Integrand size = 28, antiderivative size = 22 \[ \int \frac {-17-10 x+9 x^2}{9-17 x-5 x^2+3 x^3} \, dx=\log \left (2 \left (3-x+x \left (2+x^2-\frac {5 (4+x)}{3}\right )\right )\right ) \]
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Time = 0.01 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.73, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.036, Rules used = {1601} \[ \int \frac {-17-10 x+9 x^2}{9-17 x-5 x^2+3 x^3} \, dx=\log \left (3 x^3-5 x^2-17 x+9\right ) \]
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Rule 1601
Rubi steps \begin{align*} \text {integral}& = \log \left (9-17 x-5 x^2+3 x^3\right ) \\ \end{align*}
Time = 0.01 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.73 \[ \int \frac {-17-10 x+9 x^2}{9-17 x-5 x^2+3 x^3} \, dx=\log \left (9-17 x-5 x^2+3 x^3\right ) \]
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Time = 0.14 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.68
method | result | size |
parallelrisch | \(\ln \left (x^{3}-\frac {5}{3} x^{2}-\frac {17}{3} x +3\right )\) | \(15\) |
derivativedivides | \(\ln \left (3 x^{3}-5 x^{2}-17 x +9\right )\) | \(17\) |
default | \(\ln \left (3 x^{3}-5 x^{2}-17 x +9\right )\) | \(17\) |
norman | \(\ln \left (3 x^{3}-5 x^{2}-17 x +9\right )\) | \(17\) |
risch | \(\ln \left (3 x^{3}-5 x^{2}-17 x +9\right )\) | \(17\) |
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Time = 0.26 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.73 \[ \int \frac {-17-10 x+9 x^2}{9-17 x-5 x^2+3 x^3} \, dx=\log \left (3 \, x^{3} - 5 \, x^{2} - 17 \, x + 9\right ) \]
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Time = 0.06 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.68 \[ \int \frac {-17-10 x+9 x^2}{9-17 x-5 x^2+3 x^3} \, dx=\log {\left (3 x^{3} - 5 x^{2} - 17 x + 9 \right )} \]
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none
Time = 0.21 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.73 \[ \int \frac {-17-10 x+9 x^2}{9-17 x-5 x^2+3 x^3} \, dx=\log \left (3 \, x^{3} - 5 \, x^{2} - 17 \, x + 9\right ) \]
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Time = 0.29 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.77 \[ \int \frac {-17-10 x+9 x^2}{9-17 x-5 x^2+3 x^3} \, dx=\log \left ({\left | 3 \, x^{3} - 5 \, x^{2} - 17 \, x + 9 \right |}\right ) \]
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Time = 0.09 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.73 \[ \int \frac {-17-10 x+9 x^2}{9-17 x-5 x^2+3 x^3} \, dx=\ln \left (3\,x^3-5\,x^2-17\,x+9\right ) \]
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