Optimal. Leaf size=17 \[ e^{-\frac {20}{3}-3 e^x (1-x)+x} \]
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Rubi [F] time = 0.31, 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^{\frac {1}{3} \left (-20+3 x+e^x (-9+9 x)\right )} \left (1+3 e^x x\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^{\frac {1}{3} \left (-20+3 x+e^x (-9+9 x)\right )}+3 e^{x+\frac {1}{3} \left (-20+3 x+e^x (-9+9 x)\right )} x\right ) \, dx\\ &=3 \int e^{x+\frac {1}{3} \left (-20+3 x+e^x (-9+9 x)\right )} x \, dx+\int e^{\frac {1}{3} \left (-20+3 x+e^x (-9+9 x)\right )} \, dx\\ &=3 \int e^{\frac {1}{3} \left (-20-9 e^x+6 x+9 e^x x\right )} x \, dx+\int e^{\frac {1}{3} \left (-20+3 x+e^x (-9+9 x)\right )} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.07, size = 15, normalized size = 0.88 \begin {gather*} e^{-\frac {20}{3}+3 e^x (-1+x)+x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.62, size = 11, normalized size = 0.65 \begin {gather*} e^{\left (3 \, {\left (x - 1\right )} e^{x} + x - \frac {20}{3}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 13, normalized size = 0.76 \begin {gather*} e^{\left (3 \, x e^{x} + x - 3 \, e^{x} - \frac {20}{3}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 14, normalized size = 0.82
method | result | size |
norman | \({\mathrm e}^{\frac {\left (9 x -9\right ) {\mathrm e}^{x}}{3}+x -\frac {20}{3}}\) | \(14\) |
risch | \({\mathrm e}^{3 \,{\mathrm e}^{x} x -3 \,{\mathrm e}^{x}+x -\frac {20}{3}}\) | \(14\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.44, size = 13, normalized size = 0.76 \begin {gather*} e^{\left (3 \, x e^{x} + x - 3 \, e^{x} - \frac {20}{3}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.06, size = 16, normalized size = 0.94 \begin {gather*} {\mathrm {e}}^{3\,x\,{\mathrm {e}}^x}\,{\mathrm {e}}^{-\frac {20}{3}}\,{\mathrm {e}}^{-3\,{\mathrm {e}}^x}\,{\mathrm {e}}^x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 14, normalized size = 0.82 \begin {gather*} e^{x + \left (3 x - 3\right ) e^{x} - \frac {20}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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