Integrand size = 9, antiderivative size = 9 \[ \int 3 e^{-18+3 x} \, dx=e^{-3 (6-x)} \]
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Time = 0.00 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.78, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {12, 2225} \[ \int 3 e^{-18+3 x} \, dx=e^{3 x-18} \]
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Rule 12
Rule 2225
Rubi steps \begin{align*} \text {integral}& = 3 \int e^{-18+3 x} \, dx \\ & = e^{-18+3 x} \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.78 \[ \int 3 e^{-18+3 x} \, dx=e^{-18+3 x} \]
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Time = 0.70 (sec) , antiderivative size = 7, normalized size of antiderivative = 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 | \({\mathrm e}^{3 x -18}\) | \(7\) |
parallelrisch | \({\mathrm e}^{3 x -18}\) | \(7\) |
parts | \({\mathrm e}^{3 x -18}\) | \(7\) |
meijerg | \(-{\mathrm e}^{-18} \left (1-{\mathrm e}^{3 x}\right )\) | \(13\) |
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none
Time = 0.23 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.67 \[ \int 3 e^{-18+3 x} \, dx=e^{\left (3 \, x - 18\right )} \]
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Time = 0.04 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.56 \[ \int 3 e^{-18+3 x} \, dx=e^{3 x - 18} \]
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none
Time = 0.18 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.67 \[ \int 3 e^{-18+3 x} \, dx=e^{\left (3 \, x - 18\right )} \]
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none
Time = 0.25 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.67 \[ \int 3 e^{-18+3 x} \, dx=e^{\left (3 \, x - 18\right )} \]
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Time = 9.33 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.78 \[ \int 3 e^{-18+3 x} \, dx={\mathrm {e}}^{3\,x}\,{\mathrm {e}}^{-18} \]
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