Optimal. Leaf size=21 \[ e^{\frac {1}{3} e^{6/5} \left (e^5+e^x\right ) x^2} \]
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Rubi [A] time = 0.15, antiderivative size = 27, normalized size of antiderivative = 1.29, number of steps used = 2, number of rules used = 2, integrand size = 55, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.036, Rules used = {12, 6706} \begin {gather*} e^{\frac {1}{3} \left (e^{x+\frac {6}{5}} x^2+e^{31/5} x^2\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{3} \int e^{\frac {1}{3} \left (e^{31/5} x^2+e^{\frac {6}{5}+x} x^2\right )} \left (2 e^{31/5} x+e^{\frac {6}{5}+x} \left (2 x+x^2\right )\right ) \, dx\\ &=e^{\frac {1}{3} \left (e^{31/5} x^2+e^{\frac {6}{5}+x} x^2\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.29, size = 21, normalized size = 1.00 \begin {gather*} e^{\frac {1}{3} e^{6/5} \left (e^5+e^x\right ) x^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.52, size = 18, normalized size = 0.86 \begin {gather*} e^{\left (\frac {1}{3} \, x^{2} e^{\frac {31}{5}} + \frac {1}{3} \, x^{2} e^{\left (x + \frac {6}{5}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.25, size = 18, normalized size = 0.86 \begin {gather*} e^{\left (\frac {1}{3} \, x^{2} e^{\frac {31}{5}} + \frac {1}{3} \, x^{2} e^{\left (x + \frac {6}{5}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.15, size = 14, normalized size = 0.67
method | result | size |
risch | \({\mathrm e}^{\frac {x^{2} \left ({\mathrm e}^{\frac {6}{5}+x}+{\mathrm e}^{\frac {31}{5}}\right )}{3}}\) | \(14\) |
norman | \({\mathrm e}^{\frac {x^{2} {\mathrm e}^{\frac {6}{5}} {\mathrm e}^{x}}{3}+\frac {x^{2} {\mathrm e}^{\frac {6}{5}} {\mathrm e}^{5}}{3}}\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.47, size = 18, normalized size = 0.86 \begin {gather*} e^{\left (\frac {1}{3} \, x^{2} e^{\frac {31}{5}} + \frac {1}{3} \, x^{2} e^{\left (x + \frac {6}{5}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 6.17, size = 18, normalized size = 0.86 \begin {gather*} {\mathrm {e}}^{\frac {x^2\,{\mathrm {e}}^{x+\frac {6}{5}}}{3}+\frac {x^2\,{\mathrm {e}}^{31/5}}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.21, size = 24, normalized size = 1.14 \begin {gather*} e^{\frac {x^{2} e^{\frac {6}{5}} e^{x}}{3} + \frac {x^{2} e^{\frac {31}{5}}}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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