Integrand size = 32, antiderivative size = 24 \[ \int \frac {18+18 x-15 x^2+2 x^3}{18 x-13 x^2+2 x^3} \, dx=-4+x+\log \left (\frac {x}{3 (-3+(5-x) (-3+2 x))}\right ) \]
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Time = 0.03 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.83, number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.062, Rules used = {1608, 1642} \[ \int \frac {18+18 x-15 x^2+2 x^3}{18 x-13 x^2+2 x^3} \, dx=x-\log (9-2 x)-\log (2-x)+\log (x) \]
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Rule 1608
Rule 1642
Rubi steps \begin{align*} \text {integral}& = \int \frac {18+18 x-15 x^2+2 x^3}{x \left (18-13 x+2 x^2\right )} \, dx \\ & = \int \left (1+\frac {1}{2-x}+\frac {1}{x}-\frac {2}{-9+2 x}\right ) \, dx \\ & = x-\log (9-2 x)-\log (2-x)+\log (x) \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.71 \[ \int \frac {18+18 x-15 x^2+2 x^3}{18 x-13 x^2+2 x^3} \, dx=x+\log (x)-\log \left (18-13 x+2 x^2\right ) \]
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Time = 0.08 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.71
method | result | size |
parallelrisch | \(x +\ln \left (x \right )-\ln \left (-2+x \right )-\ln \left (x -\frac {9}{2}\right )\) | \(17\) |
risch | \(x +\ln \left (x \right )-\ln \left (2 x^{2}-13 x +18\right )\) | \(18\) |
default | \(x +\ln \left (x \right )-\ln \left (2 x -9\right )-\ln \left (-2+x \right )\) | \(19\) |
norman | \(x +\ln \left (x \right )-\ln \left (2 x -9\right )-\ln \left (-2+x \right )\) | \(19\) |
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none
Time = 0.25 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.71 \[ \int \frac {18+18 x-15 x^2+2 x^3}{18 x-13 x^2+2 x^3} \, dx=x - \log \left (2 \, x^{2} - 13 \, x + 18\right ) + \log \left (x\right ) \]
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Time = 0.06 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.62 \[ \int \frac {18+18 x-15 x^2+2 x^3}{18 x-13 x^2+2 x^3} \, dx=x + \log {\left (x \right )} - \log {\left (2 x^{2} - 13 x + 18 \right )} \]
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none
Time = 0.19 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.75 \[ \int \frac {18+18 x-15 x^2+2 x^3}{18 x-13 x^2+2 x^3} \, dx=x - \log \left (2 \, x - 9\right ) - \log \left (x - 2\right ) + \log \left (x\right ) \]
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none
Time = 0.26 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.88 \[ \int \frac {18+18 x-15 x^2+2 x^3}{18 x-13 x^2+2 x^3} \, dx=x - \log \left ({\left | 2 \, x - 9 \right |}\right ) - \log \left ({\left | x - 2 \right |}\right ) + \log \left ({\left | x \right |}\right ) \]
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Time = 0.09 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.62 \[ \int \frac {18+18 x-15 x^2+2 x^3}{18 x-13 x^2+2 x^3} \, dx=x-\ln \left (x^2-\frac {13\,x}{2}+9\right )+\ln \left (x\right ) \]
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