Optimal. Leaf size=24 \[ e^{-\left (\left (3-e^{3^{\frac {x}{e^8}}}\right ) (3-x)\right )} x \]
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Rubi [F]
time = 3.37, 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 e^{-17-e^{3^{\frac {x}{e^8}}} (-3+x)+3 x} \left (e^8 (1+3 x)+e^{3^{\frac {x}{e^8}}} \left (-e^8 x+3^{\frac {x}{e^8}} \left (3 x-x^2\right ) \log (3)\right )\right ) \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (e^{-9-e^{3^{\frac {x}{e^8}}} (-3+x)+3 x} (1+3 x)-e^{-17+3^{\frac {x}{e^8}}-e^{3^{\frac {x}{e^8}}} (-3+x)+3 x} x \left (e^8-3^{1+\frac {x}{e^8}} \log (3)+3^{\frac {x}{e^8}} x \log (3)\right )\right ) \, dx\\ &=\int e^{-9-e^{3^{\frac {x}{e^8}}} (-3+x)+3 x} (1+3 x) \, dx-\int e^{-17+3^{\frac {x}{e^8}}-e^{3^{\frac {x}{e^8}}} (-3+x)+3 x} x \left (e^8-3^{1+\frac {x}{e^8}} \log (3)+3^{\frac {x}{e^8}} x \log (3)\right ) \, dx\\ &=\int e^{-\left (\left (-3+e^{3^{\frac {x}{e^8}}}\right ) (-3+x)\right )} (1+3 x) \, dx-\int e^{-17+3^{\frac {x}{e^8}}-e^{3^{\frac {x}{e^8}}} (-3+x)+3 x} x \left (e^8+3^{\frac {x}{e^8}} (-3+x) \log (3)\right ) \, dx\\ &=\int \left (e^{-\left (\left (-3+e^{3^{\frac {x}{e^8}}}\right ) (-3+x)\right )}+3 e^{-\left (\left (-3+e^{3^{\frac {x}{e^8}}}\right ) (-3+x)\right )} x\right ) \, dx-\int \left (e^{-9+3^{\frac {x}{e^8}}-e^{3^{\frac {x}{e^8}}} (-3+x)+3 x} x+3^{\frac {x}{e^8}} e^{-17+3^{\frac {x}{e^8}}-e^{3^{\frac {x}{e^8}}} (-3+x)+3 x} (-3+x) x \log (3)\right ) \, dx\\ &=3 \int e^{-\left (\left (-3+e^{3^{\frac {x}{e^8}}}\right ) (-3+x)\right )} x \, dx-\log (3) \int 3^{\frac {x}{e^8}} e^{-17+3^{\frac {x}{e^8}}-e^{3^{\frac {x}{e^8}}} (-3+x)+3 x} (-3+x) x \, dx+\int e^{-\left (\left (-3+e^{3^{\frac {x}{e^8}}}\right ) (-3+x)\right )} \, dx-\int e^{-9+3^{\frac {x}{e^8}}-e^{3^{\frac {x}{e^8}}} (-3+x)+3 x} x \, dx\\ &=3 \int e^{-\left (\left (-3+e^{3^{\frac {x}{e^8}}}\right ) (-3+x)\right )} x \, dx-\log (3) \int \left (-3^{1+\frac {x}{e^8}} e^{-17+3^{\frac {x}{e^8}}-e^{3^{\frac {x}{e^8}}} (-3+x)+3 x} x+3^{\frac {x}{e^8}} e^{-17+3^{\frac {x}{e^8}}-e^{3^{\frac {x}{e^8}}} (-3+x)+3 x} x^2\right ) \, dx+\int e^{-\left (\left (-3+e^{3^{\frac {x}{e^8}}}\right ) (-3+x)\right )} \, dx-\int e^{-9+3^{\frac {x}{e^8}}-e^{3^{\frac {x}{e^8}}} (-3+x)+3 x} x \, dx\\ &=3 \int e^{-\left (\left (-3+e^{3^{\frac {x}{e^8}}}\right ) (-3+x)\right )} x \, dx+\log (3) \int 3^{1+\frac {x}{e^8}} e^{-17+3^{\frac {x}{e^8}}-e^{3^{\frac {x}{e^8}}} (-3+x)+3 x} x \, dx-\log (3) \int 3^{\frac {x}{e^8}} e^{-17+3^{\frac {x}{e^8}}-e^{3^{\frac {x}{e^8}}} (-3+x)+3 x} x^2 \, dx+\int e^{-\left (\left (-3+e^{3^{\frac {x}{e^8}}}\right ) (-3+x)\right )} \, dx-\int e^{-9+3^{\frac {x}{e^8}}-e^{3^{\frac {x}{e^8}}} (-3+x)+3 x} x \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.18, size = 20, normalized size = 0.83 \begin {gather*} e^{-\left (\left (-3+e^{3^{\frac {x}{e^8}}}\right ) (-3+x)\right )} x \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.77, size = 18, normalized size = 0.75
method | result | size |
risch | \(x \,{\mathrm e}^{-\left (x -3\right ) \left ({\mathrm e}^{3^{{\mathrm e}^{-8} x}}-3\right )}\) | \(18\) |
norman | \(x \,{\mathrm e}^{-\left (x -3\right ) {\mathrm e}^{{\mathrm e}^{x \ln \left (3\right ) {\mathrm e}^{-8}}}+3 x -9}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.63, size = 27, normalized size = 1.12 \begin {gather*} x e^{\left (-x e^{\left (3^{x e^{\left (-8\right )}}\right )} + 3 \, x + 3 \, e^{\left (3^{x e^{\left (-8\right )}}\right )} - 9\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 20, normalized size = 0.83 \begin {gather*} x e^{\left (-{\left (x - 3\right )} e^{\left (3^{x e^{\left (-8\right )}}\right )} + 3 \, x - 9\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 1.49, size = 22, normalized size = 0.92 \begin {gather*} x e^{3 x - \left (x - 3\right ) e^{e^{\frac {x \log {\left (3 \right )}}{e^{8}}}} - 9} \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*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.60, size = 29, normalized size = 1.21 \begin {gather*} x\,{\mathrm {e}}^{3\,x}\,{\mathrm {e}}^{-x\,{\mathrm {e}}^{3^{x\,{\mathrm {e}}^{-8}}}}\,{\mathrm {e}}^{-9}\,{\mathrm {e}}^{3\,{\mathrm {e}}^{3^{x\,{\mathrm {e}}^{-8}}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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