Integrand size = 10, antiderivative size = 20 \[ \int \left (-2 x+x^2+x^3\right ) \, dx=-x^2+\frac {x^3}{3}+\frac {x^4}{4} \]
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Time = 0.00 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \left (-2 x+x^2+x^3\right ) \, dx=\frac {x^4}{4}+\frac {x^3}{3}-x^2 \]
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Rubi steps \begin{align*} \text {integral}& = -x^2+\frac {x^3}{3}+\frac {x^4}{4} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00 \[ \int \left (-2 x+x^2+x^3\right ) \, dx=-x^2+\frac {x^3}{3}+\frac {x^4}{4} \]
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Time = 0.01 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.80
method | result | size |
gosper | \(\frac {x^{2} \left (3 x^{2}+4 x -12\right )}{12}\) | \(16\) |
default | \(-x^{2}+\frac {1}{3} x^{3}+\frac {1}{4} x^{4}\) | \(17\) |
norman | \(-x^{2}+\frac {1}{3} x^{3}+\frac {1}{4} x^{4}\) | \(17\) |
risch | \(-x^{2}+\frac {1}{3} x^{3}+\frac {1}{4} x^{4}\) | \(17\) |
parallelrisch | \(-x^{2}+\frac {1}{3} x^{3}+\frac {1}{4} x^{4}\) | \(17\) |
parts | \(-x^{2}+\frac {1}{3} x^{3}+\frac {1}{4} x^{4}\) | \(17\) |
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Time = 0.22 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.80 \[ \int \left (-2 x+x^2+x^3\right ) \, dx=\frac {1}{4} \, x^{4} + \frac {1}{3} \, x^{3} - x^{2} \]
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Time = 0.01 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.60 \[ \int \left (-2 x+x^2+x^3\right ) \, dx=\frac {x^{4}}{4} + \frac {x^{3}}{3} - x^{2} \]
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Time = 0.20 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.80 \[ \int \left (-2 x+x^2+x^3\right ) \, dx=\frac {1}{4} \, x^{4} + \frac {1}{3} \, x^{3} - x^{2} \]
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Time = 0.29 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.80 \[ \int \left (-2 x+x^2+x^3\right ) \, dx=\frac {1}{4} \, x^{4} + \frac {1}{3} \, x^{3} - x^{2} \]
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Time = 0.03 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.75 \[ \int \left (-2 x+x^2+x^3\right ) \, dx=\frac {x^2\,\left (3\,x^2+4\,x-12\right )}{12} \]
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