Integrand size = 13, antiderivative size = 13 \[ \int -15 e^{\frac {1}{5} (198-75 x)} \, dx=e^{9+15 \left (\frac {51}{25}-x\right )} \]
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Time = 0.00 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.85, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.154, Rules used = {12, 2225} \[ \int -15 e^{\frac {1}{5} (198-75 x)} \, dx=e^{\frac {3}{5} (66-25 x)} \]
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Rule 12
Rule 2225
Rubi steps \begin{align*} \text {integral}& = -\left (15 \int e^{\frac {1}{5} (198-75 x)} \, dx\right ) \\ & = e^{\frac {3}{5} (66-25 x)} \\ \end{align*}
Time = 0.03 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.69 \[ \int -15 e^{\frac {1}{5} (198-75 x)} \, dx=e^{\frac {198}{5}-15 x} \]
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Time = 0.06 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.54
method | result | size |
gosper | \({\mathrm e}^{-15 x +\frac {198}{5}}\) | \(7\) |
derivativedivides | \({\mathrm e}^{-15 x +\frac {198}{5}}\) | \(7\) |
default | \({\mathrm e}^{-15 x +\frac {198}{5}}\) | \(7\) |
norman | \({\mathrm e}^{-15 x +\frac {198}{5}}\) | \(7\) |
risch | \({\mathrm e}^{-15 x +\frac {198}{5}}\) | \(7\) |
parallelrisch | \({\mathrm e}^{-15 x +\frac {198}{5}}\) | \(7\) |
parts | \({\mathrm e}^{-15 x +\frac {198}{5}}\) | \(7\) |
meijerg | \(-{\mathrm e}^{\frac {198}{5}} \left (1-{\mathrm e}^{-15 x}\right )\) | \(13\) |
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Time = 0.24 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.46 \[ \int -15 e^{\frac {1}{5} (198-75 x)} \, dx=e^{\left (-15 \, x + \frac {198}{5}\right )} \]
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Time = 0.03 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.54 \[ \int -15 e^{\frac {1}{5} (198-75 x)} \, dx=e^{\frac {198}{5} - 15 x} \]
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Time = 0.19 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.46 \[ \int -15 e^{\frac {1}{5} (198-75 x)} \, dx=e^{\left (-15 \, x + \frac {198}{5}\right )} \]
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Time = 0.27 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.46 \[ \int -15 e^{\frac {1}{5} (198-75 x)} \, dx=e^{\left (-15 \, x + \frac {198}{5}\right )} \]
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Time = 0.04 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.54 \[ \int -15 e^{\frac {1}{5} (198-75 x)} \, dx={\mathrm {e}}^{-15\,x}\,{\mathrm {e}}^{198/5} \]
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