}\) | \(24\) |
risch | \(\frac {4 x^{2}}{15 \ln \left (3\right ) \left (x^{2} \ln \left (\frac {2}{x}\right )+9\right )}\) | \(24\) |
parallelrisch | \(\frac {4 x^{2}}{15 \ln \left (3\right ) \left (x^{2} \ln \left (\frac {2}{x}\right )+9\right )}\) | \(24\) |
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Time = 0.24 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.09 \[ \int \frac {72 x+4 x^3}{1215 \log (3)+270 x^2 \log (3) \log \left (\frac {2}{x}\right )+15 x^4 \log (3) \log ^2\left (\frac {2}{x}\right )} \, dx=\frac {4 \, x^{2}}{15 \, {\left (x^{2} \log \left (3\right ) \log \left (\frac {2}{x}\right ) + 9 \, \log \left (3\right )\right )}} \]
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Time = 0.07 (sec) , antiderivative size = 22, normalized size of antiderivative = 1.00 \[ \int \frac {72 x+4 x^3}{1215 \log (3)+270 x^2 \log (3) \log \left (\frac {2}{x}\right )+15 x^4 \log (3) \log ^2\left (\frac {2}{x}\right )} \, dx=\frac {4 x^{2}}{15 x^{2} \log {\left (3 \right )} \log {\left (\frac {2}{x} \right )} + 135 \log {\left (3 \right )}} \]
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Time = 0.31 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.32 \[ \int \frac {72 x+4 x^3}{1215 \log (3)+270 x^2 \log (3) \log \left (\frac {2}{x}\right )+15 x^4 \log (3) \log ^2\left (\frac {2}{x}\right )} \, dx=\frac {4 \, x^{2}}{15 \, {\left (x^{2} \log \left (3\right ) \log \left (2\right ) - x^{2} \log \left (3\right ) \log \left (x\right ) + 9 \, \log \left (3\right )\right )}} \]
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Time = 0.25 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.95 \[ \int \frac {72 x+4 x^3}{1215 \log (3)+270 x^2 \log (3) \log \left (\frac {2}{x}\right )+15 x^4 \log (3) \log ^2\left (\frac {2}{x}\right )} \, dx=\frac {4}{15 \, {\left (\log \left (3\right ) \log \left (\frac {2}{x}\right ) + \frac {9 \, \log \left (3\right )}{x^{2}}\right )}} \]
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Time = 9.21 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.05 \[ \int \frac {72 x+4 x^3}{1215 \log (3)+270 x^2 \log (3) \log \left (\frac {2}{x}\right )+15 x^4 \log (3) \log ^2\left (\frac {2}{x}\right )} \, dx=\frac {4\,x^2}{15\,\ln \left (3\right )\,\left (x^2\,\ln \left (\frac {2}{x}\right )+9\right )} \]
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