Optimal. Leaf size=9 \[ e^{-3 (6-x)} \]
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Rubi [A]
time = 0.00, antiderivative size = 7, normalized size of antiderivative = 0.78, number of steps
used = 2, number of rules used = 2, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {12, 2225}
\begin {gather*} e^{3 x-18} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2225
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=3 \int e^{-18+3 x} \, dx\\ &=e^{-18+3 x}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 7, normalized size = 0.78 \begin {gather*} e^{-18+3 x} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.11, size = 7, normalized size = 0.78
method | result | size |
gosper | \({\mathrm e}^{3 x -18}\) | \(7\) |
derivativedivides | \({\mathrm e}^{3 x -18}\) | \(7\) |
default | \({\mathrm e}^{3 x -18}\) | \(7\) |
norman | \({\mathrm e}^{3 x -18}\) | \(7\) |
risch | \({\mathrm e}^{3 x -18}\) | \(7\) |
meijerg | \(-{\mathrm e}^{-18} \left (1-{\mathrm e}^{3 x}\right )\) | \(13\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 6, normalized size = 0.67 \begin {gather*} e^{\left (3 \, x - 18\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 6, normalized size = 0.67 \begin {gather*} e^{\left (3 \, x - 18\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.02, size = 5, normalized size = 0.56 \begin {gather*} e^{3 x - 18} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 6, normalized size = 0.67 \begin {gather*} e^{\left (3 \, x - 18\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.84, size = 7, normalized size = 0.78 \begin {gather*} {\mathrm {e}}^{3\,x}\,{\mathrm {e}}^{-18} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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