Integrand size = 34, antiderivative size = 26 \[ \int \frac {25-7 x-18 x^2-27 x^3+18 x^4}{-9 x^2+9 x^3} \, dx=\frac {25}{9 x}-x+x^2-\log \left ((1-x) x^2\right ) \]
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Time = 0.03 (sec) , antiderivative size = 26, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.059, Rules used = {1607, 1634} \[ \int \frac {25-7 x-18 x^2-27 x^3+18 x^4}{-9 x^2+9 x^3} \, dx=x^2-x+\frac {25}{9 x}-\log (1-x)-2 \log (x) \]
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Rule 1607
Rule 1634
Rubi steps \begin{align*} \text {integral}& = \int \frac {25-7 x-18 x^2-27 x^3+18 x^4}{x^2 (-9+9 x)} \, dx \\ & = \int \left (-1+\frac {1}{1-x}-\frac {25}{9 x^2}-\frac {2}{x}+2 x\right ) \, dx \\ & = \frac {25}{9 x}-x+x^2-\log (1-x)-2 \log (x) \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.15 \[ \int \frac {25-7 x-18 x^2-27 x^3+18 x^4}{-9 x^2+9 x^3} \, dx=\frac {1}{9} \left (\frac {25}{x}-9 x+9 x^2-9 \log (1-x)-18 \log (x)\right ) \]
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Time = 1.63 (sec) , antiderivative size = 23, normalized size of antiderivative = 0.88
method | result | size |
default | \(x^{2}-x +\frac {25}{9 x}-2 \ln \left (x \right )-\ln \left (-1+x \right )\) | \(23\) |
risch | \(x^{2}-x +\frac {25}{9 x}-2 \ln \left (x \right )-\ln \left (-1+x \right )\) | \(23\) |
norman | \(\frac {\frac {25}{9}+x^{3}-x^{2}}{x}-2 \ln \left (x \right )-\ln \left (-1+x \right )\) | \(26\) |
parallelrisch | \(-\frac {-9 x^{3}+18 x \ln \left (x \right )+9 \ln \left (-1+x \right ) x +9 x^{2}-25}{9 x}\) | \(30\) |
meijerg | \(\frac {25}{9 x}-2 \ln \left (x \right )-2 i \pi -\ln \left (1-x \right )+\frac {x \left (6+3 x \right )}{3}-3 x\) | \(34\) |
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Time = 0.25 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.12 \[ \int \frac {25-7 x-18 x^2-27 x^3+18 x^4}{-9 x^2+9 x^3} \, dx=\frac {9 \, x^{3} - 9 \, x^{2} - 9 \, x \log \left (x - 1\right ) - 18 \, x \log \left (x\right ) + 25}{9 \, x} \]
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Time = 0.06 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.73 \[ \int \frac {25-7 x-18 x^2-27 x^3+18 x^4}{-9 x^2+9 x^3} \, dx=x^{2} - x - 2 \log {\left (x \right )} - \log {\left (x - 1 \right )} + \frac {25}{9 x} \]
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Time = 0.18 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.85 \[ \int \frac {25-7 x-18 x^2-27 x^3+18 x^4}{-9 x^2+9 x^3} \, dx=x^{2} - x + \frac {25}{9 \, x} - \log \left (x - 1\right ) - 2 \, \log \left (x\right ) \]
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Time = 0.26 (sec) , antiderivative size = 24, normalized size of antiderivative = 0.92 \[ \int \frac {25-7 x-18 x^2-27 x^3+18 x^4}{-9 x^2+9 x^3} \, dx=x^{2} - x + \frac {25}{9 \, x} - \log \left ({\left | x - 1 \right |}\right ) - 2 \, \log \left ({\left | x \right |}\right ) \]
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Time = 0.05 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.85 \[ \int \frac {25-7 x-18 x^2-27 x^3+18 x^4}{-9 x^2+9 x^3} \, dx=\frac {25}{9\,x}-\ln \left (x-1\right )-2\,\ln \left (x\right )-x+x^2 \]
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