Optimal. Leaf size=20 \[ e^{-16+\frac {1}{12} \left (2+\frac {14}{3 x}\right ) x^2} \]
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Rubi [A] time = 0.04, antiderivative size = 16, normalized size of antiderivative = 0.80, number of steps used = 3, number of rules used = 3, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.120, Rules used = {12, 2244, 2236} \begin {gather*} e^{\frac {x^2}{6}+\frac {7 x}{18}-16} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2236
Rule 2244
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{18} \int e^{\frac {1}{18} \left (-288+7 x+3 x^2\right )} (7+6 x) \, dx\\ &=\frac {1}{18} \int e^{-16+\frac {7 x}{18}+\frac {x^2}{6}} (7+6 x) \, dx\\ &=e^{-16+\frac {7 x}{18}+\frac {x^2}{6}}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.03, size = 16, normalized size = 0.80 \begin {gather*} e^{-16+\frac {7 x}{18}+\frac {x^2}{6}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.65, size = 11, normalized size = 0.55 \begin {gather*} e^{\left (\frac {1}{6} \, x^{2} + \frac {7}{18} \, x - 16\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 5.04, size = 11, normalized size = 0.55 \begin {gather*} e^{\left (\frac {1}{6} \, x^{2} + \frac {7}{18} \, x - 16\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 12, normalized size = 0.60
method | result | size |
gosper | \({\mathrm e}^{\frac {1}{6} x^{2}+\frac {7}{18} x -16}\) | \(12\) |
default | \({\mathrm e}^{\frac {1}{6} x^{2}+\frac {7}{18} x -16}\) | \(12\) |
norman | \({\mathrm e}^{\frac {1}{6} x^{2}+\frac {7}{18} x -16}\) | \(12\) |
risch | \({\mathrm e}^{\frac {1}{6} x^{2}+\frac {7}{18} x -16}\) | \(12\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.68, size = 11, normalized size = 0.55 \begin {gather*} e^{\left (\frac {1}{6} \, x^{2} + \frac {7}{18} \, x - 16\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.18, size = 13, normalized size = 0.65 \begin {gather*} {\mathrm {e}}^{\frac {7\,x}{18}}\,{\mathrm {e}}^{-16}\,{\mathrm {e}}^{\frac {x^2}{6}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 12, normalized size = 0.60 \begin {gather*} e^{\frac {x^{2}}{6} + \frac {7 x}{18} - 16} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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