Optimal. Leaf size=26 \[ -4-e^{e^{1+e^{-3-e^x+\frac {x}{36}}} x} \]
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Rubi [F] time = 1.95, 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}{36} \exp \left (1+e^{\frac {1}{36} \left (-108-36 e^x+x\right )}+e^{1+e^{\frac {1}{36} \left (-108-36 e^x+x\right )}} x\right ) \left (-36+e^{\frac {1}{36} \left (-108-36 e^x+x\right )} \left (-x+36 e^x x\right )\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}{36} \int \exp \left (1+e^{\frac {1}{36} \left (-108-36 e^x+x\right )}+e^{1+e^{\frac {1}{36} \left (-108-36 e^x+x\right )}} x\right ) \left (-36+e^{\frac {1}{36} \left (-108-36 e^x+x\right )} \left (-x+36 e^x x\right )\right ) \, dx\\ &=\frac {1}{36} \int \left (-36 \exp \left (1+e^{\frac {1}{36} \left (-108-36 e^x+x\right )}+e^{1+e^{\frac {1}{36} \left (-108-36 e^x+x\right )}} x\right )+\exp \left (1+e^{\frac {1}{36} \left (-108-36 e^x+x\right )}+e^{1+e^{\frac {1}{36} \left (-108-36 e^x+x\right )}} x+\frac {1}{36} \left (-108-36 e^x+x\right )\right ) \left (-1+36 e^x\right ) x\right ) \, dx\\ &=\frac {1}{36} \int \exp \left (1+e^{\frac {1}{36} \left (-108-36 e^x+x\right )}+e^{1+e^{\frac {1}{36} \left (-108-36 e^x+x\right )}} x+\frac {1}{36} \left (-108-36 e^x+x\right )\right ) \left (-1+36 e^x\right ) x \, dx-\int \exp \left (1+e^{\frac {1}{36} \left (-108-36 e^x+x\right )}+e^{1+e^{\frac {1}{36} \left (-108-36 e^x+x\right )}} x\right ) \, dx\\ &=\frac {1}{36} \int \left (-\exp \left (1+e^{\frac {1}{36} \left (-108-36 e^x+x\right )}+e^{1+e^{\frac {1}{36} \left (-108-36 e^x+x\right )}} x+\frac {1}{36} \left (-108-36 e^x+x\right )\right ) x+36 \exp \left (1+e^{\frac {1}{36} \left (-108-36 e^x+x\right )}+x+e^{1+e^{\frac {1}{36} \left (-108-36 e^x+x\right )}} x+\frac {1}{36} \left (-108-36 e^x+x\right )\right ) x\right ) \, dx-\int \exp \left (1+e^{\frac {1}{36} \left (-108-36 e^x+x\right )}+e^{1+e^{\frac {1}{36} \left (-108-36 e^x+x\right )}} x\right ) \, dx\\ &=-\left (\frac {1}{36} \int \exp \left (1+e^{\frac {1}{36} \left (-108-36 e^x+x\right )}+e^{1+e^{\frac {1}{36} \left (-108-36 e^x+x\right )}} x+\frac {1}{36} \left (-108-36 e^x+x\right )\right ) x \, dx\right )-\int \exp \left (1+e^{\frac {1}{36} \left (-108-36 e^x+x\right )}+e^{1+e^{\frac {1}{36} \left (-108-36 e^x+x\right )}} x\right ) \, dx+\int \exp \left (1+e^{\frac {1}{36} \left (-108-36 e^x+x\right )}+x+e^{1+e^{\frac {1}{36} \left (-108-36 e^x+x\right )}} x+\frac {1}{36} \left (-108-36 e^x+x\right )\right ) x \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 1.36, size = 24, normalized size = 0.92 \begin {gather*} -e^{e^{1+e^{-3-e^x+\frac {x}{36}}} x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.51, size = 18, normalized size = 0.69 \begin {gather*} -e^{\left (x e^{\left (e^{\left (\frac {1}{36} \, x - e^{x} - 3\right )} + 1\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}{36} \, {\left ({\left (36 \, x e^{x} - x\right )} e^{\left (\frac {1}{36} \, x - e^{x} - 3\right )} - 36\right )} e^{\left (x e^{\left (e^{\left (\frac {1}{36} \, x - e^{x} - 3\right )} + 1\right )} + e^{\left (\frac {1}{36} \, x - e^{x} - 3\right )} + 1\right )}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.14, size = 19, normalized size = 0.73
method | result | size |
risch | \(-{\mathrm e}^{x \,{\mathrm e}^{{\mathrm e}^{-{\mathrm e}^{x}+\frac {x}{36}-3}+1}}\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.64, size = 18, normalized size = 0.69 \begin {gather*} -e^{\left (x e^{\left (e^{\left (\frac {1}{36} \, x - e^{x} - 3\right )} + 1\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 6.32, size = 20, normalized size = 0.77 \begin {gather*} -{\mathrm {e}}^{x\,{\mathrm {e}}^{{\mathrm {e}}^{x/36}\,{\mathrm {e}}^{-3}\,{\mathrm {e}}^{-{\mathrm {e}}^x}}\,\mathrm {e}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 4.10, size = 17, normalized size = 0.65 \begin {gather*} - e^{x e^{e^{\frac {x}{36} - e^{x} - 3} + 1}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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