Optimal. Leaf size=14 \[ 4 e^{-9-e^x} x^3 \]
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Rubi [A] time = 0.03, antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.043, Rules used = {2288} \begin {gather*} 4 e^{-e^x-9} x^3 \end {gather*}
Antiderivative was successfully verified.
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Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=4 e^{-9-e^x} x^3\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 14, normalized size = 1.00 \begin {gather*} 4 e^{-9-e^x} x^3 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.91, size = 14, normalized size = 1.00 \begin {gather*} 4 \, x^{2} e^{\left (-e^{x} + \log \relax (x) - 9\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 12, normalized size = 0.86 \begin {gather*} 4 \, x^{3} e^{\left (-e^{x} - 9\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.10, size = 13, normalized size = 0.93
method | result | size |
risch | \(4 x^{3} {\mathrm e}^{-{\mathrm e}^{x}-9}\) | \(13\) |
norman | \(4 \,{\mathrm e}^{-9} x^{3} {\mathrm e}^{-{\mathrm e}^{x}}\) | \(15\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.42, size = 12, normalized size = 0.86 \begin {gather*} 4 \, x^{3} e^{\left (-e^{x} - 9\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.35, size = 12, normalized size = 0.86 \begin {gather*} 4\,x^3\,{\mathrm {e}}^{-9}\,{\mathrm {e}}^{-{\mathrm {e}}^x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.16, size = 12, normalized size = 0.86 \begin {gather*} \frac {4 x^{3} e^{- e^{x}}}{e^{9}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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