Optimal. Leaf size=20 \[ -e^{8+2 \left (4-x^2\right )^2}+\log (2) \]
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Rubi [A] time = 0.10, antiderivative size = 16, normalized size of antiderivative = 0.80, number of steps used = 2, number of rules used = 2, integrand size = 24, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.083, Rules used = {1593, 6706} \begin {gather*} -e^{2 x^4-16 x^2+40} \end {gather*}
Antiderivative was successfully verified.
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Rule 1593
Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int e^{40-16 x^2+2 x^4} x \left (32-8 x^2\right ) \, dx\\ &=-e^{40-16 x^2+2 x^4}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.07, size = 16, normalized size = 0.80 \begin {gather*} -e^{40-16 x^2+2 x^4} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.79, size = 15, normalized size = 0.75 \begin {gather*} -e^{\left (2 \, x^{4} - 16 \, x^{2} + 40\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 15, normalized size = 0.75 \begin {gather*} -e^{\left (2 \, x^{4} - 16 \, x^{2} + 40\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 16, normalized size = 0.80
method | result | size |
gosper | \(-{\mathrm e}^{2 x^{4}-16 x^{2}+40}\) | \(16\) |
norman | \(-{\mathrm e}^{2 x^{4}-16 x^{2}+40}\) | \(16\) |
risch | \(-{\mathrm e}^{2 x^{4}-16 x^{2}+40}\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.38, size = 15, normalized size = 0.75 \begin {gather*} -e^{\left (2 \, x^{4} - 16 \, x^{2} + 40\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.31, size = 16, normalized size = 0.80 \begin {gather*} -{\mathrm {e}}^{40}\,{\mathrm {e}}^{2\,x^4}\,{\mathrm {e}}^{-16\,x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 14, normalized size = 0.70 \begin {gather*} - e^{2 x^{4} - 16 x^{2} + 40} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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