Optimal. Leaf size=18 \[ e^{e^4+x^2+\frac {1}{3} (-2+2 x)} \]
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Rubi [A]
time = 0.05, antiderivative size = 22, normalized size of antiderivative = 1.22, number of steps
used = 3, number of rules used = 3, integrand size = 29, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.103, Rules used = {12, 2276, 2268}
\begin {gather*} e^{x^2+\frac {2 x}{3}+\frac {1}{3} \left (3 e^4-2\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2268
Rule 2276
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{3} \int e^{x^2+\frac {1}{3} \left (-2+3 e^4+2 x\right )} (2+6 x) \, dx\\ &=\frac {1}{3} \int e^{\frac {1}{3} \left (-2+3 e^4\right )+\frac {2 x}{3}+x^2} (2+6 x) \, dx\\ &=e^{\frac {1}{3} \left (-2+3 e^4\right )+\frac {2 x}{3}+x^2}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.02, size = 17, normalized size = 0.94 \begin {gather*} e^{-\frac {2}{3}+e^4+\frac {2 x}{3}+x^2} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.13, size = 12, normalized size = 0.67
method | result | size |
gosper | \({\mathrm e}^{{\mathrm e}^{4}+\frac {2 x}{3}-\frac {2}{3}+x^{2}}\) | \(12\) |
default | \({\mathrm e}^{{\mathrm e}^{4}+\frac {2 x}{3}-\frac {2}{3}+x^{2}}\) | \(12\) |
risch | \({\mathrm e}^{{\mathrm e}^{4}+\frac {2 x}{3}-\frac {2}{3}+x^{2}}\) | \(12\) |
norman | \({\mathrm e}^{{\mathrm e}^{4}+\frac {2 x}{3}-\frac {2}{3}} {\mathrm e}^{x^{2}}\) | \(14\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 11, normalized size = 0.61 \begin {gather*} e^{\left (x^{2} + \frac {2}{3} \, x + e^{4} - \frac {2}{3}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.43, size = 11, normalized size = 0.61 \begin {gather*} e^{\left (x^{2} + \frac {2}{3} \, x + e^{4} - \frac {2}{3}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.19, size = 17, normalized size = 0.94 \begin {gather*} e^{x^{2}} e^{\frac {2 x}{3} - \frac {2}{3} + e^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 11, normalized size = 0.61 \begin {gather*} e^{\left (x^{2} + \frac {2}{3} \, x + e^{4} - \frac {2}{3}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.88, size = 14, normalized size = 0.78 \begin {gather*} {\mathrm {e}}^{\frac {2\,x}{3}}\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^{-\frac {2}{3}}\,{\mathrm {e}}^{{\mathrm {e}}^4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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