Optimal. Leaf size=12 \[ -1+4 e^{2/5} x^3 \]
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Rubi [A] time = 0.00, antiderivative size = 10, normalized size of antiderivative = 0.83, number of steps used = 2, number of rules used = 2, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {12, 30} \begin {gather*} 4 e^{2/5} 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^{2/5}\right ) \int x^2 \, dx\\ &=4 e^{2/5} x^3\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 10, normalized size = 0.83 \begin {gather*} 4 e^{2/5} x^3 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.71, size = 7, normalized size = 0.58 \begin {gather*} 4 \, x^{3} e^{\frac {2}{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.24, size = 7, normalized size = 0.58 \begin {gather*} 4 \, x^{3} e^{\frac {2}{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 8, normalized size = 0.67
method | result | size |
gosper | \(4 x^{3} {\mathrm e}^{\frac {2}{5}}\) | \(8\) |
default | \(4 x^{3} {\mathrm e}^{\frac {2}{5}}\) | \(8\) |
norman | \(4 x^{3} {\mathrm e}^{\frac {2}{5}}\) | \(8\) |
risch | \(4 x^{3} {\mathrm e}^{\frac {2}{5}}\) | \(8\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.42, size = 7, normalized size = 0.58 \begin {gather*} 4 \, x^{3} e^{\frac {2}{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 7, normalized size = 0.58 \begin {gather*} 4\,x^3\,{\mathrm {e}}^{2/5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.05, size = 8, normalized size = 0.67 \begin {gather*} 4 x^{3} e^{\frac {2}{5}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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