Integrand size = 49, antiderivative size = 22 \[ \int \frac {72-18 x-10 x^3+3 x^4+\left (-72+4 x^2+12 x^3\right ) \log (x)}{-4 x^3+x^4+4 x^3 \log (x)} \, dx=\frac {9}{x^2}+3 x+\log (x)+\log (x-4 (1-\log (x))) \]
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Time = 0.10 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.95, number of steps used = 5, number of rules used = 3, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.061, Rules used = {6874, 14, 6816} \[ \int \frac {72-18 x-10 x^3+3 x^4+\left (-72+4 x^2+12 x^3\right ) \log (x)}{-4 x^3+x^4+4 x^3 \log (x)} \, dx=\frac {9}{x^2}+3 x+\log (x)+\log (-x-4 \log (x)+4) \]
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Rule 14
Rule 6816
Rule 6874
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {-18+x^2+3 x^3}{x^3}+\frac {4+x}{x (-4+x+4 \log (x))}\right ) \, dx \\ & = \int \frac {-18+x^2+3 x^3}{x^3} \, dx+\int \frac {4+x}{x (-4+x+4 \log (x))} \, dx \\ & = \log (4-x-4 \log (x))+\int \left (3-\frac {18}{x^3}+\frac {1}{x}\right ) \, dx \\ & = \frac {9}{x^2}+3 x+\log (x)+\log (4-x-4 \log (x)) \\ \end{align*}
Time = 0.13 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.95 \[ \int \frac {72-18 x-10 x^3+3 x^4+\left (-72+4 x^2+12 x^3\right ) \log (x)}{-4 x^3+x^4+4 x^3 \log (x)} \, dx=\frac {9}{x^2}+3 x+\log (x)+\log (4-x-4 \log (x)) \]
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Time = 0.18 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.23
method | result | size |
default | \(\frac {9+x^{2} \ln \left (x \right )+3 x^{3}}{x^{2}}+\ln \left (x -4+4 \ln \left (x \right )\right )\) | \(27\) |
norman | \(\frac {9+x^{2} \ln \left (x \right )+3 x^{3}}{x^{2}}+\ln \left (x -4+4 \ln \left (x \right )\right )\) | \(27\) |
risch | \(\frac {9+x^{2} \ln \left (x \right )+3 x^{3}}{x^{2}}+\ln \left (\frac {x}{4}+\ln \left (x \right )-1\right )\) | \(27\) |
parallelrisch | \(\frac {\ln \left (x -4+4 \ln \left (x \right )\right ) x^{2}+3 x^{3}+x^{2} \ln \left (x \right )+9}{x^{2}}\) | \(30\) |
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Time = 0.28 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.32 \[ \int \frac {72-18 x-10 x^3+3 x^4+\left (-72+4 x^2+12 x^3\right ) \log (x)}{-4 x^3+x^4+4 x^3 \log (x)} \, dx=\frac {3 \, x^{3} + x^{2} \log \left (x + 4 \, \log \left (x\right ) - 4\right ) + x^{2} \log \left (x\right ) + 9}{x^{2}} \]
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Time = 0.09 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.91 \[ \int \frac {72-18 x-10 x^3+3 x^4+\left (-72+4 x^2+12 x^3\right ) \log (x)}{-4 x^3+x^4+4 x^3 \log (x)} \, dx=3 x + \log {\left (x \right )} + \log {\left (\frac {x}{4} + \log {\left (x \right )} - 1 \right )} + \frac {9}{x^{2}} \]
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Time = 0.20 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.95 \[ \int \frac {72-18 x-10 x^3+3 x^4+\left (-72+4 x^2+12 x^3\right ) \log (x)}{-4 x^3+x^4+4 x^3 \log (x)} \, dx=\frac {3 \, {\left (x^{3} + 3\right )}}{x^{2}} + \log \left (x\right ) + \log \left (\frac {1}{4} \, x + \log \left (x\right ) - 1\right ) \]
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Time = 0.27 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.86 \[ \int \frac {72-18 x-10 x^3+3 x^4+\left (-72+4 x^2+12 x^3\right ) \log (x)}{-4 x^3+x^4+4 x^3 \log (x)} \, dx=3 \, x + \frac {9}{x^{2}} + \log \left (x + 4 \, \log \left (x\right ) - 4\right ) + \log \left (x\right ) \]
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Time = 8.64 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.86 \[ \int \frac {72-18 x-10 x^3+3 x^4+\left (-72+4 x^2+12 x^3\right ) \log (x)}{-4 x^3+x^4+4 x^3 \log (x)} \, dx=3\,x+\ln \left (\frac {x}{4}+\ln \left (x\right )-1\right )+\ln \left (x\right )+\frac {9}{x^2} \]
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