Optimal. Leaf size=25 \[ \frac {4}{3}+e^{e^{e^{-3 x/2} x \left (-1+\frac {\log (3)}{x}\right )}} \]
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Rubi [F] time = 3.17, 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 {\exp \left (e^{e^{\frac {1}{2} (-3 x+2 \log (-x+\log (3)))}}+e^{\frac {1}{2} (-3 x+2 \log (-x+\log (3)))}+\frac {1}{2} (-3 x+2 \log (-x+\log (3)))\right ) (-2+3 x-3 \log (3))}{-2 x+2 \log (3)} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {1}{2} 3^{e^{-3 x/2}} \exp \left (3^{e^{-3 x/2}} e^{-e^{-3 x/2} x}-\frac {3 x}{2}-e^{-3 x/2} x\right ) (-2+3 x-3 \log (3)) \, dx\\ &=\frac {1}{2} \int 3^{e^{-3 x/2}} \exp \left (3^{e^{-3 x/2}} e^{-e^{-3 x/2} x}-\frac {3 x}{2}-e^{-3 x/2} x\right ) (-2+3 x-3 \log (3)) \, dx\\ &=\frac {1}{2} \int \left (3^{1+e^{-3 x/2}} \exp \left (3^{e^{-3 x/2}} e^{-e^{-3 x/2} x}-\frac {3 x}{2}-e^{-3 x/2} x\right ) x-2\ 3^{e^{-3 x/2}} \exp \left (3^{e^{-3 x/2}} e^{-e^{-3 x/2} x}-\frac {3 x}{2}-e^{-3 x/2} x\right ) \left (1+\frac {3 \log (3)}{2}\right )\right ) \, dx\\ &=\frac {1}{2} \int 3^{1+e^{-3 x/2}} \exp \left (3^{e^{-3 x/2}} e^{-e^{-3 x/2} x}-\frac {3 x}{2}-e^{-3 x/2} x\right ) x \, dx+\frac {1}{2} (-2-\log (27)) \int 3^{e^{-3 x/2}} \exp \left (3^{e^{-3 x/2}} e^{-e^{-3 x/2} x}-\frac {3 x}{2}-e^{-3 x/2} x\right ) \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 1.27, size = 24, normalized size = 0.96 \begin {gather*} e^{3^{e^{-3 x/2}} e^{-e^{-3 x/2} x}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.68, size = 14, normalized size = 0.56 \begin {gather*} e^{\left (e^{\left (e^{\left (-\frac {3}{2} \, x + \log \left (-x + \log \relax (3)\right )\right )}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.20, size = 17, normalized size = 0.68 \begin {gather*} e^{\left (e^{\left (-x e^{\left (-\frac {3}{2} \, x\right )} + e^{\left (-\frac {3}{2} \, x\right )} \log \relax (3)\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.14, size = 14, normalized size = 0.56
method | result | size |
risch | \({\mathrm e}^{{\mathrm e}^{\left (\ln \relax (3)-x \right ) {\mathrm e}^{-\frac {3 x}{2}}}}\) | \(14\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.76, size = 17, normalized size = 0.68 \begin {gather*} e^{\left (e^{\left (-x e^{\left (-\frac {3}{2} \, x\right )} + e^{\left (-\frac {3}{2} \, x\right )} \log \relax (3)\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.45, size = 16, normalized size = 0.64 \begin {gather*} {\mathrm {e}}^{3^{{\mathrm {e}}^{-\frac {3\,x}{2}}}\,{\mathrm {e}}^{-x\,{\mathrm {e}}^{-\frac {3\,x}{2}}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.61, size = 14, normalized size = 0.56 \begin {gather*} e^{e^{\left (- x + \log {\relax (3 )}\right ) e^{- \frac {3 x}{2}}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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