Optimal. Leaf size=25 \[ x-3 x \left (5-e^{-10-2 e^{2 x^2}} x^2\right ) \]
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Rubi [F] time = 0.43, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int e^{-10-2 e^{2 x^2}} \left (-14 e^{10+2 e^{2 x^2}}+9 x^2-24 e^{2 x^2} x^4\right ) \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int e^{-2 \left (5+e^{2 x^2}\right )} \left (-14 e^{10+2 e^{2 x^2}}+9 x^2-24 e^{2 x^2} x^4\right ) \, dx\\ &=\int \left (-14+9 e^{-2 \left (5+e^{2 x^2}\right )} x^2-24 e^{-2 \left (5+e^{2 x^2}\right )+2 x^2} x^4\right ) \, dx\\ &=-14 x+9 \int e^{-2 \left (5+e^{2 x^2}\right )} x^2 \, dx-24 \int e^{-2 \left (5+e^{2 x^2}\right )+2 x^2} x^4 \, dx\\ &=-14 x+9 \int e^{-2 \left (5+e^{2 x^2}\right )} x^2 \, dx-24 \int e^{-2 \left (5+e^{2 x^2}-x^2\right )} x^4 \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.12, size = 22, normalized size = 0.88 \begin {gather*} -14 x+3 e^{-2 \left (5+e^{2 x^2}\right )} x^3 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.60, size = 32, normalized size = 1.28 \begin {gather*} {\left (3 \, x^{3} - 14 \, x e^{\left (2 \, e^{\left (2 \, x^{2}\right )} + 10\right )}\right )} e^{\left (-2 \, e^{\left (2 \, x^{2}\right )} - 10\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 41, normalized size = 1.64 \begin {gather*} {\left (3 \, x^{3} e^{\left (2 \, x^{2} - 2 \, e^{\left (2 \, x^{2}\right )}\right )} - 14 \, x e^{\left (2 \, x^{2} + 10\right )}\right )} e^{\left (-2 \, x^{2} - 10\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.07, size = 21, normalized size = 0.84
method | result | size |
risch | \(-14 x +3 x^{3} {\mathrm e}^{-10-2 \,{\mathrm e}^{2 x^{2}}}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.44, size = 20, normalized size = 0.80 \begin {gather*} 3 \, x^{3} e^{\left (-2 \, e^{\left (2 \, x^{2}\right )} - 10\right )} - 14 \, x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.48, size = 20, normalized size = 0.80 \begin {gather*} 3\,x^3\,{\mathrm {e}}^{-2\,{\mathrm {e}}^{2\,x^2}}\,{\mathrm {e}}^{-10}-14\,x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 8.36, size = 20, normalized size = 0.80 \begin {gather*} 3 x^{3} e^{- 2 e^{2 x^{2}} - 10} - 14 x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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