Optimal. Leaf size=19 \[ e^{(-1+x) \left (4-\left (-e^8+x\right )^2\right )} \]
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Rubi [A] time = 0.21, antiderivative size = 36, normalized size of antiderivative = 1.89, number of steps used = 1, number of rules used = 1, integrand size = 62, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.016, Rules used = {6706} \begin {gather*} \exp \left (-x^3+x^2-2 e^8 \left (x-x^2\right )+4 x+e^{16} (1-x)-4\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\exp \left (-4+e^{16} (1-x)+4 x+x^2-x^3-2 e^8 \left (x-x^2\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.29, size = 32, normalized size = 1.68 \begin {gather*} e^{-4-e^{16} (-1+x)+4 x+2 e^8 (-1+x) x+x^2-x^3} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.88, size = 32, normalized size = 1.68 \begin {gather*} e^{\left (-x^{3} + x^{2} - {\left (x - 1\right )} e^{16} + 2 \, {\left (x^{2} - x\right )} e^{8} + 4 \, x - 4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.23, size = 33, normalized size = 1.74 \begin {gather*} e^{\left (-x^{3} + 2 \, x^{2} e^{8} + x^{2} - x e^{16} - 2 \, x e^{8} + 4 \, x + e^{16} - 4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 19, normalized size = 1.00
method | result | size |
risch | \({\mathrm e}^{-\left (x -1\right ) \left (-2 x \,{\mathrm e}^{8}+x^{2}+{\mathrm e}^{16}-4\right )}\) | \(19\) |
derivativedivides | \({\mathrm e}^{\left (1-x \right ) {\mathrm e}^{16}+\left (2 x^{2}-2 x \right ) {\mathrm e}^{8}-x^{3}+x^{2}+4 x -4}\) | \(37\) |
default | \({\mathrm e}^{\left (1-x \right ) {\mathrm e}^{16}+\left (2 x^{2}-2 x \right ) {\mathrm e}^{8}-x^{3}+x^{2}+4 x -4}\) | \(37\) |
norman | \({\mathrm e}^{\left (1-x \right ) {\mathrm e}^{16}+\left (2 x^{2}-2 x \right ) {\mathrm e}^{8}-x^{3}+x^{2}+4 x -4}\) | \(37\) |
gosper | \({\mathrm e}^{2 x^{2} {\mathrm e}^{8}-x^{3}-2 x \,{\mathrm e}^{8}-x \,{\mathrm e}^{16}+x^{2}+{\mathrm e}^{16}+4 x -4}\) | \(38\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 32, normalized size = 1.68 \begin {gather*} e^{\left (-x^{3} + x^{2} - {\left (x - 1\right )} e^{16} + 2 \, {\left (x^{2} - x\right )} e^{8} + 4 \, x - 4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.21, size = 40, normalized size = 2.11 \begin {gather*} {\mathrm {e}}^{2\,x^2\,{\mathrm {e}}^8}\,{\mathrm {e}}^{4\,x}\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{-4}\,{\mathrm {e}}^{-x^3}\,{\mathrm {e}}^{-2\,x\,{\mathrm {e}}^8}\,{\mathrm {e}}^{-x\,{\mathrm {e}}^{16}}\,{\mathrm {e}}^{{\mathrm {e}}^{16}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.16, size = 31, normalized size = 1.63 \begin {gather*} e^{- x^{3} + x^{2} + 4 x + \left (1 - x\right ) e^{16} + \left (2 x^{2} - 2 x\right ) e^{8} - 4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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