Optimal. Leaf size=21 \[ e^{e^{7-e^4+e^{x^2}-\frac {x}{2}}} \]
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Rubi [F] time = 0.54, 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}{2} \exp \left (e^{\frac {1}{2} \left (14-2 e^4+2 e^{x^2}-x\right )}+\frac {1}{2} \left (14-2 e^4+2 e^{x^2}-x\right )\right ) \left (-1+4 e^{x^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}{2} \int \exp \left (e^{\frac {1}{2} \left (14-2 e^4+2 e^{x^2}-x\right )}+\frac {1}{2} \left (14-2 e^4+2 e^{x^2}-x\right )\right ) \left (-1+4 e^{x^2} x\right ) \, dx\\ &=\frac {1}{2} \int \left (-\exp \left (e^{\frac {1}{2} \left (14-2 e^4+2 e^{x^2}-x\right )}+\frac {1}{2} \left (14-2 e^4+2 e^{x^2}-x\right )\right )+4 \exp \left (e^{\frac {1}{2} \left (14-2 e^4+2 e^{x^2}-x\right )}+\frac {1}{2} \left (14-2 e^4+2 e^{x^2}-x\right )+x^2\right ) x\right ) \, dx\\ &=-\left (\frac {1}{2} \int \exp \left (e^{\frac {1}{2} \left (14-2 e^4+2 e^{x^2}-x\right )}+\frac {1}{2} \left (14-2 e^4+2 e^{x^2}-x\right )\right ) \, dx\right )+2 \int \exp \left (e^{\frac {1}{2} \left (14-2 e^4+2 e^{x^2}-x\right )}+\frac {1}{2} \left (14-2 e^4+2 e^{x^2}-x\right )+x^2\right ) x \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.32, size = 21, normalized size = 1.00 \begin {gather*} e^{e^{7-e^4+e^{x^2}-\frac {x}{2}}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.60, size = 15, normalized size = 0.71 \begin {gather*} e^{\left (e^{\left (-\frac {1}{2} \, x - e^{4} + e^{\left (x^{2}\right )} + 7\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {1}{2} \, {\left (4 \, x e^{\left (x^{2}\right )} - 1\right )} e^{\left (-\frac {1}{2} \, x - e^{4} + e^{\left (x^{2}\right )} + e^{\left (-\frac {1}{2} \, x - e^{4} + e^{\left (x^{2}\right )} + 7\right )} + 7\right )}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.13, size = 16, normalized size = 0.76
method | result | size |
norman | \({\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x^{2}}-{\mathrm e}^{4}-\frac {x}{2}+7}}\) | \(16\) |
risch | \({\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x^{2}}-{\mathrm e}^{4}-\frac {x}{2}+7}}\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.81, size = 15, normalized size = 0.71 \begin {gather*} e^{\left (e^{\left (-\frac {1}{2} \, x - e^{4} + e^{\left (x^{2}\right )} + 7\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.24, size = 18, normalized size = 0.86 \begin {gather*} {\mathrm {e}}^{{\mathrm {e}}^{-{\mathrm {e}}^4}\,{\mathrm {e}}^{-\frac {x}{2}}\,{\mathrm {e}}^7\,{\mathrm {e}}^{{\mathrm {e}}^{x^2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.54, size = 15, normalized size = 0.71 \begin {gather*} e^{e^{- \frac {x}{2} + e^{x^{2}} - e^{4} + 7}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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