Optimal. Leaf size=17 \[ x \left (-3+e^{(-3-x) x}+x+x^4\right ) \]
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Rubi [B] time = 0.03, antiderivative size = 38, normalized size of antiderivative = 2.24, number of steps used = 2, number of rules used = 1, integrand size = 32, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.031, Rules used = {2288} \begin {gather*} x^5+x^2+\frac {e^{-x^2-3 x} \left (2 x^2+3 x\right )}{2 x+3}-3 x \end {gather*}
Antiderivative was successfully verified.
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Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-3 x+x^2+x^5+\int e^{-3 x-x^2} \left (1-3 x-2 x^2\right ) \, dx\\ &=-3 x+x^2+x^5+\frac {e^{-3 x-x^2} \left (3 x+2 x^2\right )}{3+2 x}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.03, size = 16, normalized size = 0.94 \begin {gather*} x \left (-3+e^{-x (3+x)}+x+x^4\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.92, size = 22, normalized size = 1.29 \begin {gather*} x^{5} + x^{2} + x e^{\left (-x^{2} - 3 \, x\right )} - 3 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.13, size = 22, normalized size = 1.29 \begin {gather*} x^{5} + x^{2} + x e^{\left (-x^{2} - 3 \, x\right )} - 3 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 20, normalized size = 1.18
method | result | size |
risch | \(-3 x +{\mathrm e}^{-\left (3+x \right ) x} x +x^{2}+x^{5}\) | \(20\) |
default | \(-3 x +{\mathrm e}^{-x^{2}-3 x} x +x^{2}+x^{5}\) | \(23\) |
norman | \(-3 x +{\mathrm e}^{-x^{2}-3 x} x +x^{2}+x^{5}\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.49, size = 22, normalized size = 1.29 \begin {gather*} x^{5} + x^{2} + x e^{\left (-x^{2} - 3 \, x\right )} - 3 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.07, size = 18, normalized size = 1.06 \begin {gather*} x\,\left (x+{\mathrm {e}}^{-x^2-3\,x}+x^4-3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 20, normalized size = 1.18 \begin {gather*} x^{5} + x^{2} + x e^{- x^{2} - 3 x} - 3 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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