Integrand size = 6, antiderivative size = 11 \[ \int \frac {2 x}{e^2} \, dx=5+\frac {x^2}{e^2}+\log (3) \]
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Time = 0.00 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.64, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.333, Rules used = {12, 30} \[ \int \frac {2 x}{e^2} \, dx=\frac {x^2}{e^2} \]
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Rule 12
Rule 30
Rubi steps \begin{align*} \text {integral}& = \frac {2 \int x \, dx}{e^2} \\ & = \frac {x^2}{e^2} \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.64 \[ \int \frac {2 x}{e^2} \, dx=\frac {x^2}{e^2} \]
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Time = 0.03 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.64
method | result | size |
risch | \(x^{2} {\mathrm e}^{-2}\) | \(7\) |
gosper | \(x^{2} {\mathrm e}^{-2}\) | \(9\) |
default | \(x^{2} {\mathrm e}^{-2}\) | \(9\) |
norman | \(x^{2} {\mathrm e}^{-2}\) | \(9\) |
parallelrisch | \(x^{2} {\mathrm e}^{-2}\) | \(9\) |
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none
Time = 0.24 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.55 \[ \int \frac {2 x}{e^2} \, dx=x^{2} e^{\left (-2\right )} \]
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Time = 0.02 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.45 \[ \int \frac {2 x}{e^2} \, dx=\frac {x^{2}}{e^{2}} \]
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none
Time = 0.18 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.55 \[ \int \frac {2 x}{e^2} \, dx=x^{2} e^{\left (-2\right )} \]
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none
Time = 0.26 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.55 \[ \int \frac {2 x}{e^2} \, dx=x^{2} e^{\left (-2\right )} \]
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Time = 0.03 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.55 \[ \int \frac {2 x}{e^2} \, dx=x^2\,{\mathrm {e}}^{-2} \]
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