Integrand size = 13, antiderivative size = 13 \[ \int \frac {5}{2} e^{\frac {2+x}{2}} \, dx=-5+5 e^{1+\frac {x}{2}} \]
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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} \[ \int \frac {5}{2} e^{\frac {2+x}{2}} \, dx=5 e^{\frac {x+2}{2}} \]
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Rule 12
Rule 2225
Rubi steps \begin{align*} \text {integral}& = \frac {5}{2} \int e^{\frac {2+x}{2}} \, dx \\ & = 5 e^{\frac {2+x}{2}} \\ \end{align*}
Time = 0.02 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.85 \[ \int \frac {5}{2} e^{\frac {2+x}{2}} \, dx=5 e^{1+\frac {x}{2}} \]
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Time = 0.57 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.69
method | result | size |
gosper | \(5 \,{\mathrm e}^{1+\frac {x}{2}}\) | \(9\) |
derivativedivides | \(5 \,{\mathrm e}^{1+\frac {x}{2}}\) | \(9\) |
default | \(5 \,{\mathrm e}^{1+\frac {x}{2}}\) | \(9\) |
norman | \(5 \,{\mathrm e}^{1+\frac {x}{2}}\) | \(9\) |
risch | \(5 \,{\mathrm e}^{1+\frac {x}{2}}\) | \(9\) |
parallelrisch | \(5 \,{\mathrm e}^{1+\frac {x}{2}}\) | \(9\) |
parts | \(5 \,{\mathrm e}^{1+\frac {x}{2}}\) | \(9\) |
meijerg | \(-5 \,{\mathrm e} \left (1-{\mathrm e}^{\frac {x}{2}}\right )\) | \(13\) |
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Time = 0.26 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.62 \[ \int \frac {5}{2} e^{\frac {2+x}{2}} \, dx=5 \, e^{\left (\frac {1}{2} \, x + 1\right )} \]
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Time = 0.04 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.54 \[ \int \frac {5}{2} e^{\frac {2+x}{2}} \, dx=5 e^{\frac {x}{2} + 1} \]
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none
Time = 0.20 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.62 \[ \int \frac {5}{2} e^{\frac {2+x}{2}} \, dx=5 \, e^{\left (\frac {1}{2} \, x + 1\right )} \]
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Time = 0.26 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.62 \[ \int \frac {5}{2} e^{\frac {2+x}{2}} \, dx=5 \, e^{\left (\frac {1}{2} \, x + 1\right )} \]
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Time = 0.04 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.62 \[ \int \frac {5}{2} e^{\frac {2+x}{2}} \, dx=5\,{\mathrm {e}}^{x/2}\,\mathrm {e} \]
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