Integrand size = 11, antiderivative size = 11 \[ \int \frac {-4+x^2}{2+x} \, dx=-2 x+\frac {x^2}{2} \]
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Time = 0.00 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {641} \[ \int \frac {-4+x^2}{2+x} \, dx=\frac {x^2}{2}-2 x \]
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Rule 641
Rubi steps \begin{align*} \text {integral}& = \int (-2+x) \, dx \\ & = -2 x+\frac {x^2}{2} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 11, normalized size of antiderivative = 1.00 \[ \int \frac {-4+x^2}{2+x} \, dx=-2 x+\frac {x^2}{2} \]
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Time = 0.77 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.64
method | result | size |
gosper | \(\frac {x \left (x -4\right )}{2}\) | \(7\) |
meijerg | \(-\frac {x \left (-\frac {3 x}{2}+6\right )}{3}\) | \(9\) |
default | \(-2 x +\frac {1}{2} x^{2}\) | \(10\) |
norman | \(-2 x +\frac {1}{2} x^{2}\) | \(10\) |
risch | \(-2 x +\frac {1}{2} x^{2}\) | \(10\) |
parallelrisch | \(-2 x +\frac {1}{2} x^{2}\) | \(10\) |
parts | \(-2 x +\frac {1}{2} x^{2}\) | \(10\) |
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none
Time = 0.24 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.82 \[ \int \frac {-4+x^2}{2+x} \, dx=\frac {1}{2} \, x^{2} - 2 \, x \]
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Time = 0.02 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.64 \[ \int \frac {-4+x^2}{2+x} \, dx=\frac {x^{2}}{2} - 2 x \]
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none
Time = 0.19 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.82 \[ \int \frac {-4+x^2}{2+x} \, dx=\frac {1}{2} \, x^{2} - 2 \, x \]
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none
Time = 0.27 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.82 \[ \int \frac {-4+x^2}{2+x} \, dx=\frac {1}{2} \, x^{2} - 2 \, x \]
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Time = 0.01 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.55 \[ \int \frac {-4+x^2}{2+x} \, dx=\frac {x\,\left (x-4\right )}{2} \]
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