Optimal. Leaf size=22 \[ -3 e^2 \left (-2-e^{\frac {x^3}{2}}+x\right )+\log (4) \]
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Rubi [A] time = 0.03, antiderivative size = 20, normalized size of antiderivative = 0.91, number of steps used = 3, number of rules used = 2, integrand size = 26, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {12, 2209} \begin {gather*} 3 e^{\frac {x^3}{2}+2}-3 e^2 x \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2209
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{2} \int \left (-6 e^2+9 e^{2+\frac {x^3}{2}} x^2\right ) \, dx\\ &=-3 e^2 x+\frac {9}{2} \int e^{2+\frac {x^3}{2}} x^2 \, dx\\ &=3 e^{2+\frac {x^3}{2}}-3 e^2 x\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 22, normalized size = 1.00 \begin {gather*} \frac {3}{2} e^2 \left (2 e^{\frac {x^3}{2}}-2 x\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.73, size = 16, normalized size = 0.73 \begin {gather*} -3 \, x e^{2} + 3 \, e^{\left (\frac {1}{2} \, x^{3} + 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.25, size = 16, normalized size = 0.73 \begin {gather*} -3 \, x e^{2} + 3 \, e^{\left (\frac {1}{2} \, x^{3} + 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 17, normalized size = 0.77
method | result | size |
default | \(3 \,{\mathrm e}^{2} {\mathrm e}^{\frac {x^{3}}{2}}-3 \,{\mathrm e}^{2} x\) | \(17\) |
norman | \(3 \,{\mathrm e}^{2} {\mathrm e}^{\frac {x^{3}}{2}}-3 \,{\mathrm e}^{2} x\) | \(17\) |
risch | \(3 \,{\mathrm e}^{2+\frac {x^{3}}{2}}-3 \,{\mathrm e}^{2} x\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.35, size = 16, normalized size = 0.73 \begin {gather*} -3 \, x e^{2} + 3 \, e^{\left (\frac {1}{2} \, x^{3} + 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.12, size = 14, normalized size = 0.64 \begin {gather*} -3\,{\mathrm {e}}^2\,\left (x-{\mathrm {e}}^{\frac {x^3}{2}}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 17, normalized size = 0.77 \begin {gather*} - 3 x e^{2} + 3 e^{2} e^{\frac {x^{3}}{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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