Optimal. Leaf size=8 \[ \frac {9 x^2}{e} \]
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Rubi [A] time = 0.00, antiderivative size = 8, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 6, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.333, Rules used = {12, 30} \begin {gather*} \frac {9 x^2}{e} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 30
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {18 \int x \, dx}{e}\\ &=\frac {9 x^2}{e}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 8, normalized size = 1.00 \begin {gather*} \frac {9 x^2}{e} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.53, size = 7, normalized size = 0.88 \begin {gather*} 9 \, x^{2} e^{\left (-1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.32, size = 7, normalized size = 0.88 \begin {gather*} 9 \, x^{2} e^{\left (-1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 8, normalized size = 1.00
method | result | size |
risch | \(9 x^{2} {\mathrm e}^{-1}\) | \(8\) |
gosper | \(9 x^{2} {\mathrm e}^{-1}\) | \(10\) |
default | \(9 x^{2} {\mathrm e}^{-1}\) | \(10\) |
norman | \(9 x^{2} {\mathrm e}^{-1}\) | \(10\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.49, size = 7, normalized size = 0.88 \begin {gather*} 9 \, x^{2} e^{\left (-1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.03, size = 7, normalized size = 0.88 \begin {gather*} 9\,x^2\,{\mathrm {e}}^{-1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.02, size = 7, normalized size = 0.88 \begin {gather*} \frac {9 x^{2}}{e} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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