Optimal. Leaf size=11 \[ \frac {e^{4 x^3}}{12} \]
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Rubi [A]
time = 0.01, antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {2240}
\begin {gather*} \frac {e^{4 x^3}}{12} \end {gather*}
Antiderivative was successfully verified.
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Rule 2240
Rubi steps
\begin {align*} \int e^{4 x^3} x^2 \, dx &=\frac {e^{4 x^3}}{12}\\ \end {align*}
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Mathematica [A]
time = 0.01, size = 11, normalized size = 1.00 \begin {gather*} \frac {e^{4 x^3}}{12} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.01, size = 9, normalized size = 0.82
method | result | size |
gosper | \(\frac {{\mathrm e}^{4 x^{3}}}{12}\) | \(9\) |
derivativedivides | \(\frac {{\mathrm e}^{4 x^{3}}}{12}\) | \(9\) |
default | \(\frac {{\mathrm e}^{4 x^{3}}}{12}\) | \(9\) |
norman | \(\frac {{\mathrm e}^{4 x^{3}}}{12}\) | \(9\) |
risch | \(\frac {{\mathrm e}^{4 x^{3}}}{12}\) | \(9\) |
meijerg | \(-\frac {1}{12}+\frac {{\mathrm e}^{4 x^{3}}}{12}\) | \(11\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.28, size = 8, normalized size = 0.73 \begin {gather*} \frac {1}{12} \, e^{\left (4 \, x^{3}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 8, normalized size = 0.73 \begin {gather*} \frac {1}{12} \, e^{\left (4 \, x^{3}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.03, size = 7, normalized size = 0.64 \begin {gather*} \frac {e^{4 x^{3}}}{12} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 2.54, size = 8, normalized size = 0.73 \begin {gather*} \frac {1}{12} \, e^{\left (4 \, x^{3}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.04, size = 8, normalized size = 0.73 \begin {gather*} \frac {{\mathrm {e}}^{4\,x^3}}{12} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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