Integrand size = 20, antiderivative size = 6 \[ \int \frac {x+x^2}{-2 x-x^2+x^3} \, dx=\log (2-x) \]
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Time = 0.01 (sec) , antiderivative size = 6, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {1600, 31} \[ \int \frac {x+x^2}{-2 x-x^2+x^3} \, dx=\log (2-x) \]
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Rule 31
Rule 1600
Rubi steps \begin{align*} \text {integral}& = \int \frac {1}{-2+x} \, dx \\ & = \log (2-x) \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 4, normalized size of antiderivative = 0.67 \[ \int \frac {x+x^2}{-2 x-x^2+x^3} \, dx=\log (-2+x) \]
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Time = 0.02 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.83
method | result | size |
default | \(\ln \left (x -2\right )\) | \(5\) |
norman | \(\ln \left (x -2\right )\) | \(5\) |
risch | \(\ln \left (x -2\right )\) | \(5\) |
parallelrisch | \(\ln \left (x -2\right )\) | \(5\) |
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none
Time = 0.25 (sec) , antiderivative size = 4, normalized size of antiderivative = 0.67 \[ \int \frac {x+x^2}{-2 x-x^2+x^3} \, dx=\log \left (x - 2\right ) \]
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Time = 0.02 (sec) , antiderivative size = 3, normalized size of antiderivative = 0.50 \[ \int \frac {x+x^2}{-2 x-x^2+x^3} \, dx=\log {\left (x - 2 \right )} \]
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none
Time = 0.19 (sec) , antiderivative size = 4, normalized size of antiderivative = 0.67 \[ \int \frac {x+x^2}{-2 x-x^2+x^3} \, dx=\log \left (x - 2\right ) \]
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none
Time = 0.31 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.83 \[ \int \frac {x+x^2}{-2 x-x^2+x^3} \, dx=\log \left ({\left | x - 2 \right |}\right ) \]
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Time = 0.01 (sec) , antiderivative size = 4, normalized size of antiderivative = 0.67 \[ \int \frac {x+x^2}{-2 x-x^2+x^3} \, dx=\ln \left (x-2\right ) \]
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