Integrand size = 33, antiderivative size = 29 \[ \int \frac {9-12 x-x^2+2 x^5}{-3 x+6 x^2+x^3+x^6} \, dx=\log \left (3 e^2 \left (\frac {1+\frac {5+\frac {-3+x}{x}}{x}}{x}+x^2\right )\right ) \]
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Time = 0.03 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.72, number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.061, Rules used = {2099, 1601} \[ \int \frac {9-12 x-x^2+2 x^5}{-3 x+6 x^2+x^3+x^6} \, dx=\log \left (-x^5-x^2-6 x+3\right )-3 \log (x) \]
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Rule 1601
Rule 2099
Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {3}{x}+\frac {6+2 x+5 x^4}{-3+6 x+x^2+x^5}\right ) \, dx \\ & = -3 \log (x)+\int \frac {6+2 x+5 x^4}{-3+6 x+x^2+x^5} \, dx \\ & = -3 \log (x)+\log \left (3-6 x-x^2-x^5\right ) \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.72 \[ \int \frac {9-12 x-x^2+2 x^5}{-3 x+6 x^2+x^3+x^6} \, dx=-3 \log (x)+\log \left (3-6 x-x^2-x^5\right ) \]
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Time = 0.04 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.62
method | result | size |
default | \(\ln \left (x^{5}+x^{2}+6 x -3\right )-3 \ln \left (x \right )\) | \(18\) |
norman | \(\ln \left (x^{5}+x^{2}+6 x -3\right )-3 \ln \left (x \right )\) | \(18\) |
risch | \(\ln \left (x^{5}+x^{2}+6 x -3\right )-3 \ln \left (x \right )\) | \(18\) |
parallelrisch | \(\ln \left (x^{5}+x^{2}+6 x -3\right )-3 \ln \left (x \right )\) | \(18\) |
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none
Time = 0.23 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.59 \[ \int \frac {9-12 x-x^2+2 x^5}{-3 x+6 x^2+x^3+x^6} \, dx=\log \left (x^{5} + x^{2} + 6 \, x - 3\right ) - 3 \, \log \left (x\right ) \]
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Time = 0.05 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.59 \[ \int \frac {9-12 x-x^2+2 x^5}{-3 x+6 x^2+x^3+x^6} \, dx=- 3 \log {\left (x \right )} + \log {\left (x^{5} + x^{2} + 6 x - 3 \right )} \]
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none
Time = 0.21 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.59 \[ \int \frac {9-12 x-x^2+2 x^5}{-3 x+6 x^2+x^3+x^6} \, dx=\log \left (x^{5} + x^{2} + 6 \, x - 3\right ) - 3 \, \log \left (x\right ) \]
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none
Time = 0.26 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.66 \[ \int \frac {9-12 x-x^2+2 x^5}{-3 x+6 x^2+x^3+x^6} \, dx=\log \left ({\left | x^{5} + x^{2} + 6 \, x - 3 \right |}\right ) - 3 \, \log \left ({\left | x \right |}\right ) \]
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Time = 9.39 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.59 \[ \int \frac {9-12 x-x^2+2 x^5}{-3 x+6 x^2+x^3+x^6} \, dx=\ln \left (x^5+x^2+6\,x-3\right )-3\,\ln \left (x\right ) \]
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