Optimal. Leaf size=16 \[ e^{1-x+27 x^3} x^2 \]
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Rubi [A] time = 0.05, antiderivative size = 30, normalized size of antiderivative = 1.88, number of steps used = 2, number of rules used = 2, integrand size = 27, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.074, Rules used = {1594, 2288} \begin {gather*} \frac {e^{27 x^3-x+1} x \left (x-81 x^3\right )}{1-81 x^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 1594
Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int e^{1-x+27 x^3} x \left (2-x+81 x^3\right ) \, dx\\ &=\frac {e^{1-x+27 x^3} x \left (x-81 x^3\right )}{1-81 x^2}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 16, normalized size = 1.00 \begin {gather*} e^{1-x+27 x^3} x^2 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.11, size = 15, normalized size = 0.94 \begin {gather*} x^{2} e^{\left (27 \, x^{3} - x + 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.70, size = 15, normalized size = 0.94 \begin {gather*} x^{2} e^{\left (27 \, x^{3} - x + 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 16, normalized size = 1.00
method | result | size |
gosper | \({\mathrm e}^{27 x^{3}-x +1} x^{2}\) | \(16\) |
norman | \({\mathrm e}^{27 x^{3}-x +1} x^{2}\) | \(16\) |
risch | \({\mathrm e}^{27 x^{3}-x +1} x^{2}\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.79, size = 15, normalized size = 0.94 \begin {gather*} x^{2} e^{\left (27 \, x^{3} - x + 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 16, normalized size = 1.00 \begin {gather*} x^2\,{\mathrm {e}}^{-x}\,\mathrm {e}\,{\mathrm {e}}^{27\,x^3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 12, normalized size = 0.75 \begin {gather*} x^{2} e^{27 x^{3} - x + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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