Optimal. Leaf size=21 \[ e^{\frac {1}{e^{5/2}}-e^{2 x} x-x^2} \]
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Rubi [A] time = 0.18, antiderivative size = 32, normalized size of antiderivative = 1.52, number of steps used = 1, number of rules used = 1, integrand size = 48, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.021, Rules used = {6706} \begin {gather*} e^{\frac {-e^{5/2} x^2-e^{2 x+\frac {5}{2}} x+1}{e^{5/2}}} \end {gather*}
Antiderivative was successfully verified.
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Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=e^{\frac {1-e^{\frac {5}{2}+2 x} x-e^{5/2} x^2}{e^{5/2}}}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.20, size = 21, normalized size = 1.00 \begin {gather*} e^{\frac {1}{e^{5/2}}-e^{2 x} x-x^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.65, size = 21, normalized size = 1.00 \begin {gather*} e^{\left (-{\left (x^{2} e^{\frac {5}{2}} + x e^{\left (2 \, x + \frac {5}{2}\right )} - 1\right )} e^{\left (-\frac {5}{2}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.33, size = 16, normalized size = 0.76 \begin {gather*} e^{\left (-x^{2} - x e^{\left (2 \, x\right )} + e^{\left (-\frac {5}{2}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 22, normalized size = 1.05
method | result | size |
risch | \({\mathrm e}^{-\left (x^{2} {\mathrm e}^{\frac {5}{2}}+x \,{\mathrm e}^{\frac {5}{2}+2 x}-1\right ) {\mathrm e}^{-\frac {5}{2}}}\) | \(22\) |
norman | \({\mathrm e}^{\left (-x \,{\mathrm e}^{\frac {5}{2}} {\mathrm e}^{2 x}-x^{2} {\mathrm e}^{\frac {5}{2}}+1\right ) {\mathrm e}^{-\frac {5}{2}}}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.92, size = 16, normalized size = 0.76 \begin {gather*} e^{\left (-x^{2} - x e^{\left (2 \, x\right )} + e^{\left (-\frac {5}{2}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.07, size = 18, normalized size = 0.86 \begin {gather*} {\mathrm {e}}^{-x\,{\mathrm {e}}^{2\,x}}\,{\mathrm {e}}^{-x^2}\,{\mathrm {e}}^{{\mathrm {e}}^{-\frac {5}{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.17, size = 27, normalized size = 1.29 \begin {gather*} e^{\frac {- x^{2} e^{\frac {5}{2}} - x e^{\frac {5}{2}} e^{2 x} + 1}{e^{\frac {5}{2}}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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