Optimal. Leaf size=16 \[ \frac {8}{3} e^{-1+\frac {1}{16} (-5+x) x} \]
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Rubi [A]
time = 0.02, antiderivative size = 20, normalized size of antiderivative = 1.25, number of steps
used = 3, number of rules used = 3, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {12, 2276, 2268}
\begin {gather*} \frac {8}{3} e^{\frac {x^2}{16}-\frac {5 x}{16}-1} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2268
Rule 2276
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{6} \int e^{-1+\frac {1}{16} \left (-5 x+x^2\right )} (-5+2 x) \, dx\\ &=\frac {1}{6} \int e^{-1-\frac {5 x}{16}+\frac {x^2}{16}} (-5+2 x) \, dx\\ &=\frac {8}{3} e^{-1-\frac {5 x}{16}+\frac {x^2}{16}}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.03, size = 20, normalized size = 1.25 \begin {gather*} \frac {8}{3} e^{-1-\frac {5 x}{16}+\frac {x^2}{16}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.06, size = 17, normalized size = 1.06
method | result | size |
risch | \(\frac {8 \,{\mathrm e}^{\frac {1}{16} x^{2}-\frac {5}{16} x -1}}{3}\) | \(14\) |
gosper | \(\frac {8 \,{\mathrm e}^{\frac {1}{16} x^{2}-\frac {5}{16} x} {\mathrm e}^{-1}}{3}\) | \(17\) |
default | \(\frac {8 \,{\mathrm e}^{\frac {1}{16} x^{2}-\frac {5}{16} x} {\mathrm e}^{-1}}{3}\) | \(17\) |
norman | \(\frac {8 \,{\mathrm e}^{\frac {1}{16} x^{2}-\frac {5}{16} x} {\mathrm e}^{-1}}{3}\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.25, size = 13, normalized size = 0.81 \begin {gather*} \frac {8}{3} \, e^{\left (\frac {1}{16} \, x^{2} - \frac {5}{16} \, x - 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, size = 13, normalized size = 0.81 \begin {gather*} \frac {8}{3} \, e^{\left (\frac {1}{16} \, x^{2} - \frac {5}{16} \, x - 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 17, normalized size = 1.06 \begin {gather*} \frac {8 e^{\frac {x^{2}}{16} - \frac {5 x}{16}}}{3 e} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.38, size = 13, normalized size = 0.81 \begin {gather*} \frac {8}{3} \, e^{\left (\frac {1}{16} \, x^{2} - \frac {5}{16} \, x - 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.09, size = 14, normalized size = 0.88 \begin {gather*} \frac {8\,{\mathrm {e}}^{-\frac {5\,x}{16}}\,{\mathrm {e}}^{-1}\,{\mathrm {e}}^{\frac {x^2}{16}}}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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