Integrand size = 16, antiderivative size = 14 \[ \int \frac {1}{12} e^{-2+x} \left (30+5 e^4\right ) \, dx=\frac {5}{12} e^{-2+x} \left (6+e^4\right ) \]
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Time = 0.00 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {12, 2225} \[ \int \frac {1}{12} e^{-2+x} \left (30+5 e^4\right ) \, dx=\frac {5}{12} \left (6+e^4\right ) e^{x-2} \]
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Rule 12
Rule 2225
Rubi steps \begin{align*} \text {integral}& = \frac {1}{12} \left (5 \left (6+e^4\right )\right ) \int e^{-2+x} \, dx \\ & = \frac {5}{12} e^{-2+x} \left (6+e^4\right ) \\ \end{align*}
Time = 0.00 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.00 \[ \int \frac {1}{12} e^{-2+x} \left (30+5 e^4\right ) \, dx=\frac {5}{12} e^{-2+x} \left (6+e^4\right ) \]
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Time = 0.03 (sec) , antiderivative size = 15, normalized size of antiderivative = 1.07
method | result | size |
gosper | \(\frac {5 \left ({\mathrm e}^{4}+6\right ) {\mathrm e}^{-2+x}}{12}\) | \(15\) |
default | \(\left (\frac {5 \,{\mathrm e}^{4}}{12}+\frac {5}{2}\right ) {\mathrm e}^{-2+x}\) | \(16\) |
norman | \(\left (\frac {5 \,{\mathrm e}^{4}}{12}+\frac {5}{2}\right ) {\mathrm e}^{-2+x}\) | \(16\) |
risch | \(\frac {5 \,{\mathrm e}^{-2+x} {\mathrm e}^{4}}{12}+\frac {5 \,{\mathrm e}^{-2+x}}{2}\) | \(16\) |
parallelrisch | \(\left (\frac {5 \,{\mathrm e}^{4}}{12}+\frac {5}{2}\right ) {\mathrm e}^{-2+x}\) | \(16\) |
derivativedivides | \(-\left (-\frac {5 \,{\mathrm e}^{4}}{12}-\frac {5}{2}\right ) {\mathrm e}^{-2+x}\) | \(17\) |
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Time = 0.29 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.71 \[ \int \frac {1}{12} e^{-2+x} \left (30+5 e^4\right ) \, dx=\frac {5}{12} \, {\left (e^{4} + 6\right )} e^{\left (x - 2\right )} \]
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Time = 0.06 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.86 \[ \int \frac {1}{12} e^{-2+x} \left (30+5 e^4\right ) \, dx=\frac {\left (30 + 5 e^{4}\right ) e^{x - 2}}{12} \]
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Time = 0.18 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.71 \[ \int \frac {1}{12} e^{-2+x} \left (30+5 e^4\right ) \, dx=\frac {5}{12} \, {\left (e^{4} + 6\right )} e^{\left (x - 2\right )} \]
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Time = 0.29 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.71 \[ \int \frac {1}{12} e^{-2+x} \left (30+5 e^4\right ) \, dx=\frac {5}{12} \, {\left (e^{4} + 6\right )} e^{\left (x - 2\right )} \]
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Time = 13.39 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.71 \[ \int \frac {1}{12} e^{-2+x} \left (30+5 e^4\right ) \, dx=\frac {5\,{\mathrm {e}}^{-2}\,{\mathrm {e}}^x\,\left ({\mathrm {e}}^4+6\right )}{12} \]
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