Optimal. Leaf size=28 \[ \frac {1}{2} \left (-5-e^{e^4}+e^{3+x-x \left (e^{16+x}+x\right )}\right ) \]
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Rubi [A] time = 0.14, antiderivative size = 22, normalized size of antiderivative = 0.79, number of steps used = 2, number of rules used = 2, integrand size = 38, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.053, Rules used = {12, 6706} \begin {gather*} \frac {1}{2} e^{-x^2-e^{x+16} x+x+3} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{2} \int e^{3+x-e^{16+x} x-x^2} \left (1+e^{16+x} (-1-x)-2 x\right ) \, dx\\ &=\frac {1}{2} e^{3+x-e^{16+x} x-x^2}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.24, size = 22, normalized size = 0.79 \begin {gather*} \frac {1}{2} e^{3+x-e^{16+x} x-x^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.60, size = 18, normalized size = 0.64 \begin {gather*} \frac {1}{2} \, e^{\left (-x^{2} - x e^{\left (x + 16\right )} + 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 = 18, normalized size = 0.64 \begin {gather*} \frac {1}{2} \, e^{\left (-x^{2} - x e^{\left (x + 16\right )} + 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 = 19, normalized size = 0.68
method | result | size |
norman | \(\frac {{\mathrm e}^{-x \,{\mathrm e}^{x +16}-x^{2}+x +3}}{2}\) | \(19\) |
risch | \(\frac {{\mathrm e}^{-x \,{\mathrm e}^{x +16}-x^{2}+x +3}}{2}\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.42, size = 18, normalized size = 0.64 \begin {gather*} \frac {1}{2} \, e^{\left (-x^{2} - x e^{\left (x + 16\right )} + x + 3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.07, size = 20, normalized size = 0.71 \begin {gather*} \frac {{\mathrm {e}}^3\,{\mathrm {e}}^{-x\,{\mathrm {e}}^{16}\,{\mathrm {e}}^x}\,{\mathrm {e}}^{-x^2}\,{\mathrm {e}}^x}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.22, size = 15, normalized size = 0.54 \begin {gather*} \frac {e^{- x^{2} - x e^{x + 16} + x + 3}}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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