Optimal. Leaf size=14 \[ \frac {1}{2} x^2 \left (e^{4/3}+x\right ) \]
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Rubi [A] time = 0.00, antiderivative size = 20, normalized size of antiderivative = 1.43, number of steps used = 2, number of rules used = 1, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.056, Rules used = {12} \begin {gather*} \frac {x^3}{2}+\frac {1}{2} e^{4/3} x^2 \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{2} \int \left (2 e^{4/3} x+3 x^2\right ) \, dx\\ &=\frac {1}{2} e^{4/3} x^2+\frac {x^3}{2}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 20, normalized size = 1.43 \begin {gather*} \frac {1}{2} e^{4/3} x^2+\frac {x^3}{2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.51, size = 13, normalized size = 0.93 \begin {gather*} \frac {1}{2} \, x^{3} + \frac {1}{2} \, x^{2} e^{\frac {4}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.22, size = 13, normalized size = 0.93 \begin {gather*} \frac {1}{2} \, x^{3} + \frac {1}{2} \, x^{2} e^{\frac {4}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 10, normalized size = 0.71
method | result | size |
gosper | \(\frac {\left (x +{\mathrm e}^{\frac {4}{3}}\right ) x^{2}}{2}\) | \(10\) |
default | \(\frac {{\mathrm e}^{\frac {4}{3}} x^{2}}{2}+\frac {x^{3}}{2}\) | \(14\) |
norman | \(\frac {{\mathrm e}^{\frac {4}{3}} x^{2}}{2}+\frac {x^{3}}{2}\) | \(14\) |
risch | \(\frac {{\mathrm e}^{\frac {4}{3}} x^{2}}{2}+\frac {x^{3}}{2}\) | \(14\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.37, size = 13, normalized size = 0.93 \begin {gather*} \frac {1}{2} \, x^{3} + \frac {1}{2} \, x^{2} e^{\frac {4}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.28, size = 9, normalized size = 0.64 \begin {gather*} \frac {x^2\,\left (x+{\mathrm {e}}^{4/3}\right )}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.05, size = 14, normalized size = 1.00 \begin {gather*} \frac {x^{3}}{2} + \frac {x^{2} e^{\frac {4}{3}}}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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