Optimal. Leaf size=30 \[ e^{\frac {10}{3} e^{(3+x)^2}-2 x-2 x^2 \log \left (e^2+2 x\right )} \]
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Rubi [A] time = 2.69, antiderivative size = 36, normalized size of antiderivative = 1.20, number of steps used = 1, number of rules used = 1, integrand size = 111, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.009, Rules used = {6706} \begin {gather*} e^{\frac {2}{3} \left (5 e^{x^2+6 x+9}-3 x\right )} \left (2 x+e^2\right )^{-2 x^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=e^{\frac {2}{3} \left (5 e^{9+6 x+x^2}-3 x\right )} \left (e^2+2 x\right )^{-2 x^2}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.16, size = 31, normalized size = 1.03 \begin {gather*} e^{\frac {10}{3} e^{(3+x)^2}-2 x} \left (e^2+2 x\right )^{-2 x^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.61, size = 28, normalized size = 0.93 \begin {gather*} e^{\left (-2 \, x^{2} \log \left (2 \, x + e^{2}\right ) - 2 \, x + \frac {10}{3} \, e^{\left (x^{2} + 6 \, x + 9\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.21, size = 28, normalized size = 0.93 \begin {gather*} e^{\left (-2 \, x^{2} \log \left (2 \, x + e^{2}\right ) - 2 \, x + \frac {10}{3} \, e^{\left (x^{2} + 6 \, x + 9\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.12, size = 29, normalized size = 0.97
method | result | size |
risch | \(\left ({\mathrm e}^{2}+2 x \right )^{-2 x^{2}} {\mathrm e}^{\frac {10 \,{\mathrm e}^{\left (3+x \right )^{2}}}{3}-2 x}\) | \(29\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.75, size = 28, normalized size = 0.93 \begin {gather*} e^{\left (-2 \, x^{2} \log \left (2 \, x + e^{2}\right ) - 2 \, x + \frac {10}{3} \, e^{\left (x^{2} + 6 \, x + 9\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.72, size = 32, normalized size = 1.07 \begin {gather*} \frac {{\mathrm {e}}^{\frac {10\,{\mathrm {e}}^{6\,x}\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^9}{3}-2\,x}}{{\left (2\,x+{\mathrm {e}}^2\right )}^{2\,x^2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 1.01, size = 31, normalized size = 1.03 \begin {gather*} e^{- 2 x^{2} \log {\left (2 x + e^{2} \right )} - 2 x + \frac {10 e^{x^{2} + 6 x + 9}}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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