Optimal. Leaf size=11 \[ 5-e^{2 x/3} \]
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Rubi [A] time = 0.00, antiderivative size = 9, normalized size of antiderivative = 0.82, 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*} -e^{2 x/3} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2194
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\left (\frac {2}{3} \int e^{2 x/3} \, dx\right )\\ &=-e^{2 x/3}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 9, normalized size = 0.82 \begin {gather*} -e^{2 x/3} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.82, size = 6, normalized size = 0.55 \begin {gather*} -e^{\left (\frac {2}{3} \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.28, size = 6, normalized size = 0.55 \begin {gather*} -e^{\left (\frac {2}{3} \, x\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 7, normalized size = 0.64
method | result | size |
gosper | \(-{\mathrm e}^{\frac {2 x}{3}}\) | \(7\) |
derivativedivides | \(-{\mathrm e}^{\frac {2 x}{3}}\) | \(7\) |
default | \(-{\mathrm e}^{\frac {2 x}{3}}\) | \(7\) |
norman | \(-{\mathrm e}^{\frac {2 x}{3}}\) | \(7\) |
risch | \(-{\mathrm e}^{\frac {2 x}{3}}\) | \(7\) |
meijerg | \(1-{\mathrm e}^{\frac {2 x}{3}}\) | \(9\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.46, size = 6, normalized size = 0.55 \begin {gather*} -e^{\left (\frac {2}{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*} -{\mathrm {e}}^{\frac {2\,x}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.06, size = 7, normalized size = 0.64 \begin {gather*} - e^{\frac {2 x}{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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