Integrand size = 3, antiderivative size = 16 \[ \int -2 x \, dx=2-i \pi -x^2-\log (15) \]
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Time = 0.00 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.31, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.667, Rules used = {12, 30} \[ \int -2 x \, dx=-x^2 \]
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Rule 12
Rule 30
Rubi steps \begin{align*} \text {integral}& = -(2 \int x \, dx) \\ & = -x^2 \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.31 \[ \int -2 x \, dx=-x^2 \]
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Time = 0.02 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.38
method | result | size |
gosper | \(-x^{2}\) | \(6\) |
default | \(-x^{2}\) | \(6\) |
norman | \(-x^{2}\) | \(6\) |
risch | \(-x^{2}\) | \(6\) |
parallelrisch | \(-x^{2}\) | \(6\) |
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none
Time = 0.39 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.31 \[ \int -2 x \, dx=-x^{2} \]
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Time = 0.02 (sec) , antiderivative size = 3, normalized size of antiderivative = 0.19 \[ \int -2 x \, dx=- x^{2} \]
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none
Time = 0.21 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.31 \[ \int -2 x \, dx=-x^{2} \]
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none
Time = 0.27 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.31 \[ \int -2 x \, dx=-x^{2} \]
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Time = 0.02 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.31 \[ \int -2 x \, dx=-x^2 \]
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