Optimal. Leaf size=22 \[ e^{\left (4+e^{2 e^{4-3 x^2} x^2}\right ) x} \]
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Rubi [A] time = 0.34, antiderivative size = 24, normalized size of antiderivative = 1.09, number of steps used = 1, number of rules used = 1, integrand size = 67, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.015, Rules used = {6706} \begin {gather*} e^{e^{2 e^{4-3 x^2} x^2} x+4 x} \end {gather*}
Antiderivative was successfully verified.
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Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=e^{4 x+e^{2 e^{4-3 x^2} x^2} x}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 1.68, size = 24, normalized size = 1.09 \begin {gather*} e^{4 x+e^{2 e^{4-3 x^2} x^2} x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.67, size = 21, normalized size = 0.95 \begin {gather*} e^{\left (x e^{\left (2 \, x^{2} e^{\left (-3 \, x^{2} + 4\right )}\right )} + 4 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.37, size = 21, normalized size = 0.95 \begin {gather*} e^{\left (x e^{\left (2 \, x^{2} e^{\left (-3 \, x^{2} + 4\right )}\right )} + 4 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.06, size = 20, normalized size = 0.91
method | result | size |
risch | \({\mathrm e}^{\left ({\mathrm e}^{2 x^{2} {\mathrm e}^{-3 x^{2}+4}}+4\right ) x}\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.49, size = 21, normalized size = 0.95 \begin {gather*} e^{\left (x e^{\left (2 \, x^{2} e^{\left (-3 \, x^{2} + 4\right )}\right )} + 4 \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.90, size = 22, normalized size = 1.00 \begin {gather*} {\mathrm {e}}^{4\,x}\,{\mathrm {e}}^{x\,{\mathrm {e}}^{2\,x^2\,{\mathrm {e}}^4\,{\mathrm {e}}^{-3\,x^2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 5.96, size = 20, normalized size = 0.91 \begin {gather*} e^{x e^{2 x^{2} e^{4 - 3 x^{2}}} + 4 x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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