Optimal. Leaf size=19 \[ 4+e^{3+\left (\left (-4+e^2\right )^2-x\right ) x} \]
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Rubi [A] time = 0.05, antiderivative size = 20, normalized size of antiderivative = 1.05, number of steps used = 2, number of rules used = 2, integrand size = 37, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.054, Rules used = {2244, 2236} \begin {gather*} e^{-x^2+\left (4-e^2\right )^2 x+3} \end {gather*}
Antiderivative was successfully verified.
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Rule 2236
Rule 2244
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int e^{3+\left (4-e^2\right )^2 x-x^2} \left (\left (-4+e^2\right )^2-2 x\right ) \, dx\\ &=e^{3+\left (4-e^2\right )^2 x-x^2}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.06, size = 18, normalized size = 0.95 \begin {gather*} e^{3+\left (-4+e^2\right )^2 x-x^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.54, size = 20, normalized size = 1.05 \begin {gather*} e^{\left (-x^{2} + x e^{4} - 8 \, x e^{2} + 16 \, x + 3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 20, normalized size = 1.05 \begin {gather*} e^{\left (-x^{2} + x e^{4} - 8 \, x e^{2} + 16 \, x + 3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 21, normalized size = 1.11
method | result | size |
risch | \({\mathrm e}^{x \,{\mathrm e}^{4}-8 \,{\mathrm e}^{2} x -x^{2}+16 x +3}\) | \(21\) |
gosper | \({\mathrm e}^{x \,{\mathrm e}^{4}-8 \,{\mathrm e}^{2} x -x^{2}+16 x +3}\) | \(23\) |
derivativedivides | \({\mathrm e}^{x \,{\mathrm e}^{4}-8 \,{\mathrm e}^{2} x -x^{2}+16 x +3}\) | \(23\) |
default | \({\mathrm e}^{x \,{\mathrm e}^{4}-8 \,{\mathrm e}^{2} x -x^{2}+16 x +3}\) | \(23\) |
norman | \({\mathrm e}^{x \,{\mathrm e}^{4}-8 \,{\mathrm e}^{2} x -x^{2}+16 x +3}\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.38, size = 20, normalized size = 1.05 \begin {gather*} e^{\left (-x^{2} + x e^{4} - 8 \, x e^{2} + 16 \, x + 3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.19, size = 24, normalized size = 1.26 \begin {gather*} {\mathrm {e}}^{16\,x}\,{\mathrm {e}}^3\,{\mathrm {e}}^{-x^2}\,{\mathrm {e}}^{x\,{\mathrm {e}}^4}\,{\mathrm {e}}^{-8\,x\,{\mathrm {e}}^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.12, size = 20, normalized size = 1.05 \begin {gather*} e^{- x^{2} - 8 x e^{2} + 16 x + x e^{4} + 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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