Optimal. Leaf size=21 \[ 3 e^{-e^{x-\frac {x^2}{3}}}-2 x \]
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Rubi [F] time = 0.30, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \frac {1}{3} \left (-6+3 e^{-e^{\frac {1}{3} \left (3 x-x^2\right )}+\frac {1}{3} \left (3 x-x^2\right )} (-3+2 x)\right ) \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{3} \int \left (-6+3 e^{-e^{\frac {1}{3} \left (3 x-x^2\right )}+\frac {1}{3} \left (3 x-x^2\right )} (-3+2 x)\right ) \, dx\\ &=-2 x+\int e^{-e^{\frac {1}{3} \left (3 x-x^2\right )}+\frac {1}{3} \left (3 x-x^2\right )} (-3+2 x) \, dx\\ &=-2 x+\int e^{-e^{x-\frac {x^2}{3}}+x-\frac {x^2}{3}} (-3+2 x) \, dx\\ &=-2 x+\int \left (-3 e^{-e^{x-\frac {x^2}{3}}+x-\frac {x^2}{3}}+2 e^{-e^{x-\frac {x^2}{3}}+x-\frac {x^2}{3}} x\right ) \, dx\\ &=-2 x+2 \int e^{-e^{x-\frac {x^2}{3}}+x-\frac {x^2}{3}} x \, dx-3 \int e^{-e^{x-\frac {x^2}{3}}+x-\frac {x^2}{3}} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.13, size = 21, normalized size = 1.00 \begin {gather*} 3 e^{-e^{x-\frac {x^2}{3}}}-2 x \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.67, size = 46, normalized size = 2.19 \begin {gather*} -{\left (2 \, x e^{\left (-\frac {1}{3} \, x^{2} + x\right )} - e^{\left (-\frac {1}{3} \, x^{2} + x - e^{\left (-\frac {1}{3} \, x^{2} + x\right )} + \log \relax (3)\right )}\right )} e^{\left (\frac {1}{3} \, x^{2} - x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.56, size = 17, normalized size = 0.81 \begin {gather*} -2 \, x + 3 \, e^{\left (-e^{\left (-\frac {1}{3} \, x^{2} + x\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.08, size = 17, normalized size = 0.81
method | result | size |
risch | \(3 \,{\mathrm e}^{-{\mathrm e}^{-\frac {x \left (x -3\right )}{3}}}-2 x\) | \(17\) |
default | \({\mathrm e}^{-{\mathrm e}^{-\frac {1}{3} x^{2}+x}+\ln \relax (3)}-2 x\) | \(19\) |
norman | \({\mathrm e}^{-{\mathrm e}^{-\frac {1}{3} x^{2}+x}+\ln \relax (3)}-2 x\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.80, size = 17, normalized size = 0.81 \begin {gather*} -2 \, x + 3 \, e^{\left (-e^{\left (-\frac {1}{3} \, x^{2} + x\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.11, size = 17, normalized size = 0.81 \begin {gather*} 3\,{\mathrm {e}}^{-{\mathrm {e}}^{-\frac {x^2}{3}}\,{\mathrm {e}}^x}-2\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.29, size = 14, normalized size = 0.67 \begin {gather*} - 2 x + 3 e^{- e^{- \frac {x^{2}}{3} + x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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