Optimal. Leaf size=14 \[ 4 e^{1-e^3} x^3 \]
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Rubi [A]
time = 0.01, antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 14, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {12, 30}
\begin {gather*} 4 e^{1-e^3} x^3 \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 30
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\left (12 e^{1-e^3}\right ) \int x^2 \, dx\\ &=4 e^{1-e^3} x^3\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.00, size = 14, normalized size = 1.00 \begin {gather*} 4 e^{1-e^3} x^3 \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.20, size = 13, normalized size = 0.93
method | result | size |
default | \(4 \,{\mathrm e} \,{\mathrm e}^{-{\mathrm e}^{3}} x^{3}\) | \(13\) |
norman | \(4 \,{\mathrm e} \,{\mathrm e}^{-{\mathrm e}^{3}} x^{3}\) | \(13\) |
risch | \(4 x^{3} {\mathrm e}^{-{\mathrm e}^{3}+1}\) | \(13\) |
gosper | \(4 \,{\mathrm e} \,{\mathrm e}^{-{\mathrm e}^{3}} x^{3}\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 12, normalized size = 0.86 \begin {gather*} 4 \, x^{3} e^{\left (-e^{3} + 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.45, size = 12, normalized size = 0.86 \begin {gather*} 4 \, x^{3} e^{\left (-e^{3} + 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.01, size = 12, normalized size = 0.86 \begin {gather*} \frac {4 e x^{3}}{e^{e^{3}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 12, normalized size = 0.86 \begin {gather*} 4 \, x^{3} e^{\left (-e^{3} + 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 12, normalized size = 0.86 \begin {gather*} 4\,x^3\,{\mathrm {e}}^{1-{\mathrm {e}}^3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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