Optimal. Leaf size=16 \[ \frac {1}{80} e^3 x^3 (3-\log (9)) \]
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Rubi [A] time = 0.01, antiderivative size = 16, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, integrand size = 23, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.130, Rules used = {6, 12, 30} \begin {gather*} \frac {1}{80} e^3 x^3 (3-\log (9)) \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rule 12
Rule 30
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {1}{80} e^3 x^2 (9-3 \log (9)) \, dx\\ &=\frac {1}{80} \left (3 e^3 (3-\log (9))\right ) \int x^2 \, dx\\ &=\frac {1}{80} e^3 x^3 (3-\log (9))\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 14, normalized size = 0.88 \begin {gather*} -\frac {1}{80} e^3 x^3 (-3+\log (9)) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.51, size = 17, normalized size = 1.06 \begin {gather*} -\frac {1}{40} \, x^{3} e^{3} \log \relax (3) + \frac {3}{80} \, x^{3} e^{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.50, size = 17, normalized size = 1.06 \begin {gather*} -\frac {1}{40} \, x^{3} e^{3} \log \relax (3) + \frac {3}{80} \, x^{3} e^{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 14, normalized size = 0.88
method | result | size |
gosper | \(-\frac {x^{3} {\mathrm e}^{3} \left (2 \ln \relax (3)-3\right )}{80}\) | \(14\) |
norman | \(\left (-\frac {{\mathrm e}^{3} \ln \relax (3)}{40}+\frac {3 \,{\mathrm e}^{3}}{80}\right ) x^{3}\) | \(16\) |
default | \(-\frac {x^{3} {\mathrm e}^{3} \ln \relax (3)}{40}+\frac {3 x^{3} {\mathrm e}^{3}}{80}\) | \(18\) |
risch | \(-\frac {x^{3} {\mathrm e}^{3} \ln \relax (3)}{40}+\frac {3 x^{3} {\mathrm e}^{3}}{80}\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.64, size = 17, normalized size = 1.06 \begin {gather*} -\frac {1}{40} \, x^{3} e^{3} \log \relax (3) + \frac {3}{80} \, x^{3} e^{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.06, size = 13, normalized size = 0.81 \begin {gather*} -\frac {x^3\,{\mathrm {e}}^3\,\left (2\,\ln \relax (3)-3\right )}{80} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 17, normalized size = 1.06 \begin {gather*} x^{3} \left (- \frac {e^{3} \log {\relax (3 )}}{40} + \frac {3 e^{3}}{80}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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