Optimal. Leaf size=11 \[ \frac {2}{5} e^{4 x/3} \]
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Rubi [A] time = 0.00, antiderivative size = 11, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {12, 2194} \begin {gather*} \frac {2}{5} e^{4 x/3} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2194
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {8}{15} \int e^{4 x/3} \, dx\\ &=\frac {2}{5} e^{4 x/3}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 11, normalized size = 1.00 \begin {gather*} \frac {2}{5} e^{4 x/3} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.14, size = 6, normalized size = 0.55 \begin {gather*} \frac {2}{5} \, e^{\left (\frac {4}{3} \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.22, size = 6, normalized size = 0.55 \begin {gather*} \frac {2}{5} \, e^{\left (\frac {4}{3} \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 7, normalized size = 0.64
method | result | size |
gosper | \(\frac {2 \,{\mathrm e}^{\frac {4 x}{3}}}{5}\) | \(7\) |
derivativedivides | \(\frac {2 \,{\mathrm e}^{\frac {4 x}{3}}}{5}\) | \(7\) |
default | \(\frac {2 \,{\mathrm e}^{\frac {4 x}{3}}}{5}\) | \(7\) |
norman | \(\frac {2 \,{\mathrm e}^{\frac {4 x}{3}}}{5}\) | \(7\) |
risch | \(\frac {2 \,{\mathrm e}^{\frac {4 x}{3}}}{5}\) | \(7\) |
meijerg | \(-\frac {2}{5}+\frac {2 \,{\mathrm e}^{\frac {4 x}{3}}}{5}\) | \(9\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.35, size = 6, normalized size = 0.55 \begin {gather*} \frac {2}{5} \, e^{\left (\frac {4}{3} \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 6, normalized size = 0.55 \begin {gather*} \frac {2\,{\mathrm {e}}^{\frac {4\,x}{3}}}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.05, size = 8, normalized size = 0.73 \begin {gather*} \frac {2 e^{\frac {4 x}{3}}}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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