Integrand size = 21, antiderivative size = 21 \[ \int \frac {1+2 x}{-1+3 x-3 x^2+x^3} \, dx=-\frac {3}{2 (1-x)^2}+\frac {2}{1-x} \]
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Time = 0.01 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.048, Rules used = {2099} \[ \int \frac {1+2 x}{-1+3 x-3 x^2+x^3} \, dx=\frac {2}{1-x}-\frac {3}{2 (1-x)^2} \]
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Rule 2099
Rubi steps \begin{align*} \text {integral}& = \int \left (\frac {3}{(-1+x)^3}+\frac {2}{(-1+x)^2}\right ) \, dx \\ & = -\frac {3}{2 (1-x)^2}+\frac {2}{1-x} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.67 \[ \int \frac {1+2 x}{-1+3 x-3 x^2+x^3} \, dx=\frac {1-4 x}{2 (-1+x)^2} \]
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Time = 0.03 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.57
method | result | size |
norman | \(\frac {-2 x +\frac {1}{2}}{\left (x -1\right )^{2}}\) | \(12\) |
default | \(-\frac {2}{x -1}-\frac {3}{2 \left (x -1\right )^{2}}\) | \(16\) |
risch | \(\frac {-2 x +\frac {1}{2}}{x^{2}-2 x +1}\) | \(17\) |
gosper | \(-\frac {-1+4 x}{2 \left (x^{2}-2 x +1\right )}\) | \(18\) |
parallelrisch | \(\frac {1-4 x}{2 x^{2}-4 x +2}\) | \(18\) |
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Time = 0.24 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.81 \[ \int \frac {1+2 x}{-1+3 x-3 x^2+x^3} \, dx=-\frac {4 \, x - 1}{2 \, {\left (x^{2} - 2 \, x + 1\right )}} \]
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Time = 0.04 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.67 \[ \int \frac {1+2 x}{-1+3 x-3 x^2+x^3} \, dx=\frac {1 - 4 x}{2 x^{2} - 4 x + 2} \]
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Time = 0.19 (sec) , antiderivative size = 17, normalized size of antiderivative = 0.81 \[ \int \frac {1+2 x}{-1+3 x-3 x^2+x^3} \, dx=-\frac {4 \, x - 1}{2 \, {\left (x^{2} - 2 \, x + 1\right )}} \]
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Time = 0.26 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.57 \[ \int \frac {1+2 x}{-1+3 x-3 x^2+x^3} \, dx=-\frac {4 \, x - 1}{2 \, {\left (x - 1\right )}^{2}} \]
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Time = 9.28 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.57 \[ \int \frac {1+2 x}{-1+3 x-3 x^2+x^3} \, dx=-\frac {4\,x-1}{2\,{\left (x-1\right )}^2} \]
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